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\begin{document}

\title{Simulation of the present and future projection of permafrost on the
Qinghai-Tibet Plateau with statistical and machine learning models}



\author[1,1,1]{jie ni}%
\author[2,2,2]{Tonghua Wu}%
\author[2,2,2]{Xiaofan Zhu}%
\author[2,2,2]{Guojie Hu}%
\author[3,3,3]{Defu Zou}%
\author[4,4,4]{Xiaodong Wu}%
\author[5,5,5]{Ren Li}%
\author[6,6,6]{Changwei Xie}%
\author[3,3,3]{Yongping Qiao}%
\author[2,2,2]{Junmin Hao}%
\author[2,2,2]{Cheng Yang}%
\affil[1]{Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences}%
\affil[2]{Northwest Institute of Eco-environment and Resources, Chinese Academy of Sciences}%
\affil[3]{Cryosphere Research Station on Qinghai-Xizang Plateau, State Key Laboratory of Cryospheric Sciences, Northwest Institute of Eco-Environment and Resources, CAS}%
\affil[4]{Chinese Academy of Sciences (CAS)}%
\affil[5]{CRS-QTP, Cold and Arid Regions Environmental and Engineering Research Institute}%
\affil[6]{Cold and Arid Regions Environmental and Engineering Research Institute (CAREERI), CAS}%


\vspace{-1em}



  
  \date{May 17, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
The comprehensive understanding of the occurred changes of permafrost,
including the changes of mean annual ground temperature (MAGT) and
active layer thickness (ALT), on the Qinghai-Tibet Plateau (QTP) is
critical to project permafrost changes due to climate change. Here, we
use statistical and machine learning (ML) modeling approaches to
simulate the present and future changes of MAGT and ALT in the
permafrost regions of the QTP. The results show that the combination of
statistical and ML method is reliable to simulate the MAGT and ALT, with
the root-mean-square error of 0.53\selectlanguage{ngerman}°C and 0.69 m for the MAGT and ALT,
respectively. The results show that the present (2000\selectlanguage{english}?2015) permafrost
area on the QTP is 1.04 x 106 km2 (0.80\selectlanguage{english}?1.28 x 106 km2), and the average
MAGT and ALT are -1.35 +- 0.42degC and 2.3 +- 0.60 m, respectively.
According to the classification system of permafrost stability, 37.3\%
of the QTP permafrost is suffering from the risk of disappearance. In
the future (2061\selectlanguage{english}?2080), the near-surface permafrost area will shrink
significantly under different Representative Concentration Pathway
scenarios (RCPs). It is predicted that the permafrost area will be
reduced to 42\% of the present area under RCP8.5. Overall, the future
changes of MAGT and ALT are pronounced and region-specific. As a result,
the combined statistical method with ML requires less parameters and
input variables for simulation permafrost thermal regimes and could
present an efficient way to figure out the response of permafrost to
climatic changes on the QTP.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


Simulation of the present and future projection of permafrost on the
Qinghai-Tibet Plateau with statistical and machine learning models

Jie Ni \textsuperscript{1, 2}, Tonghua Wu\textsuperscript{1,3} , Xiaofan
Zhu \textsuperscript{1}, Guojie Hu\textsuperscript{1}, Defu Zou
\textsuperscript{1}, Xiaodong Wu\textsuperscript{1}, Ren Li
\textsuperscript{1}, Changwei Xie\textsuperscript{1}, Yongping Qiao
\textsuperscript{1}, Qiangqiang Pang\textsuperscript{1}, Junming Hao
\textsuperscript{1, 2, 4} and Cheng Yang \textsuperscript{1, 2}

\textsuperscript{1} Cryosphere Research Station on the Qinghai-Tibet
Plateau, State Key Laboratory of Cryospheric Science, Northwest
Institute of Eco-Environment and Resources, Chinese Academy of Sciences,
Lanzhou, Gansu 730000, China; \textsuperscript{2} University of Chinese
Academy of Sciences, Beijing 100049, China; \textsuperscript{3} Southern
Marine Science and Engineering Guangdong Laboratory, Guangzhou 511458,
China; \textsuperscript{4} School of Civil Engineering, Lanzhou
University of Technology, Lanzhou, 730050, China.

\textbf{Correspondence to:}

Tonghua Wu (\emph{thuawu@lzb.ac.cn)}

\textbf{Key Points:}

\begin{itemize}
\tightlist
\item
  The combined statistical method with machine learning is efficient to
  obtain the thermal regime of permafrost on the QTP.
\item
  The present permafrost area on the QTP is \textasciitilde{}1.04 \selectlanguage{ngerman}×
  10\textsuperscript{6} km\textsuperscript{2}, and the average MAGT and
  ALT are -1.35 ± 0.42°C and 2.3 ± 0.60 m, respectively.
\item
  The future changes of permafrost are projected to be pronounced due to
  climate change, but region-specific.
\end{itemize}

Abstract

The comprehensive understanding of the occurred changes of permafrost,
including the changes of mean annual ground temperature (MAGT) and
active layer thickness (ALT), on the Qinghai-Tibet Plateau (QTP) is
critical to project permafrost changes due to climate change. Here, we
use statistical and machine learning (ML) modeling approaches to
simulate the present and future changes of MAGT and ALT in the
permafrost regions of the QTP. The results show that the combination of
statistical and ML method is reliable to simulate the MAGT and ALT, with
the root-mean-square error of 0.53°C and 0.69 m for the MAGT and ALT,
respectively. The results show that the present (2000\selectlanguage{english}-2015) permafrost
area on the QTP is 1.04 x 10\textsuperscript{6}km\textsuperscript{2}
(0.80\selectlanguage{english}-1.28 x 10\textsuperscript{6}km\textsuperscript{2}), and the
average MAGT and ALT are -1.35 +- 0.42degC and 2.3 +- 0.60 m, respectively.
According to the classification system of permafrost stability, 37.3\%
of the QTP permafrost is suffering from the risk of disappearance. In
the future (2061\selectlanguage{english}-2080), the near-surface permafrost area will shrink
significantly under different Representative Concentration Pathway
scenarios (RCPs). It is predicted that the permafrost area will be
reduced to 42\% of the present area under RCP8.5. Overall, the future
changes of MAGT and ALT are pronounced and region-specific. As a result,
the combined statistical method with ML requires less parameters and
input variables for simulation permafrost thermal regimes and could
present an efficient way to figure out the response of permafrost to
climatic changes on the QTP.

\textbf{Keywords:} permafrost; mean annual ground temperature; active
layer; climate change; Qinghai-Tibet Plateau

1. Introduction

Frozen ground is an important component of the cryosphere, which exerts
strong influences on regional ecology, hydrology and infrastructure
engineering (Westermann et al., 2015; Wang et al., 2018a). The
Qinghai-Tibet Plateau (QTP) is underlain by typical high-altitude
permafrost region, which is undergoing more dramatic climatic warming
than its surrounding regions (Wang et al., 2019a). A growing number of
studies have reported the present status and predicted degradation of
permafrost under various global warming scenarios (Pang et al., 2010,
2012; Zhang and Wu, 2012a; Guo and Wang, 2017; Xu et al., 2017a; Wang et
al., 2018a). The degradation of permafrost may trigger the release of
organic carbon into the atmosphere (Cheng and Wu 2007; Wu et al., 2017a;
Chang et al., 2018; Wang et al., 2018b; Ran et al., 2018). It is also a
potential threat to engineering construction and maintenance. However,
most of these studies are based on linear statistical models and
equilibrium models, and mainly focused on identifying the extent of
permafrost, while researches on the present and future change of ground
thermal regimes (including: the mean annual ground temperature, MAGT,
and the active layer thickness, ALT) are relatively rare (Zhang et al.,
2012a; Wang et al., 2019a). The changes of MAGT and ALT could affect the
ecosystem of the QTP by altering the ground ice evolution, hydrological
processes, vegetation dynamics and carbon cycling, etc. (Yang et al.,
2010a; Wu et al., 2016; Niu et al., 2019; Hu et al., 2020). Therefore,
it is of great importance to investigate present and future changes of
the MAGT and ALT in the permafrost region (Qin et al., 2017; Zhang et
al., 2018).

Permafrost is a thermally-defined subsurface phenomenon (Westermann et
al 2015). Satellite sensors could obtain limited surface information,
and only portion of the microwave remote sensing could penetrate several
centimetres underground (Zhao et al., 2011; Michaelides et al., 2018; Qu
et al., 2019). In general, it is difficult to use remote sensing to
directly obtain information on changes in the physical state of
permafrost (Yang et al., 2019). The current research on permafrost
thermal regime is mostly focus on either \emph{in situ} observing or
modeling using atmospheric circulation models (Westermann et al., 2015).
Most of the existing modeling frameworks require ground-based
measurements as model inputs, while the \emph{in situ} observations of
permafrost are relatively sparse and highly non-uniform in cold regions.
The long-term and continuous \emph{in situ} observation sites for
permafrost on the QTP are mostly located along the Qinghai-Tibet Highway
and Railway, and other regions are less well distributed (Hu et al.,
2015; Qin et al., 2017; Zheng et al., 2019). The absence of observation
data would greatly weakens the accuracy of simulation results.
Therefore, it is challenging to select reliable modeling approaches with
limited data to obtain the occurrence of permafrost and its projection
due to climate change.

At present, the simulation studies on the ALT and soil thermal state of
the QTP fall into two categories, including equilibrium models and
mechanistic transient models. (Riseborough et al., 2008; Qin et al.,
2017; Aalto et al., 2018). The most commonly used equilibrium models
include Stefan formula (Zhang and Wu 2012a; Xu et al., 2017a),
Kudryavtsev formula (Pang et al., 2009; Wang et al., 2020a), the N
factor (Nan et al., 2012), and the Temperature at the Top of the
Permafrost model (TTOP) (Zou et al., 2017). The form of the equilibrium
model is relatively simple and requires fewer driving data for input
(Riseborough et al., 2008; Pang et al., 2009). However, this type of
model tend to show poor portability. In contrast, mechanistic transient
models consider more details of the hydrothermal exchange processes
between the atmosphere and ground. Examples of this model include the
Community Land Model (CLM; Oleson et al., 2010; Fang et al., 2016; Chen
et al., 2017), Noah (Gao et al., 2015; Chen et al., 2015), the
Geomorphology-based Eco-hydrological Model (GBEHM; Zheng et al., 2019),
the SHAW model (Guo et al., 2011; Liu et al., 2013), and the CoupModel
(Zhang et al., 2012b; Hu et al., 2013). Nevertheless, the processes of
these models are complex and often insufficiently account for the
hydrothermal dynamics, with the understanding of the soil physical
mechanisms increase, the parameterization processes will become more
complex (Harris et al., 2009; Hu et al., 2015; Guo and Wang, 2016). In
addition to the transient models mentioned above, in recent years, the
fine-scale tightly coupled hydro-thermal modeling of permafrost has also
made great progress (e.g., models like ATS, Jafarov et al., 2018; and
SUTRA, Walvoord et al., 2019, etc.), These models are typically based on
a multidimensional solution to address fully coupled surface/subsurface
permafrost thermal hydrology, which have played an important role to
study the permafrost of local scale and microtopography (Painter et al.,
2016).

Physics-based mechanistic models are currently the popular methods to
study the permafrost, and the simulation results can show high accuracy.
However, even with significant improvements in computer technology and
algorithm simulation (Westermann et al., 2016), the current modeling
still exists a trade-off between modeling resolution and size of the
geographical domain (Etzelmuller, 2013). Especially in the case of lack
of data and insufficient computing resources, the extensive application
of physics-based mechanistic models would be limited. Whereas, the
combined statistical method with machine learning (ML) can make up these
deficiencies. In recent years, their great power in permafrost modeling
has been confirmed (Xu et al., 2017b; Chadburn et al., 2017; Aalto et
al., 2018). The main purpose of statistical and ML model is to identify
the relationship between a dependent variable and one or more
explanatory variables (Wheeler et al., 2013). They can easily explain
environmental conditions related to topography and land cover, whereas
these factors may be difficult to express with physical parameters
(Etzelmuller, 2013). Due to the good coupling between air temperature
(often characterized by mean annual air temperature or cumulative
temperature sums) and ground thermal regime (Chadburn et al., 2017;
Aalto et al., 2018), the subsurface (\textless{}10\selectlanguage{english}-20 m) soil thermal
conditions respond well to climate change at the decadal scale (Aalto et
al., 2018). In addition, precipitation type (e.g., snow, rain and sleet)
and local environmental predictors (e.g., topography, underlying surface
condition and soil texture condition) have great impacts on soil
hydrothermal dynamics and the surface radiation budget (Lee et al.,
2013; Zhu et al., 2019).

Therefore, in this study, we employed statistical and ML methods to
investigate the MAGT and ALT across the QTP. The objective is to verify
the applicability of the combined method on the QTP and quantitatively
assess the present and future status of QTP permafrost. Firstly, we
identified the critical factors which determining the occurrence of
permafrost. Secondly, we used the combined modeling approaches
integrated with field observation data, meteorological data and
geospatial environmental predictors to calculate the present MAGT and
ALT. Thirdly, the present results were benchmarked against \emph{in
situ} measurements of ALT and ground temperatures. Finally, the optimal
modeling framework was used to predict future MAGT and ALT forced by
different RCPs. The projection of the MAGT and ALT can serve as a useful
reference and provide important information for the study of climate
change, hydrology, ecology, and geohazards resulted from permafrost
degradation on the QTP.

2. Data and Methods

\textbf{2.1. Data sources}

1) Ground temperature data

The MAGT is an important factor that reflects the thermal state of
permafrost, and is defined as the ground temperature at the zero annual
amplitude depth (ZAA, i.e., the depth at which the annual temperature
variation \textless{} 0.1degC) (Qin, 2016). Due to the harsh environment
of the QTP, some boreholes are measured manually using a multimeter once
each year (Qin et al., 2017). Most MAGTs, however, are not easily
accessible from the ZAA. In these cases, the temperature at or closest
to 10 m below the ground surface was used (Nan et al., 2002; Liu et al.,
2017). All disturbed measurement sites (e.g., sites submerged by the
rising waters of a lake) were removed. Ultimately, 84 MAGT sites (Figure
1) were selected from both field station observations (Cryosphere
Research Station on the Qinghai-Tibet Plateau, Chinese Academy of
Sciences, available at\emph{http://www.crs.ac.cn/}) and the related
literatures (Wu et al., 2012a; Qin et al., 2017; Wang et al., 2017). We
selected the period from 2000 to 2015 as the reference period, and all
observations obtained were during this period. Some sites were based on
one year of observation, while others were based on the average of
several years, from which we calculated the long-term average value.

2) Active layer thickness data

In order to better fit the ALT, we attempted to collect a large amount
of observed data from relevant literatures (Wu et al., 2012a; Qin et
al., 2017; Wang et al., 2017). An additional portion of the active layer
data came from field pit detection. A total of 77 ALT observation sites
(Figure 1) were selected. The time node selection and disturbance data
processing for ALT were the same as those used for the MAGT. Based on
the distribution of MAGT and ALT observation sites, we divided them into
five typical regions, the Wenquan typical region (WQIR), Xikunlun
typical region (XKLIR), Gaize typical region (GZIR), Aerjin typical
region (AEJIR) and Qinghai-Tibet Highway typical region (G109IR), which
represent the permafrost regions of the eastern, western, southern,
northern and central areas of the QTP, respectively.

3) Meteorological data

In order to obtain climate data for the reference periods (2000--2015),
the China Meteorological Forcing Dataset (CMFD) (available
at\emph{http://www.tpedatabase.cn/;} Yang et al., 2010b; Yang et al.,
2010b; He et al., 2020) with temporal and spatial resolutions of 3 hours
and 0.1deg x 0.1deg, respectively, was utilized in this study. The time
scale of the dataset covered the studying period. According to the study
of He et al. (2020), the CMFD was established by merging Princeton
reanalysis data, GLDAS data, GEWEX-SRB radiation data, and TRMM
precipitation data, as well as the regular meteorological observations
made by the China Meteorological Administration. The accuracy of CMFD is
between the observation data and the remote sensing data (Yang et al.,
2010b), and it has been widely used due to its high reliability (Xue et
al., 2013; Xu et al., 2017a; Wang et al., 2019a).

In the study, we used air temperature and precipitation data from the
CMFD to calculate the two key predictors, including the thawing indices
(thawing degree days, TDD) and the freezing indices (freezing degree
days, FDD), which play essential roles in the studies of the frozen
ground. As useful indicators, they have been widely applied in the
permafrost region to predict the ALT (Zhang et al., 2005; Nelson et al.,
1997; Peng et al., 2018; Shiklomanov and Nelson, 2002) and permafrost
distribution (Nelson and Outcalt, 1987). In addition, we also calculated
the other two predictors, including the solid precipitation (i.e.,
precipitation with a temperature below 0degC, Sol\_pre), and liquid
precipitation (i.e., precipitation with a temperature above 0degC,
Liq\_pre).

For future conditions, the BCC-CSM 1.1 climate change modeling data was
used (available at\emph{http://www.worldclim.org/}). It was downscaled
GCMs data from CMIP5 (IPCC Fifth Assessment). BCC-CSM1.1 is the version
1.1 of the Beijing Climate Center Climate System Model, the coupling was
realized using the flux coupler version 5 developed by the National
Center for Atmosphere Research (NCAR) (Wu et al., 2019). It was a fully
coupled model with ocean, land surface, atmosphere, and sea-ice
components, and was often used to simulate the response of global
climate to rising greenhouse gas concentrations, the performance is
satisfactory in China (Zhang and Wu, 2012b; Xin et al., 2018). In this
study, we chose the monthly average air temperature and precipitation
over the time period 2061--2080 under three Representative Concentration
Pathways (RCPs): RCP2.6, RCP4.5, and RCP8.5 (Moss et al., 2010; Taylor
et al 2012). The four predictors (TDD, FDD, Sol\_pre, and Liq\_pre) were
recalculated in the same way for each time period and RCP scenario.

4) Geospatial environmental predictors

The geospatial environmental predictors were mainly derived from
topographic data and regional environmental data. The Shuttle Radar
Topography Mission (SRTM) data for a 1-km spatial resolution digital
elevation model (DEM) (Reuter et al., 2007) were selected to calculate
the predictors of elevation (Ele) and potential incoming solar radiation
(PISR) (McCune and Keon, 2002). Soil organic matter is also an important
factor affecting the ALT of permafrost. Due to the low decomposition
rate of organic matter, high soil organic carbon has been accumulated in
the permafrost regions (Ping et al., 2008). The adiabatic properties of
organic matter relative to minerals will reduce the heat exchange
between ground and air (Molders and Romanovsky, 2006; Nicolsky et al.,
2007; Paquin and Sushama, 2015). Moreover, the organic matter can also
affect the thermal properties and the amount of unfrozen water of soil
(Romanovsky and Osterkamp, 2000; Nicolsky et al., 2009). In order to
consider the influence of the regional organic matter content (Wu et
al., 2012b), soil organic carbon content information (SOC,
ton*ha\textsuperscript{-1}) from global SoilGrids 1-km data (available
at \emph{https://soilgrids.org}; Hengl et al., 2014) was also used in
our prediction analysis. Finally, all of the data layers were resampled
to the matching spatial resolution (0.1degx0.1deg) and cropped to the study
area (QTP).

5) Glacier and lake data

The spatial distributions of the glaciers and lakes on the QTP were
collected from the Second Glacier Inventory Dataset of China and the
Chinese Cryosphere Information System provided by the Cold and Arid
Regions Science Data Center (\emph{http://westdc.westgis.ac.cn}).

\textbf{2.2. Model description}

Statistical models are general methods in the study of geography. It is
usually built on some theoretical assumptions, and the data need to obey
or approximately conform to a specific spatial distribution before the
model can obtain credible results. However, ML algorithm is a general
approximation algorithm, which generally does not require theoretical
assumptions. The spatial analysis algorithm based on ML does not need a
prior knowledge but a set of training data to learn the patterns of the
geoscience system (Lary et al., 2016). Based on the above
characteristics, we chose two statistical models and two ML algorithms
to fit the present and future MAGT and ALT in this paper. The
generalized linear modeling (GLM) and the generalized additive modeling
(GAM) are traditional statistical methods used to simulate the thermal
regimes of permafrost (Nan et al., 2002; Zhang et al., 2012a). And the
two ML algorithms are the generalized boosting method (GBM) and random
forest (RF). In this study, all the four models were executed based on
the R software program. The detailed information and characteristics of
the models are as follows:

1) Generalized linear model

The generalized linear model (GLM) is an extension of a linear model
that can deal with the nonlinear relationships between explanatory
variables and response variables (Nelder and Wedderburn, 1972):

\(g\left\{\mu\left(x\right)\right\}=\beta_{0}+\beta_{1}\left(x_{1}\right)+\beta_{2}\left(x_{2}\right)+\ldots+\beta_{i}\left(x_{i}\right)\)(1)

where \(g\left(\mu\right)\) is the link function connecting the estimated
mean to the distribution of the response variable (here is MAGT and
ALT), \selectlanguage{greek}\emph{μ} \selectlanguage{english}=\emph{E} \(\left(y/x_{1},x_{2},x_{3},\ldots,x_{i}\right)\), \emph{E} is the expected
value, \(\text{\ \ }\beta_{0}\) is the intercept component,\(\beta_{i}\)
is the regression coefficient to be estimated and\(x_{i}\) is
the predictor. For MAGT and ALT, GLM was based on first and second order
polynomials and identity--link function.

2) Generalized additive model

Generalized additive model (GAM) is semi-parametric extensions of GLM
that specify smoothing functions to fit nonlinear response curves to the
data (Hastie and Tibshirani, 1986):

\(g\left\{\mu\left(x\right)\right\}=\beta_{0}+f_{1}\left(x_{1}\right)+f_{2}\left(x_{2}\right)+\ldots+f_{i}\left(x_{i}\right)\text{\ \ \ \ }\)(2)

where \(g\left(\mu\right)\) is the link function connecting the estimated
mean to the distribution of the response variable (here is MAGT and
ALT), \selectlanguage{greek}\emph{μ} \selectlanguage{english}=\emph{E} \(\left(y/x_{1},x_{2},x_{3},\ldots,x_{i}\right)\), \emph{E} is the expected
value, \(\beta_{0}\) is the intercept component,
\(f_{i}\)is a smoothing function for each explanatory variable
and \(x_{i}\) is the predictor. To associate the MAGT and ALT
with environmental predictors, the maximum smoothing function was set to
three which were subsequently optimized by the model fitting function.

3) Generalized boosting method

The generalized boosting method (GBM, based on the R package dismo) is a
sequential integration modeling method that combines a large number of
iteratively fitted classification trees into a single model, using
cross-validation methods to estimate the optimal number of trees, and
thereby improving prediction accuracy (Elith et al., 2008). GBMs
automatically incorporate interactions between predictors and are
capable of modeling highly complex nonlinear systems (Aalto et al.,
2018). GBMs (with Gaussian--Markov error assumption) were fitted using
the gbm.step function, including the main parameters of the learning
rate, tree complexity, bagging fraction, maximum number of trees, and
others.

4) Random forest

Random forest (RF, implemented in the R package randomForest.) is a ML
algorithm based on a classification tree, which forms a ``forest'' by
generating a large ensemble of regression trees. The model uses a
bootstrap sampling method to extract multiple samples from the original
samples, conduct decision tree modeling for each sample, and then
combine the prediction of multiple decision trees in order to obtain the
final prediction result through a voting process. The model is
characterized by strong applicability, effective avoidance of
over-fitting and insensitivity to missing data and multivariate
collinearity (Breiman et al., 2001; Hutengs and Vohland 2016). It is an
effective empirical approach in the nonlinear-regression systems and its
superiority has been proved useful by a large number of applications in
the earth system (Lary et al., 2016).

To study the effects of predictors on MAGT and ALT, our models were
designed using the following specifications:

MAGT
=\(\ f_{1}\left(\text{TDD}\right)\)+\(f_{2}\left(\text{FDD}\right)\)+\(f_{3}\left(Sol\_pre\right)\)+\(f_{4}\left(Liq\_pre\right)\)+\(f_{5}\left(\text{PISR}\right)\)+\(f_{6}\left(\text{SOC}\right)\)

+\(f_{7}\left(\text{Lon}\right)\)+\(f_{8}\left(\text{Lat\ }\right)\)+\(f_{9}\left(\text{Ele}\right)\)(3)

ALT
=\(\ f_{1}\left(\text{TDD}\right)\)+\(f_{2}\left(\text{FDD}\right)\)+\(f_{3}\left(Sol\_pre\right)\)+\(f_{4}\left(Liq\_pre\right)\)+\(f_{5}\left(\text{PISR}\right)\)+\(f_{6}\left(\text{SOC}\right)\)

+\(f_{7}\left(\text{Lon}\right)\)+\(f_{8}\left(\text{Lat\ }\right)\)+\(f_{9}\left(\text{Ele}\right)\)(4)

The independent variables in these equations are same, while the
corresponding\(f_{i}\left(x_{i}\right)\) in each equation is different. In order
to fully consider the advantages and disadvantages of the above four
models and to reduce the uncertainty, we used an ensemble approach. This
method puts the average of the four models as the new results. The
optimal model was determined by comparing the key parameters of the
final five results. Model performance was assessed using a repeated
cross-validation (CV) scheme. Based on a total of 84 boreholes and 70
ALT observation sites, the models gave the simulated results after 10
times fitting processes using a random sample of 90\% of the observation
data and verification processes using the remaining 10\%. After each CV
run for all models, the predicted and observed values of MAGT and ALT
were compared in the terms of the root-mean-square error (RMSE), mean
difference (cf. bias), and R-squared (R\textsuperscript{2}).

3. Results

\textbf{3.1. Reliability assessment of MAGT and ALT}

The simulation results were compared with the \emph{in situ} observation
data using cross-validation. A comparison of the five results (Figure 2)
reveals that there was no significant bias between the simulated values
and the available borehole data on the QTP, but the RMSE and
R\textsuperscript{2} of the ensemble method imply that it was more
reliable than the other four methods. The consistency between the
measured and simulated MAGT at most sites for the five models was less
than 1\selectlanguage{ngerman}°C. Among these models, the ensemble method performed optimally,
with a simulation accuracy for 80 sites of \textless{} 1°C, which
account for 95\% of the total sites. It exhibited a strong positive
correlation between the simulated and observed MAGT
(\emph{R\textsuperscript{2}} = 0.73, \emph{p} \textless{} 0.001).
Overall, the ensemble method (Figure 2(e)) displayed the highest
accuracy among the models in forecasting the MAGT. For this reason, the
ensemble model was selected to simulate the present MAGT and future
trends.

Similarly, the simulated ALT results were compared with the
\emph{insitu} observation data using the same statistical method. For
ALT, the best fitting result was RF (Figure 3(d)), which exhibited the
highest \emph{R\textsuperscript{2}} and the lowest RMSE values of 0.51
and 0.69 m, respectively. Although the GLM method exhibited a smaller
bias, the difference between the two methods was not large. Overall, the
validations for the five results did not differ significantly. Based on
further comparison of Figures 2 and 3, it can be seen that the fitting
accuracy of MAGT was better than that of ALT,
with\emph{R\textsuperscript{2}} values of the corresponding optimal
fitting results of 0.73 and 0.51, respectively. This is due to the fact
that the spatial heterogeneity of the ALT is larger than that of the
MAGT on the QTP, and the ALT will fluctuate greatly during climate
change within a short period (Cao et al., 2017).

We calculated the error distribution for five typical regions separately
(Table 1). Overall, the distribution of RMSE and bias on the QTP was
relatively uniform, with the exception of the RMSE in the AEJIR. The
reason for this may be that there are relatively few observation sites
in the northern part of the whole investigated regions, and the
simulating accuracy has high sensitivity to single points and poor
regional representation. In addition, permafrost along the G109 Highway
is greatly affected by human activities, and there are more observation
sites in this region. Compared with the error statistics of the entire
QTP, the RMSE of MAGT in the G109IR was relatively small, while the RMSE
of ALT was relatively large. Thus, we may conclude that MAGT is
relatively less affected by human activities, while ALT is more affected
by disturbance and displays great spatial heterogeneity. In terms of
bias, the region with the largest bias was GZIR. The reason is that GZIR
located in the transition zone between permafrost and seasonally frozen
ground, and the accuracy of the results would be affected to some
extent.

\textbf{3.2. MAGT and ALT during the reference period}

Using the collected borehole data, we fitted the meteorological factors
and geographical environmental factors to obtain the MAGT distribution
of the permafrost regions on the QTP (Figure 4). We extracted the MAGT
of the QTP below 0 °C as an average range of permafrost (Chen et al.,
2015), which indicating suitable conditions for permafrost, with a total
area of 1.04 × 10\textsuperscript{6} km\textsuperscript{2} (excluding
glaciers and lakes). Considering the heterogeneity and uncertainty of
ground temperature on the QTP, the minimum permafrost extent is 0.8 ×
10\textsuperscript{6} km\textsuperscript{2} (the area within MAGT \selectlanguage{english}[?]
\selectlanguage{english}-0.5degC), and the maximum extent is 1.28 x
10\textsuperscript{6}km\textsuperscript{2} (the area within MAGT \selectlanguage{english}[?]
+0.5degC). Compared with the pan-Arctic permafrost, the permafrost
temperature on the QTP is relatively high (Obu et al., 2019). Nearly
half of the permafrost temperature area on the QTP exceed -1.0oC and the
average temperature is -1.35 +- 0.42 oC. The permafrost temperature is
not only affected by latitude, but also by altitude. As illustrated in
Figure 4, the lower-temperature permafrost on the QTP generally occurs
in high-altitude mountains, and the ground temperature gradually rises
with decreasing altitude, with the lowest value distributes in the
Kunlun Mountain and its surrounding regions. In general, the MAGT on the
QTP was found to be higher in the southern region (GZIR) than that in
the northern region (AEJIR), and higher in the eastern region (WQIR)
than that in the western region (XKLIR).

Based on permafrost extent, the spatial distribution of the ALT for the
entire QTP was obtained (Figure 5). The statistical results indicated
that the average ALT is 2.3 +- 0.60 m on the QTP, and the ALT value of
\textasciitilde{} 90\% of the permafrost region ranged from 1.6 to 3.0
m. Geographically, the ALT in the eastern part of the QTP is relatively
thinner (generally no more than 2 m) with slight variations. The ALT
along the Qinghai-Tibet Highway and in the central and western plateau
is highly heterogeneous. The overall ALT pattern is thin in the
mountains, thick on the plains, thin in the hinterlands, and thick along
the periphery of the permafrost. The maximum value appears along the
southern boundary of the permafrost and the surrounding sporadic
permafrost (generally \selectlanguage{english}[?] 3.2 m). In general, MAGT and ALT exhibit a
consistent trend in spatial distribution, with a correlation coefficient
of 0.44. The smaller value of MAGT corresponds to thinner ALTs.

\textbf{3.3. The projection of MAGT and ALT}

In view of a strong statistical rule of MAGT and ALT in climatic factors
(e.g., TDD and FDD) and topographic factors (e.g., Lon, Lat, and Ele),
most studies have begun to use similar statistical methods to
investigate the present and future development trends of the periglacial
climate realm (Koven et al., 2013; Aalto et al., 2017, 2018; Zhang et
al., 2019). In this study, the optimal fitting model for the present
state was employed to forecast MAGT and ALT under different future
climate scenarios. For ALT, the spatial domain was limited to the area
with simulated MAGT \selectlanguage{english}[?] 0degC during each associated period and/or RCP
scenario.

Due to climate change, the permafrost temperature exhibits an obvious
rising trend on the QTP. We simulated the future change of permafrost on
the QTP after half a century. The results revealed that the future
changes of MAGT and ALT are predicted to be pronounced, but
region-specific (Figure 6). The forecasted average MAGT over the QTP
permafrost regions will increase from -1.35degC (present status) to
-0.66degC by 2061\selectlanguage{english}-2080 (RCP2.6) and to 0.25degC for RCP8.5 (Table 2). The
ALT, however, was only predicted to increase from 2.3 m (2000\selectlanguage{english}-2015) to
2.7 m (2061\selectlanguage{english}-2080) for RCP8.5. The reason for the consistency or small
change of the ALT is that, the section of the permafrost with a MAGT
near 0degC is forecasted to degrade to seasonally frozen ground, and this
part of the permafrost usually corresponds to a thicker active layer.
Additionally, the uncertainties related to the forecasts of MAGT and ALT
under different RCPs in the future were given. And, the uncertainties
are characterized by the range of MAGT value and ALT value. As can be
seen in Figure 7, even under the different RCPs scenarios, the
fluctuation range of MAGT and ALT is basically the consistent.

Over the next half century, the near-surface permafrost areas are
predicted to continue to decrease by 0.13 x
10\textsuperscript{6}km\textsuperscript{2} (12\%), 0.42 x
10\textsuperscript{6}km\textsuperscript{2} (40\%) and 0.60 x
10\textsuperscript{6}km\textsuperscript{2} (58\%) on the QTP by 2070
(2061\selectlanguage{english}-2080), under the RCP2.6, RCP4.5 and RCP8.5 scenarios,
respectively. The result is basically consistent with the projected
change by Chang et al. (2018) (Figure 8). Permafrost is in
non-equilibrium under the influence of climate change, and there may be
no permafrost that is driven by the current climate. In fact, it may be
that permafrost is degrading, so the distribution range of the
simulation results may be underestimated (Zhao et al., 2019). The
changes in MAGT and ALT are not only related to the changes in
temperature and precipitation but also closely related to hydrothermal
parameters and surface energy balance (Guo and Wang, 2016; Hu et al.,
2019). Based on the existing observation data and improved soil physics,
the estimated changes in previous studies are generally larger than that
of actual change (Lawrence et al., 2012; Cheng et al., 2019; Wang et
al., 2019b).

4. Discussion

In order to project the possible future changes of permafrost, we
simulated MAGT and ALT changes under the present state and future
scenarios based on statistical and ML methods. The results show that
under different RCPs, significant degradation of the QTP permafrost may
occur (e.g., MAGT rising and ALT thickening); in particular, under
RCP8.5, more than half of the near-surface permafrost will disappear,
and regional differences were observed. In this section, to further
verify the feasibility of our results, we compared our simulated MAGT
and ALT with those of previous studies and then analyzed the
vulnerability of permafrost to climate change under the present state.
Based on these findings, we proposed urgent action should be taken to
adapt climate change. Finally, the model performance and potential
sources of the uncertainty in this study were discussed.

\textbf{4.1. Comparisons with previous results}

The most likely permafrost area on the QTP is 1.04 x
10\textsuperscript{6} km\textsuperscript{2} (the region where MAGT
\textless{} 0degC, Figure 4), or about 45.4\% of the total QTP land
surface area. Our results were compared with the permafrost distribution
map of the QTP for the period 2003--2012 based on the TTOP model, which
was basically consistent with the new permafrost area (1.06 x
10\textsuperscript{6} km\textsuperscript{2}, Zou et al., 2017). The two
results showed substantial consistency, with a kappa coefficient of 0.63
(Table 3). However, there were still certain spatial differences (Figure
9). These differences mainly occurred at the southern margin of the
continuous permafrost and the islands of permafrost in the south eastern
QTP.

For the results of MAGT and ALT, a similar study showed relatively large
deviations at the hemispheric scale (the RMSEs of MAGT and ALT were
1.6degC and 0.89 m, respectively; Aalto et al., 2018). In their study, an
interesting discovery was mentioned, for both MAGT and ALT: after
considering the area north of 60degN, the uncertainty was greatly reduced.
This is primarily due to the fact that the permafrost on the QTP is
quite different from that of the pan-Arctic region. The QTP is the
dominant by the high-altitude permafrost, while the pan-Arctic is mainly
the high-latitude permafrost. Compared with the pan-Arctic region, the
active layer on the QTP is thicker, the ground temperature is higher,
and the spatial heterogeneity is greater (Nicolsky et al., 2017; Cao et
al., 2017; Qin et al., 2017). Therefore, combining the QTP permafrost
and the pan-Arctic permafrost hemispherically will inevitably reduce the
accuracy of the results.

We further compared the simulated results of MAGT and ALT with previous
studies on the QTP. Table 4 summarizes the error statistics among
different types of permafrost models (i.e., equilibrium model, transient
model and statistical model). We can find that for the R-value, our
method combined of the statistical and ML has the similar accuracy with
the transient model. Although the RMSE of ALT in our study is the
largest among all models, the differences are not significant. Moreover,
the RMSE of MAGT in our study shows relatively smaller error. Meanwhile,
from the overall spatial distribution of the ALT, although there are
some differences in the spatial details, the distribution pattern of our
result is comparable with the presented recently (Zhao and Wu, 2019;
Wang et al., 2020b). In generally, our model can obtain a relatively
higher simulation accuracy.

We qualitatively analyzed the main reasons for these differences as
follows. Firstly, there are differences in accuracy among different
types of models, such as the equilibrium models and mechanistic
transient models. Secondly, there is a slight gap between the research
period and the data used for verification. Permafrost is often viewed as
a product of long-term climate change, which is slowly changing (Zhang
et al., 2007); this may also lead to differences between the results.
Finally, the 0.1deg resolution of our model can't capture all of regional
information on climate change, which may limit the model's ability to
capture detailed changes in the permafrost to some extent, especially in
the boundary of the permafrost region (Etzelmuller, 2013; Guo and Wang,
2016). Therefore, the ability to capture the permafrost edge information
should be further improvement. Overall, by comparing with previous
studies on the QTP, that our method is relatively simple and effective,
and thus could be a useful tool to evaluate the permafrost conditions
with a high accuracy on the QTP.

\textbf{4.2. Permafrost vulnerability}

According to Figure 4, the ground temperature of the entire QTP
permafrost is relatively high. In order to analyze the vulnerability of
the QTP permafrost to climate warming, the permafrost region with MAGTs
ranging from -0.5 to 0.5degC was extracted (Figure 10). According to the
permafrost stability classification (Cheng and Wang, 1982), permafrost
in this range is classified as unstable region. It can be observed that
0.49 x 10\textsuperscript{6} km\textsuperscript{2} of the permafrost
area over the QTP is in danger at present, which accounting for 37.3\%
of the maximum permafrost area. This unstable permafrost primarily
distributed in the transition region of permafrost and seasonally frozen
ground.

As a result of the global warming and increased anthropogenic activity,
the QTP has experienced an approximately 3-fold warming increase over
the past 50 years (Wan et al., 2018). Under the influence of this
accelerated warming, the permafrost region adjacent to the seasonally
frozen ground is becoming increasingly fragile (Qin et al., 2017). This
part of the permafrost is generally in the process of ice-water phase
transformation. A comparison with Figure 6, reveals that this region is
consistent with the areas in which permafrost will disappear under
future RCPs, but it also greatly affected by the local ground ice
content, underlying surface types, and other related factors (Nelson et
al., 2001; Yang et al., 2010c).

The Qinghai-Tibet Engineering Corridor (QTEC, the region that contains
the Qinghai-Tibet Highway and Railway, pipelines, electric transmission
lines, and so on) is an important conduit connecting mainland China and
the QTP. Under the influence of intensifying global climate change and
frequent human activities, the ecological environment along the QTEC is
fragile, and the permafrost in the QTEC has degraded significantly and
the alpine ecosystem is facing new challenges (Niu et al., 2018). Based
on Figure 10, the statistical results show that 757 km of the QTEC
crosses through the permafrost region (at its maximum extent),
accounting for nearly 40\% of its total length (from Xining to Lhasa).
Of this, approximately half of the QTEC faces the risk of the permafrost
disappearing, and the other half may experience varying degrees of
permafrost degradation in the future. This will result in huge economic
losses and threaten associated infrastructures along the QTEC.

Recent studies have shown that several cryosphere tipping points are
dangerously close (IPCC, 2019), and the permafrost in the Arctic has
begun to thaw irreversibly and release carbon dioxide and methane, but
the inevitable effects could still be mitigated by reducing greenhouse
gas emissions (Lenton et al., 2019). The stability and resilience of the
QTP permafrost is in peril. We should take urgent action to reduce
greenhouse gas emissions, and put them as the priority of the present
and future work. In order to effectively mitigate the degradation of
permafrost, all the emission reduction measures should be reflected in
words even in actions.

\textbf{4.3. Model performance and uncertainty analysis}

Our study integrated field observation data, meteorological data,
geospatial environmental predictors and multiple statistical models to
study MAGT and ALT changes in the present and future QTP permafrost
regions. Based on the CV analysis, the reliability of both predictions
displayed relatively low uncertainty. For MAGT, the benefits of using
the ensemble modeling approach were obvious, i.e., the average of the
four methods yielded the best simulation result. For ALT, large errors
still existed among the ensemble modeling approach after CV, which
indicating that the method does not always produce the most reliable
results. The simulation accuracy of ALT is lower than that of MAGT, and
the result can only represent the general change trend of ALT. The main
reason for this is that, the spatial heterogeneity of ALT on the QTP is
large, with the change rate of ALT per unit (100 m\textsuperscript{2})
reaching 80\%, thus resulting in the relatively low
R\textsuperscript{2}values and large RMSEs (Cao et al., 2017).
Additionally, our model predicts the equilibrium state of permafrost and
does not consider the lag time associated with the formation and
degradation of permafrost (Xu et al., 2017b). Compared with previous
studies, although our results show great reliability, there are still
some uncertainties embedded in the predictions, including the
measurement accuracy of the data, the equilibrium assumption in the
statistical modeling and the influence of other factors (Aalto et al.,
2018).

Due to the limitations of the observation data, we had to use one-year
or multi-year averages to represent the present state and to fit the
model. MAGT and ALT changed during this period, however, in particular,
ALT changed greatly at the inter-annual scale. We did our best to
collect datasets with MAGT and ALT, but the number of sample points used
for training was still limited, and the model was still highly sensitive
to single observations. To some extent, this also indicates that the
number of observation sites on the QTP is too sparse to represent the
present large spatial heterogeneity of the plateau.

When calculating the input factors of the model, in the future warming
scenarios, the TDD and FDD were calculated based on the monthly mean air
temperature instead of the daily mean air temperature. This approximate
calculation method will bring some unavoidable errors, especially when
the temperature is close to 0 \selectlanguage{english} (Wu et al., 2011; Shi et al., 2019).
Additionally, we simply take 0degC temperature as the critical temperature
threshold between solid precipitation and liquid precipitation, while,
in most cases, snowfall events even occur in some regions on the QTP
when the air temperature is \textgreater{} 4degC, but not 0 \selectlanguage{english} (Wang et
al., 2016).

In this study, some key soil parameters, including soil texture, soil
moisture content and bulk density, were excluded from the analyses in
the model due to missing data, which exerted strong influence on water
and heat transfer in the active layer as well as the change in
permafrost temperature (Wu et al., 2017b; Du et al., 2020). The PISR and
SOC in permafrost region are not static. However, it was assumed to be
the fixed value in our model. With the further research on the key
predictors of the permafrost region, we will add more dynamic datasets
to our model. In summary, we used statistical and ML models combined
with easily accessible data to simulate the present and future dynamics
of permafrost on the QTP. By comparison and verification, our model can
obtain high precision results through a relatively simple calculation
process.

5. Conclusions

In this study, the method combined of statistical and ML was used to
obtain the key permafrost metrics in both the present and a half-century
in the future (2061\selectlanguage{english}-2080) on the QTP. Based on the comparison with
\emph{in situ} observation data and previous researches, we found that
this method was reliable for simulating the changes in MAGT and ALT. We
demonstrated the permafrost degradation from a quantitative perspective.
Our results can provide a scientific basis for the study of climate
change in permafrost. The main conclusions are listed as follows:

\begin{enumerate}
\tightlist
\item
  A combination method of statistical and ML models is efficient to
  capture the changes in the thermal state of the permafrost on the QTP.
\item
  The present (2000\selectlanguage{english}-2015) permafrost area on the QTP is approximate to
  be 1.04 x 10\textsuperscript{6} km\textsuperscript{2}. The average
  MAGT and ALT of the permafrost region amount to -1.35 +- 0.42oC and 2.3
  +- 0.60 m, respectively.
\item
  In the future (2061\selectlanguage{english}-2080), the maximum permafrost area may be reduced
  to 0.44 x 10\textsuperscript{6} km\textsuperscript{2}. The future
  changes of MAGT and ALT are forecast to be pronounced, but
  region-specific.
\item
  The unstable permafrost mainly distributed at the edge of the
  permafrost region, and approximately half permafrost in the QTEC will
  be at risk of disappearing in the future.
\end{enumerate}

\textbf{Acknowledgements}

This work was financially supported by the Natural Science Foundations
of China (41690142; 41771076; 41961144021; 42071093), and the CAS
''Light of West China'' Program. The logistical supports from the
Cryosphere Research Station on the Qinghai-Tibet Plateau are especially
appreciated. Datasets for this research are available
at\emph{https://data.mendeley.com/datasets/hbptbpyw75/1} . We also thank
the three anonymous reviewers for their constructive suggestions.

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Y. (2019). Exploring the contribution of precipitation to water within
the active layer during the thawing period in the permafrost regions of
central Qinghai-Tibet Plateau by stable isotopic tracing. \emph{Science
of The Total Environmen} t, 661, 630-644.
https://doi.org/10.1016/j.scitotenv.2019.01.064

Zou, D., Zhao, L., Yu, S., Chen, J.\emph{,} Hu, G., Wu, T., \ldots{} \&
Wang, W. (2017). A new map of permafrost distribution on the Tibetan
Plateau.\emph{The Cryosphere} , 11(6),
2527.\emph{https://doi.org/10.5194/tc-11-2527-2017}

\textbf{Figure 1.} Location of the investigated regions and observation
sites. Green dots and red triangles stand for the mean annual ground
temperature (MAGT) and active layer thickness (ALT) monitoring sites,
respectively. The black polygons depict the five typical regions.

\textbf{Figure 2.} Observed \emph{vs} . simulated mean annual ground
temperature (MAGT) for 84 borehole sites based on four statistical
techniques (GLM = generalized linear model, GAM = generalized additive
model, GBM = generalized boosting method, RF = random forest.) and an
ensemble method (the average of the four methods). The red dashed lines
are the +-1 \selectlanguage{english} intervals around the 1:1 line (in black solid line).

\textbf{Figure 3.} Observed \emph{vs} . modeled active layer thickness
(ALT) based on four statistical techniques (GLM = generalized linear
model, GAM = generalized additive model, GBM = generalized boosting
method, RF = random forest.) and an ensemble method (the average of the
four methods). The red dashed lines are the +-1 m interval around the 1:1
line (in black solid line).

\textbf{Figure 4.} Spatial distribution of permafrost on the QTP based
on the MAGT.

\textbf{Figure 5.} Distribution of the ALT on the permafrost regions of
the QTP.

\textbf{Figure 6.} Forecast mean annual ground temperature (MAGT) and
active layer thickness (ALT) across the study domains under different
RCPs (RCP2.6, RCP4.5 and RCP8.5) for the 2070s (average of 2061\selectlanguage{english}-2080).

\textbf{Figure 7.} The uncertainty related to the spatial forecasts of
mean annual ground temperature (MAGT) and active layer thickness (ALT)
in RCP 2.6(a), RCP 4.5 (b), RCP 8.5 (c) scenarios. The uncertainty is
quantified using a repeated (n = 1,000) bootstrap sampling procedure
inside the study domain. The boxplots depict the mean, median, 1st and
3rd quartiles and range of variation over 1000 predictions for modeling
techniques.

\textbf{Figure 8.} Projections of the changes in permafrost area on the
QTP under RCP2.6, RCP4.5, RCP6.0 and RCP8.5 via 7(a) surface frost index
(SFI) and 7(b) Kudryavtsev method (KUD). The graph is derived from
Chang\emph{et al.} (2018). Shaded areas show the standard deviations
across the CMIP5 models, the black lines show the equivalent present-day
area, and the grey dotted line represent the degraded area in 2070 under
different RCPs.

\textbf{Figure 9.} Spatial differences between our results (2000--2015)
and those of Zou \emph{et al} (2003--2012; TTOP model). P and SFG
represent permafrost and seasonally frozen ground, respectively; Result
is the permafrost distribution of this study. The permafrost
distribution is obtained from Zou \emph{et al.} (2017).

\textbf{Figure 10.} Spatial distribution of the permafrost regions prone
to degradation.

\textbf{Table 1.} Model Error statistics of the ALT and MAGT in
different typical regions\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Region\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Region\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(WQIR) East\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(XKLIR) West\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(GZIR) South\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(AEJIR) North\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(G109IR) Central\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
(QTP) Entire\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
MAGT\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
RMSE ()\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.60\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.56\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.61\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.73\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.45\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.53\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Bias ()\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.025\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.06\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.15\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.14\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.03\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.02\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
ALT\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
RMSE (m)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.60\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.62\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.68\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.11\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.76\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.69\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
Bias (m)\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.24\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.06\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.46\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.09\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.18\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
-0.11\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 2.} Key characteristic metrics of permafrost under
different RCPs\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
& Present & RCP2.6 & RCP4.5 & RCP8.5\tabularnewline
\midrule
\endhead
& 2000-2015 & 2061-2080 & 2061-2080 & 2061-2080\tabularnewline
MAGT () & -1.35 & -0.66 & -0.14 & 0.25\tabularnewline
ALT (m) & 2.3 & 2.5 & 2.5 & 2.7\tabularnewline
Area (\selectlanguage{ngerman}×10\textsuperscript{6} km\textsuperscript{2}) & 1.04 & 0.91 & 0.62
& 0.44\tabularnewline
\bottomrule
\end{longtable}

Note: the statistics of mean annual ground temperatures (MAGT) in three
scenarios (RCP2.6, RCP4.5, RCP8.5) were based on the permafrost range
under present status.

\textbf{Table 3.} Discrepancy area of permafrost on QTP\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
& Area discrepancy (\selectlanguage{ngerman}×10\textsuperscript{6} km\textsuperscript{2}) &
Percentage (\%)\tabularnewline
\midrule
\endhead
Both P & 0.86 & 35.41\tabularnewline
Result P and Zou SFG & 0.18 & 7.41\tabularnewline
Result SFG and Zou P & 0.20 & 8.23\tabularnewline
Both SFG Total & 1.19 2.43 & 48.95 100\tabularnewline
\bottomrule
\end{longtable}

\textbf{Table 4.} Compare the statistical errors between different types
of models\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
\begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Numerical model\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Time period\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
RMSE\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
R\strut
\end{minipage} & \begin{minipage}[b]{0.14\columnwidth}\raggedright\strut
Source\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
MAGT ()\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Equilibrium model\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
2000-2016\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
1.85\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.20\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Obu et al., 2019\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Transient model\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2007-2010\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{0.31}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{0.93}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Wu et al., 2018\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Statistical and ML\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2000-2015\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.53\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.85\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
This study\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
ALT (m)\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Equilibrium model\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Before 2009\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
\textbf{0.47}\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
0.46\strut
\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\raggedright\strut
Pang et al., 2012\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Transient model\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2007-2010\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.57\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\textbf{0.86}\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Wu et al., 2018\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
Statistical and ML\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
2000-2015\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.69\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
0.71\strut
\end{minipage} & \begin{minipage}[t]{0.14\columnwidth}\raggedright\strut
This study\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Note: bold data represents the best result for each model.

\selectlanguage{english}
\FloatBarrier
\end{document}

