A New Method of Diagnosing the Historical and Projected Changes in Permafrost on the Tibetan Plateau

The Tibetan Plateau (TP) is the largest permafrost distribution zone at high‐altitude in the mid‐latitude region. Climate change has caused significant permafrost degradation on the TP, which has important impacts for the eco‐hydrological processes. In this study, the frost number is utilized to calculate the frost number (F) based on the air freezing/thawing index obtained from the downscaled Coupled Model Intercomparison Project Phase 6 (CMIP6) data sets. A novel method is proposed to determine the frost number threshold (Ft) for diagnosing permafrost distribution. Then the simulated permafrost distribution maps are compared with the existing permafrost distribution map, employing the Kappa coefficient as the measure of classification accuracy to identify the optimal Ft. Finally, the permafrost distribution on the TP under different Shared Socio‐economic Pathways (SSP) scenarios are diagnosed with the optimal Ft. Simulation results demonstrate that across all scenarios, the rates of permafrost degradation during the mid‐future period (2040–2060) remain comparable to those observed in the baseline period (2000), ranging from 33% ± 3% to 53% ± 4%. Conversely, during the far‐future (2080–2099), the permafrost degradation rates display significant variation across different scenarios, ranging from 37% ± 4% to 96% ± 3%. The profound impacts of permafrost degradation on the TP are reflected in decreasing trends in soil moisture and runoff, as well as a slower increasing trend in Normalized Difference Vegetation Index (NDVI) compared to other regions, indicating negative impacts on vegetation growth.

In the context of global warming, a substantial body of observational evidence indicates that the frozen ground on the TP has experienced significant degradation over the past 50 years (Cheng & Wu, 2007;Yang et al., 2010).Moreover, many studies have indicated that the frozen ground on the TP will continue to experience significant degradation in the future.For example, X. Li and Cheng (1999) showed that the degradation of permafrost on the TP will not exceed 19% in the next 20-50 years, but the permafrost on the TP will experience extensive degradation by the end of the 21st century, with a degradation ratio of 58.18%.Nan et al. (2005) predicted that with an annual temperature increase of 0.02°C a −1 , permafrost area on the TP will be reduced by 8.8% and 13.4% after 50 and 100 years, respectively, while under the scenario of 0.052°C a −1 , the permafrost will be degraded by 13.5% and 46% after 50 and 100 years, respectively.Lu et al. (2017) showed that under the RCP2.6,RCP4.5, RCP6.0, and RCP8.5 scenarios, the permafrost over the TP will be degraded by 23.95%, 32.53%, 26.96%, and 41.42% in the mid-future (2041-2070), and by 22.44%, 43.67%, 46.08%, and 64.31% in the far-future .Therefore, the frozen ground on the TP is projected to undergo significant degradation in the future, with the extent of degradation varying across different climate scenarios.In addition, discrepancies in data and methods used also contribute to variations in the projected frozen ground degradation extent.
The changes in permafrost on the TP have significant impacts on hydrogeology and vegetation.Cheng and Jin (2013) indicate that the thinning and thawing of permafrost on the TP result in the conversion of excess ice into liquid water, promoting short-term hydrogeological cycles.Wang et al. (2006) demonstrate that as the increase in the thickness of active layer in the permafrost region, there is a significant reduction in vegetation coverage and biomass in the alpine cold meadow, as well as an exponential decrease in soil organic matter content.It is important to accurately assess permafrost changes on the TP for analyzing the ecohydrological processes in this region.Because frozen ground represents the characteristics of subsurface, it is difficult to directly determine the extent of permafrost through remote sensing data (Lu et al., 2017).There are also some problems in assessing the extent of frozen ground through field investigations, especially on the TP, where the high altitude and complex terrain pose serious challenges to the field investigations.Numerous models, such as the Response Model (Cheng et al., 2012), the Mean Annual Ground Temperature Model (Nan et al., 2002), the Altitude Model (Cheng, 1984), and the Frost Number Model (Nelson & Outcalt, 1987), are crucial tools for analyzing and predicting the changes in frozen ground on the TP.Frost number model is widely used because of its simple parameterization and accurate results (Guo & Wang, 2016).According to the freezing index (DDF) and the thawing index (DDT), the frost number model is described as the Frost number F (   = √ DDF∕( √ DDF + √ DDT ).The frost number threshold (F t ) is used to diagnose the distribution of frozen ground.In the previous studies, the surface frost number F is calculated by the ground surface freezing index (DDF s ) and the ground surface thawing index (DDT s ), which are determined by the ground surface temperature, then F t is equal to 0.5, indicating that DDF s is equal to DDT s or the annual average ground temperature is 0°C (Nan et al., 2012).The permafrost is climatically possible in locations with an annual average ground temperature below 0°C (Nelson & Outcalt, 1987).Therefore, when F > F t represents the permafrost, and F ≤ F t represents the seasonally frozen ground and unfrozen ground.While extensive research has been conducted on diagnosing permafrost distribution based on ground surface temperature, this study aims to find a novel method using air temperature to complement existing methods and enhance the understanding of permafrost dynamics.The ground surface temperature is closely related to the air temperature.Therefore, it is possible to use the air temperature to diagnose the distribution of frozen ground instead of using ground surface temperature.The air temperature, along with air freezing/thawing index, reflects the thermal conditions above the ground within a certain range.The threshold value F t = 0.5 is suitable for diagnosing the distribution of permafrost in the frost number model based on ground surface temperature, while it is unreasonable to use F t = 0.5 as the threshold for diagnosing the distribution of permafrost in the frost number model based on air temperature.A more appropriate method is required to determine the optimal F t for diagnosing the permafrost distribution simulated by air freezing/thawing index.Chang et al. (2016) used the air temperature to calculate the F value to diagnose the permafrost and seasonally frozen ground with F t = 0.58 as the threshold on the TP.Guo and Wang (2016) explored the future change of global permafrost simulated by the frost number model with the air temperature from the fifth phase of the Coupled Model Inter-comparison Project (CMIP5), where F t = 0.60 was used as the frost number threshold.Although some studies have employed thresholds of 0.58 or 0.60 to diagnose the distribution of permafrost, it is not clear how to accurately obtain the optimal F t .In this study, based on the frost number model with air temperature, a new method is proposed to find the optimal F t with Kappa coefficient to diagnose the distribution of frozen ground.The range of F t is between 0 and 1, so the values of F t with an interval of 0.01 are assigned to diagnose the distribution of frozen ground.In this study, historical values of F are calculated based on the air temperature from the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP-CMIP6) (Thrasher et al., 2021(Thrasher et al., , 2022) ) in the historical period.Then compared with the frozen ground map of China (2000) produced by Ran and Li (2018), the simulated frozen ground distribution maps are evaluated with the Kappa coefficient to find the F t that can best diagnose the frozen ground distribution on the TP.Then the simulated frozen ground distribution maps with the optimal F t in the periods of 1960-1990 and 2003-2012, are compared with the International Permafrost Association (IPA) permafrost distribution map (Brown et al., 1997(Brown et al., , 2002) ) and the map of permafrost distribution on the TP (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) produced by Zou et al. (2017), respectively, to verify the reasonability of the F t determined by this method.Additionally, the threshold value for seasonally frozen ground and unfrozen ground can also be diagnosed with this method.Finally, the frost numbers F for future different scenarios are calculated based on the air freezing/thawing index obtained from the NEX-GDDP-CMIP6 (Thrasher et al., 2021(Thrasher et al., , 2022)), and the changes in permafrost and seasonally frozen ground over the TP in the 21st century are estimated.
Based on the frost number model with air temperature, this study introduces a novel perspective to find the optimal F t with Kappa coefficient to diagnose the distribution of frozen ground and contributes to understanding the impacts of climate change on permafrost regions.Additionally, the analysis examines the potential impacts of permafrost degradation on eco-hydrological processes on the TP.

Existing Permafrost Distribution Maps Used for Diagnosing and Evaluating the Simulated Distribution of Permafrost
Three permafrost distribution maps are used in this study, including the Frozen ground map of China (2000), the map of permafrost distribution on the TP (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), and the IPA permafrost distribution map , which are downloaded from the National Tibetan Plateau Data Center (TPDC) (Pan et al., 2021).Ran et al. (2012) combined several existing permafrost maps, and unified the acquisition time of data from various parts of the country to produce the Frozen ground map of China (2000) (Ran & Li, 2018) which reflected the distribution of frozen ground in China around 2000.The frozen ground in this map is divided into high-latitude permafrost, high-altitude permafrost, plateau permafrost, alpine permafrost, medium seasonal frozen ground, and shallow seasonal frozen ground.In this study, the above categories of frozen ground are reclassified into permafrost (high-latitude permafrost, high-altitude permafrost and plateau permafrost) and seasonally frozen ground (medium seasonal frozen ground and shallow seasonal frozen ground).This data set is in vector format and has been converted into a 0.25° grid format to serve as a benchmark for finding the optimal F t to diagnose the distribution of frozen ground.Zou et al. (2017) produced the map of permafrost distribution on the TP (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) based on the improved medium resolution imaging spectrometer (MODIS) surface temperature model of 1 km clear sky mod11a2 (Terra MODIS) and myd11a2 (Aqua MODIS) product (reprocessing version 5) in 2003-2012 (Zhao, 2019).The attributes in this map include permafrost, seasonally frozen ground, and unfrozen ground.The spatial resolution of this data set is 1 km, and it has been resampled to 0.25° using the nearest-neighbor interpolation method to verify the simulated frozen ground distribution map in this study.
The IPA permafrost distribution map (Brown et al., 1997(Brown et al., , 2002) ) represents the distribution of permafrost in the Northern Hemisphere before 1990.According to the continuity and underground ice content, the permafrost is divided into 20 categories.This data set is in vector format and has been converted into a 0.25° grid format to verify the simulated permafrost distribution map before 1990.

NEX-GDDP-CMIP6 Data Set for Simulating the Distribution of Permafrost
The NEX-GDDP-CMIP6 data set (Thrasher et al., 2021(Thrasher et al., , 2022) ) is downscaled by the bias correction/seasonal disaggregation (BCSD) method (Thrasher et al., 2012) based on output from Phase 6 of the Climate Model Intercomparison Project (CMIP6).The air temperature (tas) derived from the downscaled CMIP6 data sets is employed for calculating the air freezing/thawing index.These data sets include a historical experiment  and four future scenarios (SSP126, SSP245, SSP370, and SSP585) with a horizontal resolution of 0.25° and a temporal resolution of daily, covering the time range from 1950 to 2100.The name list of CMIP6 Models is shown in Table 1.

Eco-Hydrological Data Sets Used for Assessing the Impacts of Changes in Permafrost on Eco-Hydrological Processes
The ERA5-Land reanalysis data sets (Muñoz Sabater, 2019) are utilized to analyze the impacts of permafrost changes on hydrological processes, including soil moisture content at four different depths (0-7 cm, 7-28 cm, 28-100 cm, and 100-289 cm), surface runoff, and sub-surface runoff, with a spatial resolution of 0.1° and a temporal resolution of monthly.To maintain consistency with the spatial resolution of the frozen ground distribution, these data sets are resampled to a resolution of 0.25° using the first-order conservative interpolation method (Jones, 1999) which preserves the total quantity or mass of the data being resampled.Then the mean annual data sets are obtained by calculating the arithmetic mean of the data over a year.It is worth noting that the soil moisture content derived from the ERA5-Land reanalysis data sets does not distinguish the liquid water and solid water content (Chang et al., 2022;Liu & Yang, 2022).NDVI (Normalized Difference Vegetation Index) is a dimensionless index to reflect vegetation growth status, which is derived from the global 8 km GIMMS smooth NDVI data set from 1981 to 2015 (Dong & Yang, 2021;Yang et al., 2019).The temporal resolution of the raw data is bimonthly and the spatial resolution is 8 km.In this study, the data sets are resampled to 0.25° using the conservative interpolation method to be consistent with the spatial resolution of the simulated frozen ground.The mean annual NDVI is obtained by calculating the arithmetic mean of the data over a year.These data sets are used to analyze the impact of changes in frozen ground distribution on the ecological processes.

Surface Frost Number Model for Diagnosing the Distribution of Permafrost
The surface frost number model is a simple statistical method based on experience, which is calculated by the ground surface freezing/thawing index (Nelson & Outcalt, 1987).The surface frost number F is used to diagnose the permafrost and seasonally frozen ground.The equation is as follows: where DDF s and DDT s represent the freezing and thawing index (°C d) based on ground surface temperature data, respectively.The surface frost number threshold F t is equal to 0.5, where F > F t indicates the presence permafrost, while F ≤ F t indicates the presence of seasonally frozen ground or unfrozen ground.
The ground surface freezing index DDF s refers to the sum of the daily average ground surface temperature below 0°C, which can be calculated as follows: where T i is the daily mean ground surface temperature.The freezing period is i = 1, 2, …,N, which is defined as the period from July to June of the following year during the continuous cold season to encompass the entire duration of freezing events (Peng et al., 2020).
The ground surface thawing index DDT s refers to the sum of the daily average ground surface temperature above 0°C, which can be calculated as follows: where the thawing period is i = 1, 2, …,M, which represents the continuous warm season from January to December of the year to consider the entire duration of thawing events.

A New Method for Diagnosing Permafrost Based on Air Frost Number With Kappa Coefficient
Although ground surface temperature and its freezing/thawing index directly reflect the thermal state of the ground, there are limitations in obtaining ground surface temperature data, especially for future scenarios.
Although influenced by the insulative role of the vegetation cover and soil texture (especially organic matter), the air temperature and its freezing/thawing index reflect the thermal conditions within a certain range above the ground and have a close relationship with ground surface temperature.Nelson and Outcalt (1987) calculated surface frost number by combining the snow insulation effect with air temperature to reflect ground surface thermal conditions.However, the snow insulation effect alone can not account for the complex relationship between the ground and air temperature.Chang et al. (2016) used the air temperature to calculate the F value, with F t = 0.58 as the threshold in TP to diagnose permafrost.Guo and Wang (2016) used F t = 0.60 as the threshold for frost number model to diagnose the continuous permafrost.However, they did not provide detailed information about the determination process of the frost number threshold based on air temperature.In this study, a new method for diagnosing permafrost based on the air freezing/thawing index is proposed to accurately simulate the distribution of permafrost by finding the optimal F t .The equation for the air frost number is as follows: where DDF a and DDT a represent the freezing and thawing index (°C d) based on air temperature data, respectively.
The core of the new method is to accurately determine the optimal F t for diagnosing the distribution of frozen ground.The detailed steps are as follows: first, based on the frost number model, the frost number F is calculated according to the air freezing/thawing index obtained from the downscaled CMIP6 data sets in the historical period.Then, a new method incorporating the optimal frost number threshold F t with kappa coefficient is used to diagnose the distribution of frozen ground.The range of F t is between 0 and 1, so values of F t from 0 to 1 with an interval of 0.01 are assigned to diagnose the distribution of frozen ground.Then the optimal F t can be determined by comparing the simulated frozen ground distribution maps with the existing frozen ground distribution map.In this study, the Frozen ground map of China ( 2000) (Ran & Li, 2018) serves as a benchmark for finding the optimal F t to diagnose the distribution of frozen ground.Here, the kappa coefficient is used as the index to measure the classification accuracy to find the optimal F t .The Kappa values of ≥0.8, 0.6-0.8,0.4-0.6,0.2-0.4,and 0-0.2 indicate almost perfect, substantial, high, fair, and low fit, respectively, between the two maps.Finally, the F t with the highest Kappa coefficient is determined as the optimal F t that can best diagnose the frozen ground distribution.
The equation of the Kappa coefficient is as follows: where p o represents the overall accuracy, which is calculated as the sum of the number of correctly classified grid cells for each category divided by the total number of grid cells.n is total number of the grid cells.a 1 , a 2 , …, a c are the numbers of actual grid cells for each category, b 1 , b 2 , …, b c are the numbers of predicted grid cells for each category.

Application of the New Method: A Case Study on the TP
The simulated frozen ground distribution maps (2000) are compared with the frozen ground map of TP ( 2000) (Ran & Li, 2018;Ran et al., 2012), with the evaluation based on the Kappa coefficient.Optimal diagnosis of permafrost and seasonally frozen ground simulated by the multi-model mean is achieved with F t1 = 0.58 (Kappa = 0.70) (see Figure 1a).For diagnosing seasonally frozen ground and unfrozen ground simulated by multi-model mean, the maximum kappa coefficient is obtained when F t2 = 0.01 (Kappa = 0.69).Therefore, F t2 = 0.01 is the threshold that can best diagnose seasonally frozen ground and unfrozen ground (see Figure 1b).

Robust Validation of the New Method: Comparison With Existing Frozen Ground Distribution Maps
According to the optimal frost number thresholds, with F t1 = 0.58 for diagnosing permafrost and seasonally frozen ground and F t2 = 0.01 for diagnosing seasonally frozen ground, the frozen ground distribution maps in different periods on the TP are produced.The robustness of the new method is validated by comparing the simulated frozen ground distribution maps with existing frozen ground distribution maps in different periods on the TP, including the frozen ground map of the TP (2000), the map of permafrost distribution on the TP (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), and the IPA permafrost distribution map .

Comparison With the Frozen Ground Map of the TP (2000)
Compared with the frozen ground map of the TP (2000), the frozen ground map of the TP in 2000 simulated by the multi-model mean is evaluated, as shown in Figure 2. The Kappa coefficient of these two maps is 0.70 and  2.

Comparison With the Map of Permafrost Distribution on the TP (2003-2012)
The frozen ground map of the TP from 2003 to 2012 simulated by the multi-model mean is compared with the map of permafrost distribution on the TP (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), as shown in Figure 3.The simulated frozen ground map successfully reproduces the spatial distribution pattern of permafrost and seasonally frozen ground on the TP.The Kappa coefficient between the two maps is 0.60, and the overall accuracy is 0.80, indicating a substantial level of agreement between the two maps.The statistics of frozen ground area of the two maps are shown in Table 3.

Comparison With the IPA Permafrost Distribution Map
As the IPA permafrost distribution map represents the permafrost state before 1990, the permafrost distribution of the TP simulated by the multi-model mean from 1960 to 1990 is compared with the IPA permafrost distribution map in this study (Figure 4).With a Kappa coefficient of 0.69 and an overall accuracy of 0.79, it is evident that there is a substantial agreement between the two maps.The area of IPA permafrost distribution map is 1.55 × 10 6 km 2 , and the permafrost area of the TP in this study is 1.35 ± 0.02 × 10 6 km 2 .
By using thresholds of F t1 = 0.58 and F t2 = 0.01, combined with the future air freezing/thawing index, the future changes in frozen ground distribution on the TP are projected for different scenarios and periods.

Spatial Distribution of Frozen Ground Under Different Periods and Scenarios
The frozen ground distribution on the TP is projected to change to varying degrees under different scenarios and periods (Figure 5 and Table 4).In the mid-future (2040-2060), the spatial distribution pattern of frozen ground on the TP is similar under different scenarios, with permafrost mainly distributed in the northwest and northeast of the TP.In the far-future (2080-2099), the spatial distribution pattern of frozen ground on the TP is different under different scenarios.Under the SSP126 scenario, the spatial distribution of frozen ground in the far-future is similar to that in the mid-future.Compared with the simulated permafrost map of the TP in 2000, the permafrost degrades by 33% ± 3% and 37% ± 4% in the mid and far-futures, respectively, as shown in Table 5.Under the SSP245 scenario, compared with the permafrost in 2000, permafrost degradation mainly occurs at the eastern and southern edges of the permafrost in the far-future.The permafrost degrades by 41% ± 4% in the mid-future and 64% ± 5% in the far-future.Under the SSP370 scenario, the permafrost degradation is significant in the far-future, with 89% ± 3% of the permafrost  degraded.Under the SSP585 scenario, the permafrost of the TP is almost completely degraded in the far-future, with 96% ± 3% of the permafrost degraded.
Under the SSP126 scenario, the degradation of permafrost and seasonally frozen ground is insignificant in the mid and far-futures (Figure 6).The permafrost degradation mainly occurs in the eastern and southern edges of the permafrost distribution regions, and some seasonally frozen ground degenerates into unfrozen ground.
Under the SSP245 scenario, the degradation of permafrost is significant in the southern edge of the permafrost distribu tion regions, especially in the far-future.Under the SSP370 scenario, the degradation trend of permafrost in the mid period is similar to that under the SSP245 scenario.But the degradation trend of permafrost in the far-future is particularly significant, with most of the continuous permafrost being degraded, leaving only permafrost in the central and northeast of the TP.Additionally, the degradation of seasonally frozen ground to unfrozen ground is also significant in the southern of the TP.Under the SSP585 scenario, the degradation of permafrost in the mid period mainly occurs at the edge of the permafrost distribution regions.In the far-future, the permafrost of the entire TP has almost completely degraded, leaving some sporadic permafrost in the central of the TP.It is worth noting that there are few regions where permafrost directly degrades into unfrozen ground, which are not marked in Figure 6.

Trends in Frozen Ground Under Different Periods and Scenarios
There is a clear decreasing trend in permafrost area on the TP from 1950 to 2099 (Figure 7).During the historical period , the permafrost area decreases at a rate of 0.364 × 10 4 km 2 /yr.Under the SSP126, SSP245, SSP370, and SSP585 scenarios, the permafrost area decreases at rates of 0.358 × 10 4 , 0.883 × 10 4 , 1.413 × 10 4 , and 1.580 × 10 4 km 2 /yr, respectively.The decreasing rate of permafrost area in the historical period on the TP is similar to that under the SSP126 scenario. Bsed on the Mann-Kendall test, under the SSP126 scenario, the permafrost area exhibits a significant decreasing trend in the first half of the 21st century, followed by a stable condition in the second half.Under the SSP245, SSP370, and SSP585 scenarios, the decreasing trend of permafrost area on the TP is very significant, particularly under the SSP585 scenario, where permafrost will almost completely degrade by the end of the 21st century.

Hydrological Impacts of Changes in Frozen Ground
Based on ERA5-Land reanalysis data, the hydrological impacts of changes in frozen ground over the TP are further analyzed.Figure 8 illustrates the changes in frozen ground distribution from 1950 to 2014 over the TP. Figure 9 shows the changing trends of soil moisture at different soil depths from 1950  to 2014 over the TP.The first, second, third, and fourth soil layers show increasing trends in soil moisture in 54.88%, 60.29%, 58.89%, and 38.80% of the TP, respectively.Table 6 provides an overview of the changing trends in soil moisture at different depths in different frozen ground regions.In regions where permafrost remains unchanged over the years, there is a significant increase in soil moisture in the first to third soil layers, while the fourth soil layer experiences a decreasing trend.In regions where seasonally frozen ground remains unchanged, soil moisture show decreasing trends.In regions where permafrost degrades into seasonally frozen ground, there is a highly significant decreasing trend in soil moisture.The rate of soil moisture decrease in the permafrost degradation regions is higher than that in regions where seasonally frozen ground remains unchanged, with rates of −0.97 × 10 −4 m 3 m −3 yr −1 , −0.45 × 10 −4 m 3 m −3 yr −1 , −0.71 × 10 −4 m 3 m −3 yr −1 , and −2.23 × 10 −4 m 3 m −3 yr −1 from the first to fourth soil layers, respectively.In regions where seasonally frozen ground degrades into unfrozen ground, there is also a significant decrease in soil moisture, and the rate of decrease is faster than in regions where seasonally frozen ground and unfrozen ground remain unchanged.
Figure 10 shows the changing trends in surface runoff and sub-surface runoff on the TP from 1950 to 2014.Surface runoff and subsurface runoff show increasing trends in 47.61% and 49.83% of the regions, respectively.Table 7 presents the changing trends in surface runoff and sub-surface runoff in different frozen ground regions  on the TP.In regions where permafrost remains unchanged, both surface runoff and sub-surface runoff exhibit increasing trends, while in regions where seasonally frozen ground remains unchanged, surface runoff and sub-surface runoff show decreasing trends.In regions where permafrost degradation occurs, the majority of regions exhibit decreasing trends in surface runoff and subsurface runoff.
Based on the regional average trends of soil moisture and runoff in different frozen ground zones during the historical period, combined with the changes in frozen ground under different climate scenarios, the projected changes in soil moisture and runoff in the future are estimated.This estimation only focuses on the impact of changes in frozen ground on soil moisture and runoff.As shown in Figure 11, compared to the period from 2010 to 2014, soil moisture in layer 1 tends to decrease in the mid-future.The regional average soil moisture bias ranges from −4.02 × 10 −3 to −4.72 × 10 −3 m 3 /m −3 under different scenarios.In the far-future, there are significant spatial differences in soil moisture under different scenarios, with regional average bias values of −3.32 × 10 −3 m 3 /m −3 for SSP126, −5.56 × 10 −3 m 3 /m −3 for SSP245, −8.47 × 10 −3 m 3 /m −3 for SSP370, and −8.89 × 10 −3 m 3 /m −3 for SSP585.Under the SSP126 scenario, the decreasing trend of soil moisture is mitigated compared to the mid-future, while under the SSP245 scenario, soil moisture slightly decreases but remains close to that in the mid-future.In the SSP370 and SSP585 scenarios, there is a significant decreasing trend in soil moisture due to the significant degradation of permafrost.Similar changing trends in soil moisture can also be found in the other layers.With the degradation of permafrost, it is projected that the soil moisture on the TP will show significant decreasing trends in the future, as shown in Figures S1-S3 of the Supporting Information S1.
Compared to the period from 2010 to 2014, there is a slight decrease in surface runoff during the mid-future, and the variations in surface runoff are modest for different scenarios (Figure 12).In the far-future, substantial changes in surface runoff are projected across the scenarios.In the SSP126 scenario, there is a moderate decrease in surface runoff in the far-future.In the SSP370 and SSP585 scenarios, due to the significant degradation of permafrost, the surface runoff is projected to decrease significantly on the TP.The sub-surface runoff also shows a similar decreasing trend in the future, as shown in Figure S4 of the Supporting Information S1.

Ecological Impacts of Changes in Frozen Ground
Figure 13 shows the trends in NDVI in different frozen ground regions on the TP from 1981 to 2014.The NDVI in 79.47% of the TP exhibits an increasing trend.As shown in Table 8, in regions where seasonally frozen ground may degrade into unfrozen ground, the highest increasing trend in NDVI is observed, with a rate of 4.60 × 10 −4 yr −1 .In regions where permafrost degrades into seasonally frozen ground, the increasing trend in NDVI is lower than in other regions, with a rate of 0.97 × 10 −4 yr −1 , indicating that permafrost degradation may have a negative impact on vegetation growth.The degradation of permafrost can lead to changes in soil properties (Cheng & Wu, 2007).As the permafrost thaws and the active layer deepens, it can result in soil  instability, nutrient leaching, and increased water drainage, which can have detrimental effects on plant root systems and overall vegetation health (Jin et al., 2009;Mu et al., 2020;Qin et al., 2017).These factors contribute to a less pronounced increase in NDVI compared to regions with unchanged permafrost or non-permafrost conditions.Based on the trends of NDVI for different frozen ground zones, the projected changes in NDVI on the TP are estimated, considering alone the changes in frozen ground, as shown in Figure 14.Overall, there is an increasing trend in NDVI under different scenarios.Compared to the period from 2010 to 2014, in the mid-future, the spatial distribution pattern of NDVI is similar for different scenarios, with an average bias ranging from 1.82 × 10 −2 to 1.84 × 10 −2 .In the far-future, the NDVI exhibits an increasing trend compared to the mid-future, and the increasing trends in NDVI are also similar across different scenarios.Even in the SSP370 and SSP585 scenarios, where permafrost degradation is significant, the changes in NDVI are similar to that in the SSP245 scenario, with average biases of 4.75 × 10 −2 and 4.74 × 10 −2 , respectively.Overall, considering alone the impact of frozen ground changes on NDVI, the TP shows a greening trend in vegetation under different scenarios in the future.

Comparison With Previous Results of Projected Permafrost Changes on the TP
Permafrost degradation on the TP has been a subject of study in various research.In this study, the projected permafrost degradation on the TP is estimated under different climate scenarios.The results indicate that the projected permafrost degradation rates in this study are higher compared to previous research.
Overall, the projections in this study indicate a higher rate of permafrost degradation on the TP compared to previous research.The higher rate of permafrost degradation in this study can be primarily attributed to the emphasis on air temperature, which is a key influencing factor of permafrost degradation.This emphasis on the atmospheric environment provides a crucial perspective, highlighting the sensitivity of permafrost to climate change and reinforcing the urgency of mitigating greenhouse gas emissions to mitigate further permafrost degradation.These findings contribute to our understanding of the future impacts of climate change on permafrost in the TP and emphasize the need for continued research in this critical region.However, Peng et al. (2023) indicated that besides climatic factors, the distribution of permafrost are influenced by vegetation, landforms, snow cover, organic carbon, lithology, and ground ice.Future research is necessary to further refine the methods for simulating permafrost distribution.

Eco-Hydrological Impacts of Changes in Frozen Ground
As an impermeable layer, permafrost plays a crucial role in preventing surface runoff infiltration (Woo et al., 2008).
Permafrost degradation has significantly changed the hydrological process in alpine regions (Lamontagne-Hallé  , 2018;Woo et al., 2008).With the degradation of permafrost, the impermeability of permafrost decreases, leading to an increase in infiltration capacity.Therefore, rapid permafrost degradation can lower the groundwater table and restrain vegetation growth, especially for the vegetation with shallow roots (Jin et al., 2009).In addition, permafrost and its associated heat and water-budget processes control the growth and range of the vegetation, and permafrost degradation can cause surface drying and a reduction in vegetation cover, thereby increasing the risk SM1 (10 −4 m 3 m −3 yr −1 ) SM2 (10 −4 m 3 m −3 yr −1 ) SM3 (10 −4 m 3 m −3 yr −1 ) SM4 (10 −4 m 3 m −3 yr −1 ) Note.According the Mann-Kendall test, the trends for all grid points are examined.The "Trend_Avg" column represents the average trend for each region.The "Trend" column provides the average trend value for grid points exhibiting increasing trends, as well as the average trend value for all grid points exhibiting decreasing trends."Area ratio" represents the proportion of area exhibiting increasing, unchanged, and decreasing trends relative to the total area.  of desertification (Jin et al., 2021;Yang et al., 2010).The degradation of frozen ground has significant impacts on the eco-hydrological processes.
Regarding soil moisture, this study shows that in regions where permafrost degrades into seasonally frozen ground, there is a highly significant decreasing trend in soil moisture, which is consistent with previous studies (Teufel & Sushama, 2019;Wu et al., 2017;Yang et al., 2013;Zhao et al., 2019).The significant decrease in soil moisture observed in regions where permafrost degrades into seasonally frozen ground highlights the profound effects of permafrost thawing on water dynamics.As permafrost degrades into seasonally frozen ground, the impermeable layer formed by the permafrost weakens, and the reduced ice content and increased permeability  can lead to a phenomenon where moisture within the soil migrates downward and is more prone to infiltration, which can reduce the surface soil moisture content.Based on analysis of transient climate change simulations performed using a state-of-the-art regional climate model, Teufel and Sushama (2019) showed that soil moisture would decrease in response to permafrost degradation over large areas of the permafrost region.Cheng et al. (2019) found that the degradation of permafrost resulted in a decrease in the ability of the grassland ecosystem to regulate runoff and an overall reduction in soil moisture content.However, Jin et al. (2022) pointed out that as permafrost degradation, lowlands with permafrost become wetter, while uplands and mountain slopes become drier.It is worth noting that interactions between permafrost, soil moisture, and other hydrological processes  are influenced by numerical factors and exhibit complex dynamic changes.Future research should integrate more methods and data to further analyze the impacts of permafrost degradation on soil moisture.
In terms of runoff, this study shows that in regions where permafrost remains unchanged, both surface runoff and sub-surface runoff exhibit increasing trends.However, in regions where seasonally frozen ground remains unchanged, surface runoff and sub-surface runoff show decreasing trends.
Permafrost acts as a natural barrier, reducing the capacity for water infiltration and increasing surface and subsurface water flow (Gao et al., 2021).In regions where permafrost degradation, 65.26% of regions exhibit a decreasing trend in surface runoff, while 56.80% of regions show a decreasing trend in subsurface runoff.Connon et al. (2014) pointed out that the permafrost degradation enhanced hydrologic connectivity.However, it is worth noting that in addition to permafrost degradation, various other factors, including the rising temperature, intensified evapotranspiration, and lowered groundwater table, may reduce the runoff (Liang et al., 2010).This alteration in runoff patterns can have implications for water availability downstream, influencing streamflow, groundwater recharge, and overall watershed hydrology (Jin et al., 2022).
Our study primarily relied on historical trends within the baseline period to estimate these changes in the context of permafrost degradation.While this approach provides valuable insights into the potential impacts of permafrost dynamics on hydrological processes, it simplifies the assessment by not explicitly accounting for the full range of inherent variability and uncertainty in how the hydrothermal regime of permafrost has operated in the past and its potential status in the future.At the same time, the analysis in this study considered only the impact of frozen ground changes on vegetation growth, without taking into account other factors.However, it is important to acknowledge that the observed increasing trend in NDVI on the TP is influenced by a combination of multiple environmental factors, including variations in frozen ground, climate change, and other ecosystem processes.Understanding the complex interactions among these factors is crucial for accurately assessing the effects of permafrost degradation on vegetation growth and predicting future changes in the region.Future research should incorpo-  rate more models and methods to comprehensively understand the impacts of permafrost degradation on eco-hydrological processes on the TP.

Potential Sources of Uncertainty for the New Method
The air temperature is a key factor in frozen ground distribution.In this study, the downscaled CMIP6 data sets are utilized to simulate the frozen ground distribution on the TP, aiming to reduce the temperature bias arising from different CMIP6 models.However, even with the use of downscaled data sets, there may still be other inherent biases in the air temperature outputs from the CMIP6 models (Wu et al., 2023), which introduces a certain level of uncertainty in this study.
It is worth noting that the optimal F t1 for diagnosing permafrost and seasonally frozen ground simulated by different CMIP6 models, exhibit a small range of fluctuation between 0.57 and 0.59, with kappa coefficients ranging from 0.69 to 0.71 (Figure S5 in Supporting Information S1 and Table 9).This indicates that the optimal F t1 for different models show a relatively narrow range of variability.The small range of fluctuation implies a certain degree of uncertainty in determining the optimal F t1 .The observed variation in the optimal F t1 among different CMIP6 models underscores the potential sensitivity of frozen ground classification to model-specific characteristics and input data.The slight differences in the optimal F t1 can arise from variations in model physics and parameterizations.The shallow depths of the soil along with simplified parameterizations in the models limit the soil memory effect and impact the simulation of temperature (Xue et al., 2021(Xue et al., , 2022)).Some of the ESMs used in this study have a shallow soil column, which inadequately represents the thermal dynamics of permafrost, introducing uncertainty in simulating the distribution of permafrost.Therefore, the ESMs should be used with utmost caution, and future research should further evaluate the impact of different ESMs on simulating the distribution of permafrost.
Considering the narrow range of variation in the optimal F t1 and the consistent agreement with the existing frozen ground distribution map, it can be inferred that the optimal F t1 is robust for distinguishing permafrost and seasonally frozen ground.However, the presence of slight variations among different CMIP6 models emphasizes the need for caution when interpreting and generalizing the results.Further research and validation efforts are warranted to refine the optimal F t1 and minimize uncertainties associated with frozen ground classification.Although the optimal frost number threshold F t2 for diagnosing seasonally frozen ground and unfrozen ground is consistently found to be 0.01 across different CMIP6 models (Figure S6 in Supporting Information S1), it is essential to acknowledge the potential uncertainty in identifying seasonally frozen ground and unfrozen ground.It should be noted that the unfrozen ground regions on the TP are very small, which may introduce uncertainty in distinguishing the seasonally frozen ground and unfrozen ground.Therefore, future research should focus on validating the reasonability of the optimal F t2 in a larger region.Furthermore, in future research, we will apply the method proposed in this study to simulate the future distribution of permafrost in North America, Scandinavia, and the north of Eurasia to validate its applicability of this method in other regions.
In addition, the benchmark for diagnosing the distribution of permafrost in this study is the Frozen ground map of China (2000) (Ran & Li, 2018) which did not employ the continuity criterion to compile this map.Cheng and Francesco (1992) pointed out that the continuity criterion was a concept closely related to scale and was not suitable for the classification of high-altitude permafrost.Therefore, the classification in the Frozen ground map of China (2000) (Ran & Li, 2018) was based on whether permafrost was present within mapping units (grids or regions).Therefore, the simulated distribution of permafrost in this study did not take into account the probability of permafrost for each grid pixel, and permafrost area was calculated by counting the total area of all grid pixels where permafrost was present, which may introduce uncertainty into the calculation of permafrost area and potentially result in an overestimation of permafrost area.Future research should explore potential refinements to consider the probability of permafrost for each grid pixel to improve this method.Note.The optimal F t1 represents the optimal threshold to diagnose the permafrost, and the optimal F t2 represents the optimal threshold to diagnose the seasonally frozen ground.

Table 9
The Optimal Frost Number Thresholds Obtained From Different CMIP6 Models

Conclusion
In this study, the frost number model and air temperature derived from the downscaled CMIP6 data sets were used to simulate the distribution of frozen ground on the TP.The optimal frost number thresholds (F t1 = 0.58 for diagnosing permafrost and seasonally frozen ground, and F t2 = 0.01 for diagnosing seasonally frozen ground and unfrozen ground) were found to simulate the distribution of frozen ground on the TP under different future scenarios.The main findings are summarized as follows.
Permafrost degradation on the TP mainly occurs at the eastern and southern edges of the permafrost zone.
In the mid-future period, under different scenarios, the spatial distribution patterns of permafrost are similar, with permafrost predominantly located in the central and northwestern parts of the TP.In the far-future period, the spatial distribution patterns of permafrost vary significantly under different scenarios.Under the SSP126 scenario, the degradation of permafrost on the TP reaches 33% ± 3% and 37% ± 4% in the mid-future and far-future, respectively.Under the SSP245 scenario, the permafrost is projected to degrade by 41% ± 4% and 64% ± 5% in the mid-future and far-future, respectively.Under the SSP370 scenario, permafrost degradation of the TP is significant, with degradation of 44% ± 3% and 89% ± 3% in the mid-future and far-future, respectively.Under the SSP585 scenario, permafrost on the TP almost completely degrades, with degradation of 53% ± 4% and 96% ± 3% in the mid-future and far-future, respectively.
The impacts of permafrost changes on eco-hydrological processes on the TP are analyzed based on the historical data from 1950 to 2014.The research results indicate that in regions where permafrost degrades into seasonally frozen ground, the soil moisture and runoff exhibit significantly decreasing trends.Based on the historical changing trends of soil moisture and runoff in different frozen ground zones, future changes in soil moisture and NDVI can be estimated.The results show significant reductions in soil moisture and runoff under different scenarios, particularly in the high-emission scenario.Although NDVI shows an overall increasing trend, it is worth noting that in the SSP370 and SSP585 scenarios, where permafrost degradation is significant, there is insignificant increasing trend in NDVI.Therefore, the degradation of permafrost may have a negative impact on vegetation growth.
Overall, permafrost of the TP is projected to undergo significant changes in the 21st century, especially in the far-future.The degradation of permafrost will have important impacts on the hydrological cycle and ecological environment of the TP.The research results of this study will be useful for gaining a better understanding of the permafrost changes on the TP.

Figure 1 .
Figure 1.Change of Kappa coefficient with F t .(a) The F t1 is the threshold for diagnosing permafrost and seasonally frozen ground.(b) The F t2 is the threshold for diagnosing seasonally frozen ground and unfrozen ground.

Figure 2 .
Figure 2. (a) Observed frozen ground map of the TP (2000) resampled to 0.25° (Ran & Li, 2018); (b) frozen ground map of the TP (2000) simulated using the multi-model mean air temperature in the frost number model.

Figure 3 .
Figure 3. (a) Observed map of permafrost distribution on the TP (2003-2012) resampled to 0.25° (Zhao, 2019); (b) frozen ground map of the TP (2003-2012) simulated using the multi-model mean air temperature in the frost number model.

Figure 4 .
Figure 4. (a) Observed IPA permafrost distribution map resampled to 0.25°(Brown et al., 2002); (b) frozen ground map of the TP) simulated using the multi-model mean air temperature in the frost number model.

Figure 5 .
Figure 5.The frozen ground distribution on the Tibetan Plateau (TP) under different scenarios and periods.(a-d) represent the mid-future (2020-2040) under the SSP126, SSP245, SSP370, and SSP585 scenarios, respectively.(e-h) represent the far-future (2080-2099) under the SSP126, SSP245, SSP370, and SSP585 scenarios, respectively.Assuming that glaciers and lakes on the TP remain unchanged in different scenarios and periods, as their changes are not the focus of this study.

Figure 6 .
Figure 6.The changes in frozen ground under different scenarios and periods."PF − >SFG" represents regions where permafrost may degrade into seasonally frozen ground."SFG − >UFG" indicates regions where seasonally frozen ground may degrade into unfrozen ground.

Figure 7 .
Figure 7. Trends in permafrost area on the Tibetan Plateau (TP) from 1950 to 2099.The top and bottom bounds of the shaded region are the maximum and minimum of the area from the Earth System Models (ESMs).

Figure 8 .
Figure 8. Changes in the frozen ground distribution over the Tibetan Plateau (TP) from 1950 to 2014.

Figure 10 .
Figure 10.Trends in surface runoff (a) and sub-surface runoff (b) over the Tibetan Plateau (TP) from 1950 to 2014.Black dots indicates regions where the trend is statistically significant (P < 0.05).

Figure 11 .
Figure 11.Compared to the period from 2010 to 2014, the spatial distribution of soil moisture bias in the layer 1 (0-7 cm) for the mid-future (a-d), and far-future (e-h).The values in the bottom left corner represent the regional average bias.

Figure 12 .
Figure 12.Compared to the period from 2010 to 2014, the spatial distribution of surface runoff bias in the layer 1 for the mid-future (a-d), and far-future (e-h).The values in the bottom left corner represent the regional average bias.

Figure 13 .
Figure 13.Trends in Normalized Difference Vegetation Index (NDVI) over the Tibetan Plateau (TP) from 1981 to 2014.Black dots indicates regions where the trend is statistically significant (P < 0.05).

Figure 14 .
Figure 14.Compared to the period from 2010 to 2014, the spatial distribution of Normalized Difference Vegetation Index (NDVI) for the mid-future (a-d), and far-future (e-h).The values in the bottom left corner represent the regional average bias.

Table 1
List of CMIP6 Models Used in This Study

Table 4
Statistics of the Frozen Ground Area (Multi-Model Mean ± 90% Confidence Interval × 10 6 km 2 ) in the TP Under Different Scenarios and Periods Note. "−" indicates the decrease of frozen ground."+" indicates the increase of frozen ground.

Table 5
Statistics of the Change Rate (Multi-Model Mean ± 90% Confidence Interval) of the Permafrost and Seasonally Frozen Ground in the TP Under Different Scenarios and Periods

Table 6
Trends in Soil Moisture at Different Soil Layers (SM1, SM2, SM3, and SM4) in Different Frozen Ground Regions Over the TP From 1950 to 2014

Table 7
Trends of Surface Runoff and Sub-Surface Runoff in Different Frozen Ground Regions on the TP From 1950 to 2014

Table 8
Trend of Normalized Difference Vegetation Index (NDVI) in Different Frozen Ground Regions on the Tibetan Plateau (TP) From 1981 to 2014