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Journal of Geographical Sciences >

2022 , Vol. 32 >Issue 8: 1581 - 1600

DOI: https://doi.org/10.1007/s11442-022-2011-8

Research Articles

Simulation of frozen ground distribution in northeast China based on a surface frost number model

  • ZHAN Daqing , 1, 2 ,
  • MAN Haoran 1, 2 ,
  • ZANG Shuying 1, 2 ,
  • LI Miao , 1, 2, *
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  • 1. College of Geographical Science, Harbin Normal University, Harbin 150025, China
  • 2. Heilongjiang Province Key Laboratory of Geographical Environment Monitoring and Spatial Information Service in Cold Regions, Harbin 150025, China
* Li Miao (1984-), Associate Professor, specialized in remote sensing image processing and application. E-mail:

Zhan Daqing (1997-), Master, specialized in permafrost degradation and land use change. E-mail:

Received date: 2021-08-26

  Accepted date: 2022-03-09

  Online published: 2022-10-25

Supported by

National Natural Science Foundation of China(41901072)

National Natural Science Foundation of China(41971151)

Joint Key Program of the NSFC and Heilongjiang Province of China(U20A2082)

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Abstract

Against the background of global warming, environmental and ecological problems caused by frozen ground degradation have become a focus of attention for the scientific community. As the temperature rises, the permafrost is degrading significantly in the frozen ground region of northeast China (FGRN China). At present, research on FGRN China is based mainly on data from meteorological stations, and the research period has been short. In this study, we analyzed spatial and temporal variation in the ground surface freezing index (GFI) and ground surface thawing index (GTI) from 1900 to 2017 for FGRN China, with the air freezing index (AFI) and air thawing index (ATI) using the University of Delaware (UDEL) monthly gridded air temperature dataset. The turning point year for annual mean air temperature (AMAT) was identified as 1985, and the turning point years for GFI and GTI were 1977 and 1996. The air temperature increased by 0.01 ℃ per year during 1900-2017, and the GFI and GTI increased at rates of -0.4 and 0.5 ℃ d per year before the turning point year; after the turning point, these rates were -0.7 and -2.1 ℃ d per year. We utilized a surface frost number model to study the distribution of frozen ground in FGRN China from 1900 to 2017. When the empirical coefficient E value is 0.57, the simulated frozen ground distribution is basically consistent with the existing frozen ground maps. The total area of permafrost in FGRN China decreased by 22.66×104 km2 from 1900 to 2017, and the permafrost boundary moved northward with obvious degradation. The results of this study demonstrate the trend in permafrost boundary degradation in FGRN China, and provide basic data for research on the hydrological, climate, and ecological changes caused by permafrost degradation.

Key words： permafrost degradation; frozen ground distribution; freezing/thawing indices; surface frost number model; northeast China

Cite this article

ZHAN Daqing , MAN Haoran , ZANG Shuying , LI Miao . Simulation of frozen ground distribution in northeast China based on a surface frost number model[J]. Journal of Geographical Sciences, 2022 , 32(8) : 1581 -1600 . DOI: 10.1007/s11442-022-2011-8

1 Introduction

Frozen ground generally refers to various rocks or soils containing ice whose temperature is maintained at or below 0℃. Permafrost refers to rock or soil that has been frozen continuously for two or more years. The formation and development of frozen ground is affected by many factors, with temperature being one of the most important (Zhang et al., 2008; Farbrot et al., 2013; Guo and Wang, 2016; Liu et al., 2021a). The assessment report of the sixth meeting of the Intergovernmental Panel on Climate Change (IPCC) pointed out that the global average temperature has been rising continuously over the last 100 years (1850-1990) and is 1℃ higher than 100 years ago (Zhou, 2021). Compared with the global average temperature trend, the warming trend in high-latitude and high-altitude regions is more significant (Wu et al., 2018; Peng et al., 2019). As frozen ground is found in low-temperature environments, increasing temperatures will lead to its degradation (Zhao et al., 2010; Guo et al., 2018). The degradation of frozen ground can affect the ecology, climate, productivity, and living conditions in cold regions (Ebel et al., 2019; Kong et al., 2019; Schneider et al., 2021), resulting in a decline in soil water storage capacity (Qin et al., 2016a; Jin et al., 2020), shrinkage of lakes and wetlands (Jin et al., 2009a), increase in greenhouse gas emissions (Schuur et al., 2015; Kirkwood et al., 2021); and increases in engineering, construction, operation and maintenance costs (Niu et al., 2012; Luo et al., 2019).
Currently, long-term time series research on frozen ground in China has focused mainly on the Tibet Plateau, whereas studies on the frozen ground region of northeast China (FGRN China) are less common (Zhang et al., 2020; Ran et al., 2021). With climate warming, the frozen ground in FGRN China is showing clear degradation. Luo et al. (2014) calculated freezing (thawing) indices based on observational data from 21 meteorological stations in FGRN China obtained between 1972 and 2005. The results showed that the air freezing index/ground surface freezing index (AFI/GFI) showed a significant downward trend, whereas the air thawing index/ground surface thawing index (ATI/GTI) increased significantly and the frozen ground degraded significantly. Gong et al. (2021) analyzed the temporal and spatial changes in ground temperature and freezing depth, based on data from 144 national meteorological stations in northeast China from 1951 to 2016. They found that climate warming caused the ground temperature of all layers (ground surface and belowground soil temperature at 5, 10, 15, 20, 40, 80, 160, and 320 cm depths) in the region to rise, the freezing depth to reduce and the freezing period to shorten, especially in the permafrost regions and the adjacent high-latitude seasonal frozen ground regions. Zhang et al. (2021) analyzed the degradation of permafrost using data from 258 meteorological stations and reanalyzed data from FGRN China from the 1950s to the 2010s. They found that the total permafrost area decreased from 4.8 × 105 km2 to 3.1 × 105 km2 over the analysis period, the southern boundary of the permafrost moved 0.1°-1.1° northward, and its average altitude rose by 160.5 m. Existing research suggests that frozen ground in FGRN China is continuously degrading, and the active layer is thickening; the thickness of the frozen layer is declining; the thawing region is expanding, the southern boundary of permafrost is moving northward, and the area of island permafrost is decreasing. The area of high latitude wetland is declining, causing degradation of forest land and reducing its foundation-bearing capacity, thereby damaging both ecology and engineering infrastructure (Zhang et al., 2018). It is therefore urgent to understand the distribution of frozen ground degradation in FGRN China (Chen et al., 2018).
The development of frozen ground distribution maps can be divided into two methodological phases. In the first phase, manual analysis of field-measured data such as temperature and data from boreholes were used to construct distribution maps. Xin and Ren (1956) made a systematic summary of the distribution characteristics of permafrost in northeast China by collating previous survey data from FGRN China, and marked the southern boundary of permafrost in the resulting distribution map. In the second methodological phase, during the late 20th century, rapid development of 3S technology (i.e., geographic information systems, global positioning systems, and remote sensing) enabled researchers to use models to simulate the spatial distribution of frozen ground (Wei et al., 2011). Because of the influence of terrain and environment, artificial mapping based on field measurements and investigations is difficult to use for large-scale frozen ground mapping in harsh climatic environments such as the Qinghai-Tibet Plateau. The use of empirical models has solved this problem well. Remote sensing data combined with empirical modeling can simulate permafrost distribution on a large scale. However, the accuracy of the empirical model is also affected by the resolution of the remote sensing data and the number of parameters. Although there are deficiencies, model simulation remains an effective way to assess permafrost distribution at present (Ran and Li, 2019). Liu et al. (2021b) and Shi et al. (2019) mapped the permafrost distribution in the upper Brahmaputra River Basin from 1900 to 2017 and the circum-Arctic region from 2000 to 2015, using a surface frost number model and achieved good results. Many studies have shown that such models are highly accurate for large-scale simulations of frozen ground distribution.
Although there have been several studies of the temporal and spatial changes in frozen ground distribution in various frozen ground regions in China (Park et al., 2016; Peng et al., 2017; Peng et al., 2018), most have been based on observational data obtained from meteorological stations (Jiang et al., 2008; Qin et al., 2016b; Zhang et al., 2018). However, the spatial distribution of meteorological stations in the FGRN China is irregular, and the time periods of the data records are also relatively short. In addition, previous research results have mainly produced a single frozen ground distribution map, and it is difficult to ascertain the specific degradation of frozen ground from these results. In this study, the annual mean temperature (AMAT), AFI/ATI, and GFI/GTI from 1900 to 2017 in FGRN China were calculated based on monthly air temperature reanalysis data, and their spatial and temporal characteristics were analyzed. The distribution range of frozen ground over the past 118 years was simulated using a surface frost number model. Distribution maps of frozen ground in FGRN China were drawn for ten-year periods, and the results provide an intuitive representation of the degradation of frozen ground in FGRN China. These results provide scientific and technological support for the sustainable development of FGRN China against the background of climate warming.

2 Data and methods

2.1 Study area

The study area, located in northeast China (38°40′N-53°34′N, 115°05′E-135°02′E), is the second largest frozen ground region and the principal high-latitude frozen ground region in China (Figure 1). The region consists mainly of seasonal frozen ground and continuous and discontinuous permafrost. The permafrost is mainly distributed in the Da Hinggan Mountains, the Xiao Hinggan Mountains, the northern Songnen Plain and other high altitude sub-regions (Jin et al., 2009b). Compared with high-altitude frozen ground, FGRN China is more susceptible to climate warming because of its thin and relatively warm frozen ground (Zhang et al., 2021). FGRN China spans the mid-temperate zone in the south to the cold-temperate zone in the north. It has a temperate monsoon climate with four distinct seasons. Summer is warm (typically 25℃) and rainy, and winter is cold (typically -20℃) and dry. The annual mean air temperature of the whole region is about 2-11℃ from north to south, and the annual mean precipitation is 460 mm (Bi, 2019). The mean altitude of FGRN China is 452.7 m, and the terrain is mostly plains. There are a small number of high-altitude mountains (i.e. >1200 m) in the north and south, and there are many rivers. Forest and cultivated land resources are distributed throughout the Da Hinggan Mountains and Xiao Hinggan Mountains and on the Northeast China Plain composed of the Sanjiang Plain, the Songnen Plain and the Liaohe Plain.
Figure 1 Location of the study area (a) and permafrost distribution (b) in the frozen ground region of northeast China

2.2 Data

Data used in this study included meteorological station data; monthly air temperature reanalysis data; land cover data; soil moisture data and frozen ground map of China (Table 1).
Table 1 Description of the datasets adopted in this study
Number Name Time Fuction Source
1 Meteorological station data 1977-2017 Calculating the value of N National Meteorological Information Centre of China (http://data.cma.cn/)
2 Monthly air temperature reanalysis data 1900-2017 Calculating the freezing/thawing indices University of Delaware (http://climate.geog.udel.edu/climate/)
3 Land cover data 2020 Calculating the value of N National Geomatics Center of China
(http://www.globallandcover.com/)
4 Soil moisture data 2002-2018 Calculating the correlation between freezing/thawing indices and soil moisture National monthly scale soil moisture dataset (https://zenodo.org/record/4922393)
5 Frozen ground map of China 1998 and 2000 Accuracy evaluation National Tibetan Plateau Data Center (http://www.tpdc.ac.cn/)

2.2.1 Meteorological station data

Daily air temperature (Ta) and ground surface temperature (GST) data from 104 national meteorological stations in FGRN China were obtained from the National Meteorological Information Centre of China (http://data.cma.cn/). The distribution of stations is shown in Figure 1. Data were obtained for the period from 1977 to 2017.
As continuous time series were needed, missing data in the dataset were replaced with interpolated values as follows: (1) for missing values of one day, the mean temperatures of the two days before and after the missing date were used to interpolate the missing day; (2) for missing values of two consecutive days, the mean temperature of the previous two days was used for the first missing day, and the mean temperature of the two days after the missing day was used for the second day; (3) for missing values of two or more days, but less than one month, the mean temperature values of the corresponding months two years before and two years after the missing year were used for interpolation (Yu, 2015).

2.2.2 Monthly air temperature reanalysis data

Monthly air temperature reanalysis data from 1900 to 2017 were obtained from the University of Delaware (http://climate.geog.udel.edu/climate/). The spatial resolution was 0.5°× 0.5°. Correlations between annual mean air temperatures at the meteorological stations and the reanalysis data were calculated, and the observed temperatures at the stations were in good agreement with the reanalysis data. The correlation coefficient R2 and the RMSE between observed annual mean air temperature of the meteorological stations and the reanalysis data were 0.971 (p<0.01) and 0.0234, respectively. The temperatures recorded at the meteorological stations were higher than those in the reanalysis data across the whole study area from 1977 to 2017 (see Supplementary File A, Figure A2). The annual mean bias errors of the two datasets at each station in FGRN China were between -1.9 and 0.9℃ (see Supplementary File A, Figure A1). Although the temperatures of the reanalysis data were higher than those of the meteorological station data at some stations, they were lower for the majority of stations. On the whole, the reanalysis data temperatures were still lower than the meteorological station temperatures. The errors in the central and marginal regions of the study area were higher than those in other regions, and this is mainly related to the local surface conditions (altitude, SM, land cover, etc.).

2.2.3 Land cover data and soil moisture data

Global land cover data from the National Geomatics Center of China were obtained with a spatial resolution of 30 m (http://www.globallandcover.com/). Land cover was classified using 10 categories: Cultivated land, Forest, Grassland, Shrubland, Wetland, Water bodies, Tundra, Artificial Surfaces, Bare Land, and Permanent snow and ice (Chen et al., 2014). Soil moisture (SM) data were obtained from the National monthly scale soil moisture dataset (https://zenodo.org/record/4922393) (Meng et al., 2021).

2.2.4 Frozen ground maps of China

Frozen ground maps of China were obtained for 1998 and 2000 from the National Tibetan Plateau Data Center (http://www.tpdc.ac.cn/) (Ran and Li, 2018; Shi and Mi, 2013). The frozen ground map of China in 1998 was obtained by geometric correction and digitization on the basis of the 1988 map of Snow Ice and Frozen Ground in China (1:4,000,000). The frozen ground map for 2000 was obtained from a model simulation that integrated several existing frozen ground maps (Ran and Li, 2018). The maps from these two years reflect the distribution of frozen ground in FGRN China in the 1980s and 2000s.

2.3 Methodology

The distribution of frozen ground in FGRN China was simulated using a surface frost number model that used GFI and GTI as the main parameters. AFI and ATI were obtained by accumulating air temperatures, and these values were then converted into GFI and GTI using N-factors. Mann-Kendall (M-K) tests were carried out on annual mean air temperature, GFI and GTI to explore the effects of the turning points in these parameters on the frozen ground distribution.
First, the daily observational data from the 104 national meteorological stations were used to calculate the freezing/thawing N-factors (Nf and Nt) in the study region. The land cover type at each meteorological station was obtained by superposition of the land cover data and the meteorological station vector data to obtain the freezing/thawing N-factors for each land cover type. Monthly AFI/ATI values were then the calculated using the monthly air temperature reanalysis data. Finally, monthly GFI/GTI values were calculated using the monthly AFI/ATI values and N-factors. The F-value spatial distributions, calculated using the GFI/GTI values, gave the distribution of frozen ground in the study area (Figure 2).
Figure 2 Flowchart of research design

2.3.1 Mann-Kendall (M-K) test and interpolation

The Mann-Kendall (M-K) test was used to identify the timing of turning points in the trends of annual mean air temperature and GFI/GTI in the time series. The M-K test is a non-parametric statistical test used to analyze increasing or decreasing trends in a data series over time. It is often used for the analysis of hydrological and meteorological data. The Kriging interpolation method was used to interpolate the freezing and thawing indices and the simulated frozen ground distribution in ArcGIS 10.5.

2.3.2 Freezing/thawing indices

Freezing index (FI) includes the AFI and GFI, and the thawing index (TI) includes the ATI and GTI (Luo et al., 2014). The GFI and GTI values were calculated using cumulative values of GST below/above 0℃ over days or months, and the AFI and ATI values were calculated using cumulative values of Ta below/above 0℃ over days or months (using units of ℃ d or ℃ mon). The freezing index was calculated from July 1 to June 30 of the following year, and the thawing index was calculated from January 1 to December 31 of each year (Luo et al., 2018). The following formulas were used:
$FI\text{=}\underset{i\text{=7}}{\overset{{{M}_{F}}}{\mathop \sum }}\,\left| {{{\bar{T}}}_{i}} \right|\cdot {{D}_{i}}\text{(}{{\bar{T}}_{i}}\text{0)}$
$TI\text{=}\underset{i\text{=1}}{\overset{{{M}_{T}}}{\mathop \sum }}\,\left| {{{\bar{T}}}_{i}} \right|\cdot {{D}_{i}}\text{(}{{\bar{T}}_{i}}\text{0)} $
where FI is the freezing index (GFI and AFI), TI is the thawing index (GTI and ATI), ${{\bar{T}}_{i}}$ is the monthly mean temperature (Ta or GST) in the ith month and Di is the number of days in the ith month.

2.3.3 N-factors

Owing to a lack of ground surface temperature data from 1900 to 2017, GFI and GTI could not be calculated directly, and N-factors were therefore used to calculate GFI and GTI through AFI and ATI. N-factors characterize the thermal effects of surface conditions with different land cover types on the ground surface; they are calculated as the ratio of GFI to AFI and of GTI to ATI (Swanson et al., 2021), i.e.:
${{N}_{f}}\text{=}\frac{GFI}{AFI}{{N}_{t}}\text{=}\frac{GTI}{ATI}$
where Nf is the freezing N-factor and Nt is the thawing N-factor.

2.3.4 Frozen ground distribution model (surface frost number model)

The surface frost number model uses the ratio of freezing index and thawing index to delimit the boundary of permafrost(Nelson and Outcalt, 1987; Nan and Li, 2012). The relevant formula is as follows:
$F\text{=}\frac{\sqrt{GFI}}{\sqrt{GFI}\text{+}E\times \sqrt{GTI}}$
where E is an empirical value for estimating the status of frozen ground. F is used as the basis for judging the existence of permafrost and as the parameter for distinguishing between different types of permafrost. The E value was determined from the existing frozen ground map. A value of F=0.5 is defined as the threshold for estimating the presence/absence of permafrost, i.e.: 0 ≤ F < 0.5 indicates no permafrost; F ≥ 0.5 indicates permafrost (Lü et al., 2008).

2.3.5 Accuracy evaluation

The over accuracy (OA) and kappa coefficient (Ka) were used to evaluate the consistency of the simulation results with the existing frozen ground map of China (Shi et al., 2018). OA is the ratio of the number of correctly classified pixels to the total number of pixels in the sample. Ka is used to measure the consistency of the simulated result map with the existing frozen ground map.
$OA\text{=}\frac{s}{n}$
$Ka=\frac{OA-({{a}_{0}}{{b}_{0}}+{{a}_{1}}{{b}_{1}})/{{n}^{2}}}{1-({{a}_{0}}{{b}_{0}}+{{a}_{1}}{{b}_{1}})/{{n}^{2}}}$
where n is the total number of pixels, s is the total number of correctly classified pixels, a0 is the total number of existing frozen ground map pixels with permafrost, a1 is the total number of simulated result pixels with permafrost, b0 is the total number of pixels of seasonal frozen ground in the existing frozen ground map, and b1 is the total number of pixels of seasonal frozen ground in the simulated result. Shi et al. (2018) proposed quality values for Ka as follow: Ka ≥ 0.8 represents excellent agreement, 0.6 ≤ Ka < 0.8 represents substantial agreement, 0.4 ≤ Ka < 0.6 represents moderate agreement, 0.2 ≤ Ka < 0.4 represents fair agreement, and Ka < 0.2 indicates lack of agreement.

3 Results

We calculated Nf/Nt, AMAT, AFI/ATI and GFI/GTI in FGRN China from 1900 to 2017 using monthly air temperature reanalysis data and meteorological stations data as described above. A surface frost number model was used to simulate changes in the distribution of frozen ground between 1900 and 2017. The results are as follows.

3.1 N-factors

Based on the temperature data recorded by 104 meteorological stations from 1977 to 2017, we calculated the distribution of freezing/thawing N-factors (Nf/Nt) in FGRN China (Figure 3). The freezing N-factors ranged between 0.06 and 0.85, and high values were concentrated mainly in the western grassland region, whereas low values were found in the southeast. Grassland had the highest Nf value, a finding that was mainly related to the higher altitude in the western part of FGRN China. The change in air temperature with altitude is greater than the change in ground surface temperature. Air temperature is controlled by the atmospheric state equation and is closely related to air pressure; it therefore declines rate with altitude. However, ground surface temperature is controlled by the surface energy balance equation and has no direct relationship with air pressure and altitude. Moreover, due to the large area of cultivated land and forest in FGRN China, the values of freezing N-factors were generally close to 0.4 (Table 2). The thawing N-factors varied between 1.14 and 1.34, and there was stratification across FGRN China: higher thawing N-factors in the north and lower thawing N-factors in the south. The values of thawing N-factors were distributed mainly between 1.2 and 1.3, with small differences. In conclusion, the GFI of each land cover type in FGRN China was about 0.4-0.6 times that of AFI, and GTI was about 1.2-1.3 times that of ATI, based on the values of Nf and Nt.
Table 2 Nf/Nt values of various land cover types in the frozen ground region of northeast China
Land cover types Nf Nt
Cultivated land 0.43 1.30
Grassland 0.63 1.33
Forest 0.39 1.21
Water bodies 0.40 1.25
Artificial surfaces 0.44 1.26
Figure 3 Spatial distribution of Nf (a) and Nt (b) in the frozen ground region of northeast China from 1977 to 2017

3.2 Annual mean air temperature

AMAT varied between -7.86℃ and 11.30℃ from north to south in FGRN China (Figure 4). The spatial distribution of AMAT in FGRN China shows relatively warm temperatures in the south and cooler temperatures in the north, with clear latitudinal zonality. However, there are slight differences between the southeast (Changbai Mountains) and the whole FGRN China.
Figure 4 Spatial distribution of annual mean air temperature (AMAT) 1900-2017 in the frozen ground region of northeast China
The M-K test showed that a turning point in AMAT occurred in 1985 (Figure 5). AMAT increased by 0.03 ℃/10a up to 1985 and then increased by 0.13 ℃/10a after that year. The difference in warming rate before and after the AMAT turning point was therefore on the order of 0.1 ℃/10a. Based on the annual anomaly of AMAT (see Sup
Figure 5 Annual mean air temperature (AMAT) in the frozen ground region of northeast China from 1900 to 2017 (marginally significant at the p<0.1 level, with a 90% confidence level)
plementary File A, Figure A3), AMAT increased by 0.01℃ per year over the period from 1900 to 2017 (p<0.05). Although the warming rate was low, FGRN China has experienced continuous warming. Before 1985, positive and negative AMAT anomalies accounted for 38% and 62% of the anomalies, respectively. An extreme negative anomaly occurred in 1969. After 1985, positive and negative AMAT anomalies accounted for 97% and 3%, respectively, with a positive extreme value in 2007. There is therefore a remarkable difference in positive and negative anomalies before and after the AMAT turning point.

3.3 Air freezing/thawing index

Average values of AFI and ATI in FGRN China between 1900 and 2017 were also clearly dependent on latitude (Figure 6). The AFI was significantly higher in the north than in the south. The maximum AFI was about 4158.4 ℃ d in the north of FGRN China, and the minimum AFI was about 137.3 ℃ d in the south. The spatial distribution of ATI was opposite to that of AFI, with the minimum ATI (1279.2 ℃ d) in the north, and the maximum ATI (3764.9 ℃ d) in the south. AFI increased gradually with increasing latitude, whereas ATI decreased gradually with increasing latitude, as shown by the spatial distribution of AFI and ATI (Zhang et al., 2018).
Figure 6 The average (a) air freezing index (AFI) and (b) air thawing index (ATI) (℃ d) over the period from 1900 to 2017 in the frozen ground region of northeast China
The rates of change in AFI and ATI from 1900 to 2017 are shown in Figure 7. The rate of change in AFI varied greatly in the north and south of FGRN China. Areas showing increasing trends in AFI were distributed in a small area in the south of the region, whereas all other areas showed decreasing trends. Areas with large decreases were mainly concentrated in the northern mountains and the central and southern water-rich plains. The rate of change in ATI was higher in the northern and southwestern parts of the region, and values in the northern part of Heilongjiang Province showed the most rapid change. The overall rate of change was low in the south, showing an upward trend. The decrease in AFI and the increase in ATI indicate that the temperature in the FGRN China has increased year by year from 1900 to 2017. The changes in AFI and ATI were consistent with that in AMAT.
Figure 7 Spatial distribution of the rate of change in (a) air freezing index (AFI) and (b) air thawing index (ATI) over the period from 1900 to 2017 in the frozen ground region of northeast China (the plus sign indicates p<0.01 and the asterisk indicates p<0.05)

3.4 Ground freezing/thawing index

Average values of GFI and GTI calculated over the period from 1900 to 2017 are shown in Figure 8. The spatial distributions of GFI and GTI were similar to those of AFI and ATI respectively, and were significantly affected by latitude (p<0.01, see Supplementary File A, Figure A4). The maximum GFI was 1663.4 ℃ d in the north, and the maximum GTI was 4517.9 ℃ d in the south. In addition to latitude, altitude and soil moisture (SM) also affected both GFI and GTI (p<0.01, see Supplementary File A, Figure A4). GFI was higher at local high altitudes than in surrounding lower altitude areas (i.e. in the southeast of FGRN China), whereas GTI was significantly lower than in surrounding areas. GFI is proportional to altitude and increases with the altitude, whereas GTI shows the opposite trend. As with altitude, soil moisture is proportional to GFI and inversely proportional to GTI (see Supplementary File A, Figure A4).
Figure 8 The average (a) ground surface freezing index (GFI) and (b) ground surface thawing index (GTI) (℃ d) over the period from 1900 to 2017 in the frozen ground region of northeast China
The spatial distribution of the rate of change in GFI and GTI was similar to that in AFI and ATI, although there were differences in numerical values (Figure 9). The rate of change in GFI was lower than that in AFI, with the highest values in the north and lower values in the south. The high values were mainly found in the Xiao Hinggan Mountains. Large rates of GFI decline often coexisted with large rates of GTI increase. For example, both GFI and GTI had relatively high rates of change in the area of Heihe city in Heilongjiang Province. Although the spatial pattern of the rate of change in GTI was similar to that in ATI, the rate of change in GTI was higher. The difference in the absolute value of the change rate between GFI and GTI was greater than that between AFI and ATI. This phenomenon indicates that the ground surface temperature experienced a stronger warming process than the near-surface air temperature from 1900 to 2017 (Liu et al., 2021b).
Figure 9 Spatial distribution of the rate of change in (a) ground surface freezing index (GFI) and (b) ground surface thawing index (GTI) over the period from 1900 to 2017 in the frozen ground region of northeast China (the plus sign indicates p<0.01 and the asterisk indicates p<0.05)
The years when trends in GFI and GTI abruptly changed identified by the M-K test were 1977 and 1996 respectively (Figure 10). The annual change rates of GFI and GTI were -0.4 ℃ d per year and 0.5 ℃ d per year before the turning point years. GFI showed an accelerating downward trend after 1977, and the annual rate of change from -0.4 ℃ d per year to -0.7 ℃ d per year. Although the annual rate of change in GTI decreased from 0.5 ℃ d per year to -2.1 ℃ d per year, the overall value was still higher than that before 1996. The decreasing trend in GTI after 1996 may be related to a global warming hiatus (Xu et al., 2019).
Figure 10 Time series of (a) ground surface freezing index (GFI) and (b) ground surface thawing index (GTI) during the period from 1900 to 2017 in the frozen ground region of northeast China (marginally significant at the p<0.1 level, with a 90% confidence level)

3.5 Spatial and temporal changes in frozen ground

3.5.1 E value and accuracy evaluation

The frozen ground distributions in the 1980s and 2000s were simulated to determine a suitable E value for the surface frost number model of FGRN China. The simulation results with E=0.57 are shown in Figure 11, and the simulation accuracy was high with this E value. The OA values of the 1980s and 2000s were 0.95 and 0.93, and the Ka values were 0.89 and 0.81. Differences between the existing frozen ground map and the simulation results appeared mainly near the boundary of permafrost and seasonal frozen ground. Therefore, we used 0.57 as the empirical factor for the surface frost number model, and meteorological data from each decade were used to simulate the distributional range of permafrost in FGRN China from 1900 to 2017 (Figures 12 and 13).
Figure 11 Spatial differences in permafrost distribution between the frozen ground map and simulation result for the 1980s (a) and the frozen ground map and simulation result for the 2000s (b) in the frozen ground region of northeast China
Figure 12 Changes in permafrost and seasonal frozen ground area in the frozen ground region of northeast China from 1900 to 2017
Figure 13 Decadal changes in permafrost in the frozen ground region of northeast China from 1900 to 2017

3.5.2 The distribution of frozen ground

Permafrost in FGRN China has been continuously degraded from 1900 to 2017 (Figure 12). The permafrost area was 52.97×104 km2 from 1900 to 1909 but decreased to 30.31×104 km2 from 2010 to 2017. Changes in permafrost in FGRN China can be divided into two stages. The first stage was from 1900 to 1969. In this stage, the permafrost area decreased slowly, and it recovered slightly from 1940 to 1969. The permafrost area changed mainly in the central and southern regions, accounting for 32% of the total decrease in area. The second stage was from 1970 to 2017. In this stage, the permafrost area decreased rapidly, accounting for 68% of the total decrease in area. The permafrost area decreased particularly significantly between 1980-1989 and 1990-1999, consistent with the AMAT turning point during 1980-1989.
The simulation results show that permafrost in FGRN China is mainly distributed in the high latitude regions, with a transition from permafrost to seasonal frozen ground from north to south (Figure 13). With climate warming, the permafrost boundary has moved north. The simulated spatial distributions of both kinds of frozen ground are similar to those of AMAT, AFI and GFI, with strong latitudinal zonality. However, some isolated permafrost points are also present within the regions of seasonal frozen ground. These isolated permafrost points occur at high altitudes in the eastern part of the study area. This is similar to the distribution of permafrost on the Tibetan Plateau, which is affected by altitude (Nan et al., 2013). As the climate warms, these isolated permafrost points are disappearing. The AFI and GFI spatial distributions are more consistent with the spatial distribution of frozen ground than is the AMAT distribution, more accurately reflecting the change in permafrost, but there are still some differences in small area.

4 Discussion

4.1 Change in AMAT, freezing and thawing indices

The turning point of AMAT in FGRN China occurred in 1985, whereas the turning point of AMAT in the Qinghai-Tibet Plateau occurred in the mid-1990s (Ding and Zhang, 2008), indicating that temperatures in the high latitude region are more prone to change than those in the low latitude region (Lu et al., 2005). A physical explanation may be as follows. As temperatures rise in FGRN China, the seasonal snow on the surface thaws earlier, which leads to a decrease in ground surface reflectance, large amounts of solar radiation absorption by the ground surface, and enhancement of ground surface radiation, causing the AMAT turning point to occur earlier. Influenced by the change in AMAT, the freezing and thawing indices also changed significantly in FGRN China (Ding and Zhang, 2008). The spatial distributions of average GFI and GTI in FGRN China from 1900 to 2017 were similar to those of AFI and ATI, but there were numerical differences (Figures 6 and 8). The AFI of FGRN China averaged over 1900-2017 was 2462.4 ℃ d, higher than the average value of the upper Brahmaputra River Basin in the Tibetan Plateau (937.4 ℃ d) (Liu et al., 2021b) and of the upper reaches of the Yellow River Basin (1153.9 ℃ d) (Wang et al., 2019). The average GFI of FGRN China is 1028.7 ℃ d, which is also higher than that of the upper Brahmaputra River Basin (627.6 ℃ d) (Liu et al., 2021b) and the upper reaches of the Yellow River Basin (850.6 ℃ d) (Wang et al., 2019). Moreover, the average ATI is 2659.5 ℃ d, and the GTI is 3193.6 ℃ d; both are higher than their corresponding values in the Qinghai-Tibet Plateau (1396.2 ℃ d and 2389.7 ℃ d) (Wu et al., 2018). Therefore, the temperature of frozen ground in FGRN China may be higher than that in the Qinghai-Tibet Plateau. In this study, we only considered the influence of land cover types on ground surface freezing/thawing. Previous studies have shown that the GFI and GTI are also influenced by other local natural conditions (topography, soil texture, etc.), and the true distribution of GFI and GTI may therefore be more complex (Luo et al., 2018).

4.2 The surface frost number model and permafrost

In the absence of long-term field monitoring, the surface frost number model is an effective way to estimate the distribution of frozen ground in FGRN China. The accuracy of frozen ground distribution simulation can be improved by adjusting the E value during the process of applying the surface frost number model. In this paper, when E=0.57, the simulation results showed good agreement with existing frozen ground maps from 1998 and 2000. Nan et al. (2013) used E values of 0.94 and 0.99 to simulate frozen ground distribution in the western Tibetan Plateau, and Liu et al. (2021b) used an E value of 1.2 to simulate frozen ground distribution in the upper Brahmaputra River Basin; all were higher than the E value used in this paper. This may be related to differences in soil physical properties and temperature datasets. When the simulated results were compared with the two existing frozen ground maps (Table 3), the simulated results were overestimated in both cases. Overestimation of permafrost distribution occurred mainly in the Da Hinggan Mountains and at some higher altitudes in the southeastern region (Figure 11). This overestimation may reflect insufficient consideration of local soil types, snow cover, solar radiation and altitude (Nan et al., 2012). We simulated the distribution of frozen ground in FGRN China from 1900 to 2017 using the surface frost number model. The simulation results showed that the permafrost boundary in FGRN China has moved northward and has degraded significantly from 1900 to 2017. Overall, with the increase in AMAT, permafrost experienced a significant warming process in FGRN China. In this study, ArcGIS was used for interpolation, and the effect of altitude was ignored in the interpolation process; therefore, the F value may provide only a rough estimate of the permafrost boundary.
Table 3 Existing frozen ground map and simulated permafrost areas in the frozen ground region of northeast China
Year Permafrost zone in existing frozen
ground map (104 km2)		 Simulated permafrost
zone (104 km2)
1980-1989 38.54 40.82
2000-2009 24.75 30.31

4.3 Limitations and future prospects

Although the surface frost number model used in this study performed well, there are many uncertainties in the simulated results. This model considers only the influence of temperature when simulating the distribution of frozen ground. Although the empirical factor E is added, there are some errors in simulating the distribution of frozen ground for complex surface conditions. In addition, the F value is the key to determining the boundary between permafrost and seasonal frozen ground. However, the F value is only theoretical, and may therefore differ from the actual value. Further investigation of the F value is required. A reasonable F value is helpful for improving the accuracy of the model. Finally, the resolution of the temperature reanalysis data used in this paper was 0.5°×0.5°; this low spatial resolution may produce large errors in local regions. In the future, higher resolution temperature data should be used to construct more accurate frozen ground distribution maps that incorporate soil properties, solar radiation, precipitation and other factors.

5 Conclusion

We analyzed the characteristics of ground surface freezing and thawing indices in FGRN China from 1900 to 2017 and simulated the distribution of frozen ground in FGRN China using a surface frost number model. The GFI and GTI in FGRN China varied significantly with latitude. The GFI decreased gradually from north to south, whereas the GTI increased gradually from north to south. The simulation results of the surface frost number model were compared with existing frozen ground maps. The OA values were 0.95 and 0.93 for maps from the 1980s and 2000s, and Ka values were 0.89 and 0.81. These results show that the surface frost number model can accurately simulate the distribution of frozen ground in FGRN China. According to the simulation results from 1900 to 2017, the total area of permafrost in FGRN China decreased from 52.97×104 km2 to 30.31×104 km2, with a large change in area. In order to fully represent the permafrost degradation in FGRN China, a new map of permafrost distribution is necessary.

Supplementary File A

Figure A1 The spatial distribution of annual mean bias errors between the monthly air temperature reanalysis data and the meteorological station data in the frozen ground region of northeast China
Figure A2 Changes in annual mean air temperature (AMAT) in the frozen ground region of northeast China from 1977 to 2017
Figure A3 Time series of regional anomalies in annual mean air temperature (1900-2017) in the frozen ground region of northeast China
Figure A4 Correlation of GFI with latitude (a); correlation of GTI with latitude (b); correlation of GFI with altitude (c); correlation of GTI with altitude (d); correlation of GFI with SM (e); and correlation of GTI with SM (f)

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