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Article

Permafrost Probability Mapping at a 30 m Resolution in Arxan Based on Multiple Characteristic Variables and Maximum Entropy Classifier

by
Ying Guo
1,2,3,
Shuai Liu
1,2,3,
Lisha Qiu
1,2,3,
Yan Wang
1,2,3,
Chengcheng Zhang
1,2,3 and
Wei Shan
1,2,3,*
1
Institute of Cold Regions Science and Engineering, Northeast Forestry University, Harbin 150040, China
2
Ministry of Education Observation and Research Station of Permafrost Geo-Environment System in Northeast China (MEORS-PGSNEC), Harbin 150040, China
3
Collaborative Innovation Centre for Permafrost Environment and Road Construction and Maintenance in Northeast China (CIC-PERCM), Harbin 150040, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(19), 10692; https://doi.org/10.3390/app131910692
Submission received: 31 August 2023 / Revised: 20 September 2023 / Accepted: 25 September 2023 / Published: 26 September 2023
(This article belongs to the Special Issue Applications of Machine Learning in Earth Sciences—2nd Edition)
Browse Figures
Versions Notes

Abstract

:
High-resolution permafrost mapping is an important direction in permafrost research. Arxan is a typical area with permafrost degradation and is situated on the southern boundary of the permafrost region in Northeast China. With the help of Google Earth Engine (GEE), the maximum entropy classifier (MaxEnt) is used for permafrost mapping using the land surface temperature (LST) of different seasons, deviation from mean elevation (DEV), solar radiation (SR), normalized difference vegetation index (NDVI), and normalized difference water index (NDWI) as the characteristic variables. The prior data of permafrost distribution were primarily based on 201 borehole data and field investigation data. A permafrost probability (PP) distribution map with a resolution of 30 m was obtained. The receiver operating characteristic (ROC) curve was used to test the distribution results, with an area under the curve (AUC) value of 0.986. The results characterize the distribution of permafrost at a high resolution. Permafrost is mainly distributed in the Greater Khingan Mountains (GKM) in the research area, which run from the northeast to the southwest, followed by low-altitude area in the northwest. According to topographic distribution, permafrost is primarily found on slope surfaces, with minor amounts present in peaks, ridges, and valleys. The employed PP distribution mapping method offers a suggestion for high-resolution permafrost mapping in permafrost degradation areas.

1. Introduction

As an important part of the cryosphere, permafrost is mainly distributed in the high-latitude and high-altitude area of the northern hemisphere, and the areal extent of permafrost regions (permafrost probability > 0) is approximately 19.82 × 106 km2 [1]. Permafrost research is the basis for studying the surface hydrological process, climate change, and ecological environment change. It is of great significance for understanding the soil water/ice condition, geomorphic process, and geomorphic and landscape development, as well as the stability of engineering construction and disaster reduction. In the 21st century, the warming rate of the pan-Arctic permafrost region is expected to be twice the global average warming rate [2]. Accelerated warming leads to the degradation of permafrost, including the increase in the permafrost temperature, the deepening of active layer thickness (ALT), and the reduction in the permafrost area [3,4]. Permafrost degradation not only aggravates climate and ecological changes but also affects biochemical processes and human infrastructure [5]. Therefore, under the background of climate warming, high-precision permafrost mapping is of great significance for assessing regional ecology, hydrology, and especially engineering impact [6,7].
The response of the permafrost region to climate change has obvious spatial heterogeneity. At the local scale, there are many factors affecting the distribution of permafrost, including geographical location, terrain, climate, vegetation, snow cover, water body, and soil type. These factors regulate the regional energy exchange process, and therefore also regulate the temperature of the ground and soil [8]. The distribution of permafrost blocks, vegetation, and carbon sequestration in forests and wetlands are all significantly influenced by topography, which also regulates the redistribution of soil water in both horizontal and vertical directions [9,10]. The annual and seasonal changes in air temperature directly affect the thawing rate and maximum thawing depth of the active layer (AL). The physical and mechanical properties of permafrost have obvious temperature dependence [11]; precipitation directly affects ALT by changing the hydrothermal properties of the AL [12]; snow affects the distribution of permafrost and its response to climate change through its albedo, emissivity, absorptivity, and latent heat and low thermal conductivity [13]; vegetation affects the distribution of permafrost by intercepting snow, reducing solar radiation and changing the water and thermal conditions of the AL [14]; soil type also has an important impact on the degradation of permafrost [3]. The current monitoring methods of permafrost use surface indicators, such as surface temperature, vegetation cover, topography, and geomorphology, or the combination of different surface characteristics [15] to qualitatively infer the occurrence conditions of permafrost.
Permafrost exists below the surface with uneven properties, and most of them are located in remote areas. Therefore, it is difficult to obtain field measurements of permafrost conditions. With the development of permafrost-monitoring tools and remote sensing technology, the availability of high-resolution remote sensing data provides strong data support for the study of permafrost at the micro-scale; statistical and machine learning classification algorithms have also been successfully applied to the inversion of permafrost spatial distribution [16]. Texture classification is a computer vision task aimed at categorizing images or image regions based on their texture features. This task relies on extracting texture features, such as gray-level co-occurrence matrix (GLCM) [17] and local binary patterns (LBP) [18], to describe the statistical and local texture structures within the image regions. These features are subsequently used to train classifiers, such as support vector machines (SVMs), or neural networks to differentiate between different texture categories, and it finds wide applications including in medicine (e.g., identifying tumors in MRI images) and remote sensing (e.g., land cover classification). In permafrost research, these technologies have been used in geomorphic mapping, geomorphic characterization, and permafrost mapping. Based on borehole data, Li et al. [19] analyzed the influence of topographic and climatic factors on the distribution of permafrost by using 90 m digital elevation model (DEM) data and developed a binary logistic regression model and a multi-standard analysis model. The prediction probability of permafrost is in good agreement with the field investigation results. To map the permafrost spatial distribution in depth at the micro-scale, Deluigi et al. [16] investigated another modeling approach and employed three classification methods of statistics and machine learning (logistic regression, SVM, and random forest (RF)). Wang et al. [7] applied a logistic regression model and six multi-criteria analysis methods to assess the distribution and dynamic changes in permafrost on the Qinghai–Tibet Plateau from 1980 to 2010. Haq and Baral [20] calculated the probability of permafrost distribution in the Himalayan observation sample belt by using Sentinel-2A data and a logistic regression model. With the development of remote sensing cloud-computing technology, data production methods are becoming more diversified [21], and it is more convenient to comprehensively apply massive-source remote sensing data to data production [22]. Such conditions provide more ideas for permafrost mapping.
The permafrost in Northeast China is mainly distributed in Greater Khingan Mountains (GKM), Lesser Khingan mountains (LKM), and Changbai Mountains, which are sensitive to climate change. Due to the influence of climate warming, the discontinuous permafrost in this region has degraded by 38% in recent decades, and the south boundary of the permafrost range has an obvious tendency to move northward [23]. The degradation of permafrost shows zonality in altitude and latitude, and the degradation order is from hillside to valley and from sunny slope to shady slope; environmental effect has an obvious influence on permafrost [24]. The degradation of permafrost increases carbon emissions [25], freezing and thawing disasters, and the risk of safe operation of infrastructure [26]. Arxan is located in the south boundary of the permafrost in Northeast China. Affected by climate change, the permafrost in this location has significantly degraded in recent years. Our observation results show that the permafrost in Arxan results from latitude and altitude zonality, but there is a lack of detailed research. The high-resolution permafrost data have stronger data availability, higher visualization, and wider application range. The refined permafrost mapping at the regional scale has practical significance for comprehensively understanding the distribution of permafrost and its response to climate warming.
Among the existing permafrost distribution data in Northeast China, the highest resolution is 1 km. Higher resolution mapping of permafrost in Northeast China has not been conducted. However, in engineering construction, especially in road construction, the 1 km resolution permafrost distribution data cannot meet the requirements. Therefore, in order to serve the regional development, it is urgent to obtain a high-resolution permafrost data or mapping method. In the process of road construction, a large number of survey data along the road can be obtained. These data have strong spatial continuity. Due to cost reasons, continuous monitoring cannot be conducted on the time scale. However, these data can reflect the spatial difference of permafrost well. The combination of these survey data and statistical models may be an effective method to study the distribution of the permafrost in Northeast China. It should be noted that there is a significant amount of fossil permafrost in Northeast China [27]. However, this study is mainly aimed at shallow and modern permafrost.
The main aim of this study is to conduct a high-resolution (30 m) mapping of permafrost probability (PP) in Arxan by applying maximum entropy classifier (MaxEnt). In addition, this study analyzes and discusses the distribution pattern of the permafrost and its relationship with environmental variables in Arxan, as well as the applicability of the mapping method. It is expected to provide information and a reference to guide high-resolution permafrost mapping in permafrost degradation areas.

2. Materials and Methods

2.1. Overview of the Study Area

Arxan is located in the northeast of Inner Mongolia Autonomous Region of China, in the southwestern foothills of GKM [28] (119°30′–121°15′ N, 46°30′–47°45′ E; Figure 1a). With an altitude of 490–1750 m, the topography is high in the northeast and low in the southwest. The warm, humid airflow from the southeast ocean and the cold, dry wind from the northwest both have a significant impact on Arxan’s climate. It has a cold temperate, continental monsoon climate. The characteristics of the local microclimate are clear [29]. Long and chilly winters alternate with wet summers. Arxan has a short frost-free period and a large daily temperature difference. The annual average air temperature is −2 to 0 °C, and the extreme minimum temperature can reach −45 °C [30]. The annual average precipitation is about 450 mm, concentrated from June to August. The snow cover season lasts from October to April of the following year, with the period from January to March seeing the majority of the maximum snow depth [31]. The vegetation coverage rate in Arxan is 81.20%. The vegetation is mainly Eurasian coniferous forest, and there are a few Eurasian grasslands and East Asian summer green broad-leaved forests. There are large areas of Carex and meadows in valleys and depressions, and the thickness of the peat layer in some areas reaches more than 66 cm [32].
The study area is located in the south boundary of the permafrost region in Northeast China, most of which belong to the zone of seasonally frozen ground and some are permafrost regions. The strong seasonal freezing and thawing effect results in a deep seasonal freezing depth, and the maximum can reach more than 2.5 m [33]. The main ridge of the GKM forms a potent low-temperature arc in the south due to the temperature differential effect brought on by elevation. Peat moss blueberry swamp extends from Arxan to the vast GKM permafrost area in the north. Previously, there was sheet-like permafrost around the Taiping mountains in Arxan. Therefore, the permafrost near Arxan is considered to be the result of the southward extension of the island-like permafrost-thawing area outside the continuous permafrost sub-region at the northern end of the GKM [34]. Under the background of global climate warming and global permafrost degradation, the south boundary of the permafrost in Northeast China is moving northward [35]. These have led to the gradual change in the climate and permafrost in Arxan in recent years. During the period of 2001–2020, the climate in Arxan continued to warm, and the mean annual ground surface temperature (MAGST) and mean annual land surface temperature (MALST) of the study area increased by 0.047 °C and 0.265 °C, respectively, per year (Figure 1b). MAGST is calculated based on the monitoring data of the National Meteorological Station (NMS) in Arxan, and MALST is calculated based on the MODIS MOD11A2 V6 (https://ladsweb.modaps.eosdis.nasa.gov/, (accessed on 1 October 2022)) [36] remote sensing data. The permafrost temperature (PT) in the study area increased from −2.46 °C in 2003–2013 to −2.78 °C in 2014–2019. More information about PT is provided in Section 2.2.3.

2.2. Research Data

2.2.1. Permafrost Prior Data

Permafrost has special subgrade conditions that need to be considered in road engineering. In the route selection and design stage of the road project, it is necessary to determine the geological conditions of the road route through drilling, geophysical prospecting, and geological exploration in combination with prior data.
In this study, the permafrost prior data consists of borehole data from road surveys, field investigation data, and special ground features, in which the borehole data from the road survey are the main data (Figure 2a). Although most data are located on the road line and the spatial position is not random enough, the survey data cover a variety of terrain, and the altitude is widely distributed. It is scattered on the line with a total length of 80 km and is representative.
The provincial highway 308 (S308) of the Inner Mongolia Autonomous Region is located in the study area. The geological investigation report of S308 includes 431 boreholes altogether, from which 201 borehole data with permafrost information were selected (92 non-permafrost boreholes and 109 permafrost boreholes; the report was obtained in July 2017). Because of costs, temperature measurements were not conducted in the boreholes. These boreholes are mainly distributed along the design line of the road, with an interval ranging from 500 m to 1 km between each other. In special sections, the interval is shortened to 40 m. A few boreholes are located on both sides of the line. The depth of boreholes mainly ranges from 15 m to 35 m, and some special positions, such as where the permafrost layer is thick, increase to 40 m. Because the boreholes serve the road survey, most of the boreholes are located at the flat position or at the foot of the slope, some of the boreholes are located on the gentle slope, and a few of the boreholes are located on the steep slope.
Borehole data were mainly used to construct the permafrost prior data. The principle of construction is to take each permafrost borehole and non-permafrost borehole as the center of the circle and build the buffer zone with a certain radius (Figure 2d–f). It is believed that the presence of permafrost at the center of the circle can represent the presence of permafrost in the buffer zone. Based on the observation and experience of the geological investigation of S308, this radius was taken as 50 m in the study area.
The main rock of Arxan is basalt. Some towns have existed for decades and the buildings in the towns have not subsided. Therefore, these towns are generally considered to be free of permafrost. In addition, the mountain lakes in Arxan are mainly evolved from former volcanoes [32]. It is believed that no permafrost exists below. These towns and lakes were also added to the permafrost prior data as non-permafrost areas (Figure 2b,c). In order to avoid affecting the boundaries of towns and lakes, the selected samples were located inside the towns and lakes and kept at a distance from their boundaries. In addition, during the field investigation, some locations with permafrost were found by the high-density resistivity method (Figure 2g).
Based on the above principles, a total of 2.292 km2 of permafrost samples (1.225 km2 based on boreholes and 1.067 km2 based on field investigations) and 1.9706 km2 of non-permafrost samples (0.9257 km2 based on boreholes and 1.0449 km2 from towns and lakes) were obtained in the total area of 7420.02 km2 in Arxan.

2.2.2. Characteristic Variables for Permafrost Mapping

As remote sensing technology has advanced and a growing number of remote sensing products have been produced, the characteristics variables employed in permafrost mapping methods have seen significant growth in recent years [37]. The practice of permafrost mapping currently fully utilizes the permafrost environmental elements gathered by remote sensing observation, such as surface temperature, vegetation indices, snow cover indices, and soil characteristics [37]. Permafrost distribution mapping can be considered from the perspective of the formation mechanism of permafrost and the performance characteristics of permafrost [6]. In addition, the resolution of the available characteristic variable data is also a key consideration. Especially in high-resolution permafrost mapping research, the resolution of the characteristic variable should be close to the result resolution. In this study, the environmental variables used and their relationship with the characteristics of permafrost were as follows:
  • Land surface temperature (LST). For permafrost connected with contemporary climate, i.e., in contact with AL, the difference in the temperature field between permafrost areas and non-permafrost areas is reflected in the difference in the surface thermal state. Limited by the observation technology and the observation cost, the resolution of existing ground (land) temperature data is always 1 km or lower. In this study, we hoped to obtain the observed temperature data at a resolution of 30 m. Based on Landsat data, LST with 30 m resolution can be obtained. The satellite image data used to retrieve the surface temperature should be cloud-free or possess only a small amount of clouds. ALT in the study area reaches the minimum in spring and the maximum in autumn. The satellite image data of these two seasons can better distinguish the permafrost area from the non-permafrost area [38]. At the same time, the interference of deciduous plants on the surface heat radiation is weakened in spring and autumn. Referring to the period of data selected by a commonly used method, the surface frost number model, in permafrost mapping [39], is suitable to add winter surface temperature data. Based on the above principles, in this study, three Landsat-8 OLI image data covering the study area were selected to retrieve the surface temperature (PATH: 122; ROW: 027), and the acquisition times were 25 April 2021, 16 September 2021, and 23 February 2022. The method used for the inversion of the surface temperature was the radiative transfer equation (RTE) algorithm, which is a commonly used algorithm for the inversion of the surface temperature [40]. The research of Liang and Liu. [41,42] indicated that the results of the inversion of the surface temperature by the RTE algorithm have good reliability in Northeast China. Therefore, three surface temperature data, LST1 (25 April 2021), LST2 (16 September 2021), and LST3 (23 February 2022), in the study area were calculated using the RTE algorithm. The spatial resolution of LST1, LST2, and LST3 was 30 m.
  • Deviation from mean elevation (DEV). In Arxan, extensive vegetation coverage and abundant groundwater resources make the occurrence of permafrost be closely related to the spatial distribution of soil moisture [43]. At present, the remote sensing monitoring of soil moisture is not comparable to LST in terms of spatial and temporal resolution. Some scholars use high-resolution DEM to calculate topographic indexes, such as TPI [44], TWI [45], and DEV [46], to study the relative distribution of water in a certain area. According to the pretest of selecting characteristic variables, in the study area, DEV has a good correlation with the borehole data of permafrost. DEV calculates the elevation standard deviation and the central point’s topographic position [47]. The topographic position is measured by DEV as a percentage of the local relief normalized to the local surface roughness. The DEV was determined using the NASA Land Processes Distributed Active Archive Center’s free 30 m Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) (SRTMGL1_003 https://lpdaac.usgs.gov/, (accessed on 1 October 2022)) [48]. In this study, the radius used to calculate DEV was taken as 1 km.
  • Solar radiation (SR). Solar radiation can reflect the amount of solar radiation energy that can be absorbed by the Earth’s surface. For a long time, the permafrost in Northeast China has been in a degraded state, and its degradation trend has a certain degree of correlation with the solar radiation absorbed [24]. The method in the hemispheric horizon algorithm created by Rich et al. [49] and further developed by Fu [50] was adopted to calculate the solar radiation received by the research area in the non-snow period (from 15 April to 15 October). The solar radiation results are considered as one of the characteristic variables in the mapping of permafrost distribution. The DEM data used to calculate solar radiation were also SRTMGL1_ 003.
  • NDVI and NDWI. There are a large number of virgin forests in the permafrost region of Northeast China. The growth pattern of plants on the ground alters during the permafrost degradation process due to changes in soil moisture and heat, and even tree species succession [51]. Such vegetation changes lead to corresponding changes in NDVI values. Therefore, NDVI was applied as one of the characteristic variables of permafrost mapping. On the other hand, to eliminate the interference of surface water in mapping, NDWI was also applied as a characteristic variable. To reduce the uncertainty caused by seasonal changes in vegetation and water, we used Landsat-8 OLI image data and adopt the simple cloud-mask algorithm [52] to synthesize the annual minimum cloud amount image of the study area in 2021. NDVI and NDWI data are obtained by band operation with this image.
The spatial resolutions of LST1, LST2, LST3, DEV, SR, NDVI, and NDWI mentioned above are all 30 m. The relationship between these characteristic variables and permafrost prior data is further discussed in Section 4.1.

2.2.3. Supplementary Data

To further explore the spatial distribution characteristics of permafrost in the study area, in the Results Section of the article, slope, aspect, and Landform datasets were used, which are all based on SRTMGL1_003 data. The Landform dataset provides landform classes created by combining the continuous heat-insolation load index and the multi-scale topographic position index (SRTM mTPI) datasets [53].
In addition, we compared the research results with the permafrost temperature (PT) dataset [54] and the permafrost continuity (PC) dataset [55]. PT is simulated by establishing the numerical relationship between the surface frost number (SFN) and temperature obtained from monitoring sites at the depth of zero annual amplitude (ZAA). PC data were obtained based on the temperature at the top of permafrost (TTOP) algorithm, and permafrost type was divided into continuous, discontinuous, sporadic, and isolated patches.

2.3. Methods

2.3.1. Maximum Entropy Classifier (MaxEnt)

In the permafrost degradation area, the traditional permafrost mapping methods, such as frost number model [56], Stefan formula [57], and GIPL model [58], are not suitable for the high resolution of 30m. With the continuous development of image-processing technology, there are more and more research on the mapping of permafrost using machine learning methods [1].
In this study, the sample had two aspects of particularity. First, the observation data of permafrost were limited in spatial distribution. The distribution was relatively concentrated, and it was mainly located in accessible places. Secondly, there were only two types of samples observed, i.e., samples with permafrost and samples without permafrost. For the above two reasons, common classification algorithms, such as RF and SVM, are prone to under-fitting or over-fitting in the pre-experiment. MaxEnt is a one-class classification specialized in studying species distribution. The principle of maximum entropy requires that the selected probability model must meet the existing fact, i.e., the constraint conditions. The uncertain part is equal possibility, and the equal possibility is represented by the maximization of entropy [59]. This is a good fit for the above two particularities of the sample.
MaxEnt is frequently used to simulate species distribution probability utilizing environmental data from several “background” information in addition to confirmed presence locations [60,61]. In addition to species distribution prediction, some scholars have applied it to one-class classification [62], such as the simulation of tree species distribution [63], tree species classification [64], and extraction of fire-burned land [65]. Permafrost has special environmental attributes, and it proliferates or degenerates with changes in climate and environment [66]. In this study, MaxEnt was applied to map the distribution of permafrost in the study area.
The receiver operating characteristic (ROC) curve is used for analysis during the creation of the classification model, and the area under the curve (AUC) is used to assess the model’s accuracy [60,67]. The true positive rate, which is the ratio that both exists and is expected to exist, serves as the ordinate on the ROC curve, while the false positive rate, which is the ratio that neither exists nor is expected to exist, serves as the abscissa. AUC has a range of 0 to 1. The more closely the AUC value approaches 1, the more accurate the model is. The distance from the random distribution increases as the AUC value grows. The association between environmental factors and the expected geographic distribution of species increases with the increase in the AUC value. The better ability of the model to predict outcomes is shown by a higher AUC value [68]. Failure (0.5–0.6), poor (0.6–0.7), fair (0.7–0.8), good (0.8–0.9), or excellent (0.9–1.0) are the four performance categories for the model [21].
In this study, the permafrost prior data were divided into “samples with permafrost” and “samples without permafrost”, and they were taken as input samples to train the classification. A total of 75% of the samples were randomly selected as the training data, and the remaining 25% of the samples were used as the test data. The environmental characteristic variables considered in the classification included LST1, LST2, LST3, DEV, SR, NDVI, and NDWI. After the model was classified, the continuous data covering the study area was output, and an estimated probability value was ascribed to each pixel in the study area to evaluate the PP existence on that point [62]. This probability can range from 0 to 1. Figure 3 shows the technical flowchart of this study.

2.3.2. Data Use and Processing

Google Earth Engine (GEE) is a cloud-based platform with vast databases for geospatial analysis on a global scale [69]. GEE has incomparable advantages in the processing of large-scale remote sensing data over a large period. The RTE algorithm, the simple cloud-mask algorithm, the MaxEnt classification, and the ROC test used in this paper are all programmed by the GEE platform. All datasets used can be obtained from GEE for free or processed based on free open datasets.

3. Results

The final classification model’s ROC curve is displayed in Figure 4. The AUC values of the training and test sets in this study are 0.986 and 0.975, respectively, and much higher than the AUC value of a random prediction (0.5). This demonstrates how accurate the MaxEnt model was at forecasting the PP distribution in the study area.
The PP distribution of Arxan is shown in Figure 5a. The PP values of 92 boreholes and 16 investigation points with permafrost were mainly distributed in the high-value domain, while the PP values of 109 boreholes without permafrost were mainly distributed in the low-value domain (Figure 5b,c). Among the 109 boreholes without permafrost, only one borehole has a PP value higher than 0.5, accounting for 0.9% of boreholes without permafrost. We took 1% as the tolerable error limit; so, we chose 0.5 as a cut-off point for the PP value. The area with a PP value lower than 0.5 was considered as a low probability of permafrost. Additionally, PP values between 0.5 and 1.0 were separated into five parts at 0.1 intervals to evaluate the PP distribution in the study area.
The distribution of permafrost in Arxan is greatly affected by geographical factors (Figure 5a). The terrain of the study area is high in the middle and low in the west and southeast, and the permafrost is mainly distributed in the middle and west of the study area. It can be seen that the permafrost is mainly distributed in the GKM from the northeast to the southwest, followed by the low-altitude area in the northwest. It is only distributed in a small amount in the southeast of the GKM. PP gradually decreases from the middle to the west. The area with PP > 0.5 is 3079.6 km2, accounting for 41.9% of the total study area. Among them, the area with PP > 0.8 is mainly distributed in the high-altitude area in the middle and southwest of the study area, accounting for 13.1% of the total study area. The area with a PP value of 0.6–0.8 accounts for 18.9% of the total study area and is distributed around the area with PP > 0.8. The area with a PP value of 0.5–0.6 is widely distributed in the west and north of the study area.
Approximately 28% of the study area has a PP value distributed between 0 and 0.1 (Figure 6a). For areas with PP values higher than 0.5, the area with PP > 0.9 is the smallest, and the area of the remaining PP value intervals have a similar area proportion.
The distribution of permafrost in the study area follows a vertical zonation law and is affected by altitude (Figure 6d). On the whole, for the area with PP < 0.8, the higher the PP value, the higher the altitude. The area with PP ≤ 0.5 is widely distributed in the southeast part of the study area (Figure 5a), and the elevation in this part is mainly between 500 and 1600 m. The frequency increases with the elevation and reaches its peak at 1300 m. For the area with 0.5 < PP ≤ 0.7, the altitude is mainly between 1100 and 1400 m, and the frequency peak is about 1350 m. The area with 0.7 < PP ≤ 0.8 is mainly distributed between 1300 and 1500 m, and the frequency peak is about 1450 m. The area with PP > 0.8 is not distributed at higher altitudes, and the altitude distribution of the 0.8 < PP ≤ 0.9 area is closer to that of the 0.5 < PP ≤ 0.7 area. The area with 0.9 < PP ≤ 1 is not only distributed in high altitude levels, but also distributed in low altitude levels. These low altitude areas are mainly distributed in the northwest of the study area. The cold air in the Mongolian Plateau is blocked from moving eastward, and it accumulates in this area. At the same time, the grass and shrub plants in this area are dense and keep the ground at a low temperature. These conditions are conducive to the preservation of permafrost. In general, for the area with 0 < PP ≤ 0.8, the higher the PP value, the higher the altitude; the altitude distribution of the area with PP > 0.8 is wide.
Areas with different PP values have significant differences in aspect distribution (Figure 6b). The area with PP ≤ 0.5 has the largest distribution frequency in the southeast, followed by east and south, and the north is the least, which is very different from the overall aspect distribution in the study area. The area with 0.5 < PP ≤ 0.8 is mainly distributed in the west and north directions, which is similar to the overall aspect distribution in the study area. The area with 0.8 < PP ≤ 0.9 is mainly distributed in the north direction, while the area with PP > 0.9 is widely distributed in the north, west, northeast, and southwest aspects, and other aspects are rarely distributed. In terms of slope distribution (Figure 6c), areas do not show different distribution laws due to different PP values. In each PP value interval, the increase in the slope reduces the relative frequency.
To further explore the distribution law of permafrost on the terrain, we used the terrain classification data proposed by Theobald et al. [53]. In the dataset, the terrain is divided into four categories: upper slope, lower slope, valley, and peak/ridge, and more finely divided into 15 subcategories (Figure 6e). According to statistics, in all p-value intervals, the relative proportions of lower slope and upper slope are significantly higher than those of valley and peak/ridge. When PP ≤ 0.5, the terrain distribution is lower slope > upper slope > valley > peak/ridge; when PP > 0.5, the terrain distribution is upper slope> lower slope > valley > peak/ridge. With the increase in the probability value, the relative frequency of the upper slope is higher and higher, and the relative frequency of the lower slope is lower and lower. It means that the distribution law of permafrost in the study area is mainly distributed on the slope surface, while a small amount is distributed on the peak/ridge and valley. On the slope surface, there is more permafrost located on the upper slope than on the lower slope.
Pearson’s correlation values showed a strong correlation between PP and each characteristic variable (Table A1, Appendix A). The correlation values between PP and LST1, LST2, LST3, NDVI, and NDWI were significant at the 0.01 level (2-tailed), and correlation values between PP and SR were significant at the 0.05 level. PP was negatively correlated with LST1, LST2, LST3, SR, and NDVI and positively correlated with DEV. The correlation values between PP and LST1, LST2, and LST3 were approximate and significantly higher than those of the other characteristic variables.
In the permafrost areas and non-permafrost areas, the correlation between LST1, LST2, and LST3 was significant at the 0.01 level (Table A2 and Table A3). The association between NDVI and LST1 was only significant at the 0.05 level in non-permafrost areas, whereas it was significant at the 0.01 level in permafrost areas for LST1, LST3, and DEV.

4. Discussion

4.1. Relationship between Variables and Permafrost Prior Data

Both the training samples composed of permafrost prior data and the selected characteristic variables play an important role in the results of the model. The suitable training samples and characteristic variables can significantly improve the calculation efficiency and classification accuracy of the model. This section discusses the relationship between the characteristic variables used and the permafrost prior data, the correlation between each characteristic variable, and the correlation between characteristic variables and PP.
Permafrost prior data are very valuable measured data. The specific regularities between permafrost and characteristic variables are an important subject of permafrost research. They could be discovered by analyzing the differences between permafrost areas and non-permafrost areas (Figure 7). In the analysis of LST1, LST2, and LST3, the surface temperature distribution of the samples with permafrost are more concentrated, and the average level of the surface temperature is lower than that of samples without permafrost. This also proves that the surface temperature can reflect the occurrence state of permafrost. As for DEV, the DEV distribution of the samples without permafrost is more concentrated and lower than that of the samples with permafrost. It should be noted that the definition of permafrost has been supplemented with the concept of cryotic state, which also covers the part of it which, despite remaining at a temperature of ≤0 °C for a certain time, remains not frozen [70]. In the judgment of boreholes, the cryotic state may be mistaken for non-permafrost. So, the discussion of DEV needs further study [71]. Compared with the distribution of SR values of the two, the dispersion is similar, but it can be seen that the samples with permafrost are in the low-value range; on the contrary, the solar radiation values of the samples without permafrost are in the relatively high-value range. This is consistent with the trend of permafrost degradation in Northeast China [24]. In this study, the difference of SR between permafrost and non-permafrost samples is the largest, and the overlap part is the least. Therefore, in similar studies, SR may become a significant distinguishing variable of permafrost areas. As for NDVI and NDWI, it can be seen that, for samples without permafrost, there is a small range of concentration at the low-value range of NDVI and the high-value range of NDWI, which is due to the addition of some water bodies in the samples without permafrost [72]. To sum up, it can be considered that the selected seven characteristic variables are representative and offer a good distinction between permafrost areas and non-permafrost areas in the study area.
In addition, soil types are not considered as a characteristic variable. It is because the geological conditions are very complex in the study area [73], and the resolution of the available soil types is poor, which does not meet the needs of high-resolution mapping. If conditions permit, in a follow-up study or the study of other areas, soil type or other new characteristic variables should be added.
From Table A1, it can be seen that PP was negatively correlated with LST1, LST2, LST3, and SR and positively correlated with DEV. This means that, the lower the surface temperature in spring, autumn, and winter, the lower the solar radiation value, the higher the soil moisture, and the higher the PP. It should be noted that there is a negative correlation between PP and NDVI. In combination with the current environmental conditions in the study area, it is speculated that the process of permafrost degradation will be accompanied by changes in tree species from coniferous forest to broad-leaved forest, and the results of these changes will lead to an increase in NDVI [74]. As mentioned in the Results Section, the correlation values between PP and LST1, LST2, and LST3 are approximate and significantly higher than those of the other characteristic variables. This is because LST is the most direct and main characteristic that distinguishes permafrost from seasonal frozen soil, while other variables describe environmental characteristics to indirectly estimate the occurrence probability of permafrost. Since spring and autumn have similar ground features and there is no interference of snow cover, the correlation value between LST1 and LST2 is higher than that of LST3.
In the permafrost areas and non-permafrost areas, the correlation between LST1, LST2, and LST3 is significant at the 0.01 level. However, the absolute values of the correlation values of the three in the permafrost areas are higher than they are in the non-permafrost areas (Table A2 and Table A3). This suggests that LST in non-permafrost areas changes significantly with the change in seasons, while the surface temperature in permafrost areas is more stable. This is because permafrost water (ice) has the ability to regulate temperature. Additionally, the association between NDVI and LST1 is only significant at the 0.05 level in non-permafrost areas, whereas it is significant at the 0.01 level in permafrost areas for LST1, LST3, and DEV. This is connected to the previously discussed phenomena of vegetation evolution brought on by permafrost degradation. Due to the destruction of the water and heat conditions of the soil necessary for the establishment of native tree species as the permafrost area degraded into a non-permafrost environment, vegetation evolved [51,74]. The connection between NDVI and NDWI is much higher than that of other characteristic variables, whether in permafrost areas, non-permafrost areas, or the entire area. The correlation value is over 0.98 in absolute terms. This is connected to the variable band operation principle. The dimension reduction in characteristic variables can thus be further taken into account in future research.

4.2. Comparison of PP with Permafrost Temperature (PT) and Permafrost Continuity (PC)

Compared with the existing PT dataset [54,75] and PC dataset [55] in the study area, the greatest advantage and improvement of this study is that the spatial resolution is increased to 30 m. Due to the improvement in spatial resolution, the dataset is applicable to the engineering field and meets the requirements of engineering reference data. However, it is impractical to achieve the mapping goal of the presence or absence of permafrost in such a resolution [16]. In high-resolution permafrost mapping, it is more feasible to take the probability of permafrost occurrence as the result than to provide the location of permafrost.
Under the environmental background of permafrost degradation, a lower PT and higher PC should lead to a higher PP; from another perspective, a higher PT and lower PC should lead to a lower PP. Compared with the existing PT datasets and PC datasets, although the PP datasets provided in this study have different description angles and a higher resolution for permafrost, the spatial distribution law is consistent with the speculation (Figure 8).
The PP data, PT data, and PC data in the study area were compared (Figure 9). It can be seen that the three data have similar distribution patterns of permafrost in Arxan, that is, the permafrost is mainly distributed in the GKM from the northeast to the southwest, followed by the low-altitude area in the northwest. This is closely related to the geographical and climatic conditions of the region. The GKM generally runs from northeast to southwest, blocking the Mongolian High from entering the Northeast China Plain [76], making the northwest of the GKM colder than the southeast. The research area is located in a high-latitude area of the northern hemisphere, and the solar radiation received by the surface is higher in the south than in the north. All these are the reasons why there is more permafrost in the northwest of the study area than in the southeast.
The area with PP > 0.5 is similar in spatial distribution to the area with PT ≤ 0 °C and PC > 10% (Figure 9a–c). The coincidence rate between the area with PP > 0.5 and the latter two is 89.9% and 97.3% respectively. The above three ranges exclude the southeast and the small urban areas in the northwest of the study area. The spatial location of the area described as a high-level permafrost area by the three datasets is close. The area with PP > 0.8 has a coincidence rate of 73.3% with the area with PT ≤ −3 °C and a coincidence rate of 47.6% with the area with PC > 50%. This means that the spatial distribution of the three permafrost datasets has a high degree of coincidence in the whole study area. In the evaluation of the high-level permafrost area, the results of the three permafrost datasets are similar.
Due to the improvement in high resolution, the permafrost probability data at 30 m show its strengths in distinguishing lakes, and the description of the burned area is more detailed (Figure 9d). The lakes located in cold regions have a long ice cover period and less radiation energy, which leads to the error of the remote sensing method for permafrost mapping (Figure 9(d4)). This kind of error is reduced in MaxEnt. In some areas, different data results have similar boundaries (Figure 9e). On the one hand, it confirms the applicability of the data; on the other hand, it is also valuable for the study of regional permafrost boundaries.

4.3. Ecological and Environmental Significance of the Topographic Distribution of Permafrost in Arxan

In GKM and LKM, permafrost is known as the “Xing’an-Baikal” permafrost. This region exhibits distinct patterns of permafrost distribution, with permafrost being more extensively developed (colder and thicker) at lower elevations in intermontane basins and lowlands, as opposed to elevational permafrost [24,77]. However, as mentioned in the Results Section, the distribution law of the permafrost in Arxan is mainly distributed on the slope surface, while a small amount is distributed on the peak/ridge and valley. On the slope surface, there is more permafrost located on the upper slope than on the lower slope. It can also be considered that the degradation law of permafrost is that the peak/ridge and valley are degraded first, and then the lower slope degradation and the upper slope degradation. This is different from the distribution characteristics of “Khingan–Baikal” permafrost [78]. It may be related to the special geothermal environment of Arxan, that is, widely distributed hot springs continuously transport heat to lower areas [79], resulting in such distribution characteristics.
The lower parts of Arxan are warm and humid, while the higher parts are relatively dry and cold, which contributes to lush vegetation and ecosystem diversity. However, the climate differences formed by the high and low terrain make it easy for the region to form microclimates, and different regions may have their own unique climate and vegetation. In addition, this also makes the temperature reversal layer between high and low ground more common, causing the formation of an inversion layer in the low ground layer, which affects air quality and meteorological conditions, especially in spring and autumn. The low ground beneath the inversion layer may be affected by the accumulation of air pollution and uneven temperature, which has important implications for environmental, ecological, and meteorological predictions.
In Arxan, the thawing of permafrost in lower areas typically precedes that in higher areas, which can lead to geological hazards, such as landslides. This occurs because the thawing in lower area results in the soil becoming wetter and looser, while permafrost in higher areas remains stable, creating an imbalance in moisture and soil stability. In such a situation, rainfall or melting snow can infiltrate the lower areas, increasing soil moisture and potentially triggering soil instability, potentially causing landslides and other geological hazards. The uneven thawing sequence of permafrost can increase the risk of geological hazards, necessitating timely monitoring and management measures to mitigate potential dangers.

4.4. Potential Research Directions or Applications of High-Resolution Permafrost Mapping

The high-resolution mapping of permafrost can help to identify and define permafrost regions, providing the clear boundaries of permafrost. The potential applications of high-resolution permafrost mapping in the fields of ecological conservation, water resource utilization, and geological hazard prediction are significant. In terms of ecological conservation, it can be utilized for identifying and safeguarding ecologically sensitive areas, monitoring changes in species habitats, and preserving wetland ecosystems within permafrost regions. Moreover, it aids in optimizing water resource management by accurately predicting the extent and timing of permafrost thawing, which has a substantial impact on water availability. In the realm of geological hazard prediction, high-resolution permafrost mapping assists in identifying risk areas for landslides and soil erosion, enabling proactive measures to be taken, and offers considerable insights into the potential impacts of climate change on geological hazards, thereby enhancing our capacity to respond to environmental and climatic challenges. These applications collectively provide robust tools and information support for environmental conservation and natural disaster management.
By providing detailed underground permafrost information, high-resolution permafrost mapping helps planners to better understand the stability and sustainability of land in land use planning. This information can be used to determine appropriate locations for buildings, infrastructure, and agricultural activities to minimize interference with permafrost, thereby promoting sustainable land use and reducing environmental risks. For example, in highway engineering, understanding the clear distribution of permafrost can help to effectively avoid and handle permafrost sections, thus reducing the cost of highway geological surveys, construction processes, and maintenance after completion.

5. Conclusions

  • MaxEnt is capable of modeling the 30 m resolution permafrost probability of Arxan by using multi-source environmental variable data. The simulation results depict a detailed distribution pattern of permafrost and provide clear boundaries of permafrost areas. The results can provide a reference for research in the fields of ecology, environment, and engineering.
  • The permafrost in Arxan is mainly located in the GKM from the northeast to the southwest, followed by a low-altitude area in the northwest. The area with PP > 0.5 is 3079.6 km2, accounting for 41.9% of the total study area. Topographically, the permafrost is mainly distributed on the slope surface, while a small amount is distributed on the peak/ridge and valley. On the slope surface, there is more permafrost located on the upper slope than on the lower slope. There is more permafrost in the north and west slope aspects than in the south and east.
  • Samples with permafrost and samples without permafrost have differences in the selected environmental variables, among which the difference of SR is the largest and the overlap part is the least.

Author Contributions

Conceptualization, Y.G.; data curation, S.L. and L.Q.; formal analysis, W.S. and S.L.; funding acquisition, W.S.; methodology, Y.G. and S.L.; project administration, W.S. and Y.G.; software, S.L.; supervision, W.S.; writing—original draft, Y.G., S.L., L.Q. and Y.W.; writing—review and editing, W.S., S.L., L.Q., Y.W. and C.Z. All authors have read and agreed to the published version of the manuscript.

Funding

We thank the National Natural Science Foundation of China (Grant No. 41641024) and the Science and Technology Project of the Heilongjiang Communications Investment Group (Grant No. JT-100000-ZC-FW-2021-0182) for providing financial support and the Field scientific observation and research station of the Ministry of Education-Geological environment system of permafrost area in Northeast China (MEORS-PGSNEC).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Related data are available upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Pearson’s Correlation between PP and Each Characteristic Variable

Table A1. Pearson’s correlation between PP and the characteristic variables throughout the study area. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
Table A1. Pearson’s correlation between PP and the characteristic variables throughout the study area. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
n = 100PPLST1LST2LST3DEVSRNDVINDWI
PP1
LST1−0.601 **1
LST2−0.629 **0.887 **1
LST3−0.573 **0.314 *0.293 *1
DEV0.12−0.092−0.223 *0.1681
SR−0.238 *0.286 *0.266 **0.113−0.0611
NDVI−0.324 **0.429 **0.360 **0.044−0.0220.233 *1
NDWI0.333 **−0.476 **−0.435 **−0.0340.067−0.299 **−0.980 **1
Table A2. Pearson’s correlation between the characteristic variables in 92 boreholes with permafrost and 16 investigation points with permafrost. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
Table A2. Pearson’s correlation between the characteristic variables in 92 boreholes with permafrost and 16 investigation points with permafrost. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
n = 108LST1LST2LST3DEVSRNDVINDWI
LST11
LST20.864 **1
LST3−0.814 **−0.560 **1
DEV0.242 *0.088−0.523 **1
SR0.0570.1340.0610.241 *1
NDVI0.328 **0.146−0.472 **0.489 **0.1071
NDWI−0.321 **−0.1750.431 **−0.438 **−0.134−0.985 **1
Table A3. Pearson’s correlation between the characteristic variables in 109 boreholes without permafrost. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
Table A3. Pearson’s correlation between the characteristic variables in 109 boreholes without permafrost. The symbols (* and **) denote that the Pearson’s correlation value is significant at the 0.05 level (2-tailed) or 0.01 level (2-tailed), respectively.
n = 109LST1LST2LST3DEVSRNDVINDWI
LST11
LST20.857 **1
LST3−0.472 **−0.497 **1
DEV0.007−0.012−0.0761
SR0.0610.178−0.0150.0471
NDVI0.231 *0.116−0.102−0.138−0.1301
NDWI−0.283 **−0.1620.1010.0960.125−0.990 **1

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Figure 1. The geographical location of the study area (Arxan) (a). Mean annual ground surface temperature (MAGST) and mean annual land surface temperature (MALST) changes in 2001–2020 (b).
Figure 1. The geographical location of the study area (Arxan) (a). Mean annual ground surface temperature (MAGST) and mean annual land surface temperature (MALST) changes in 2001–2020 (b).
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Figure 2. Permafrost prior data. (a) is the schematic diagram of the zoomed out prior data; (b,c) refers to the cities and towns, and lakes that are artificially designated as non-permafrost areas; (d–f) are the permafrost prior data constructed by the borehole data of S308; and (g) is the permafrost ice layer taken during the investigation in the study area.
Figure 2. Permafrost prior data. (a) is the schematic diagram of the zoomed out prior data; (b,c) refers to the cities and towns, and lakes that are artificially designated as non-permafrost areas; (d–f) are the permafrost prior data constructed by the borehole data of S308; and (g) is the permafrost ice layer taken during the investigation in the study area.
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Figure 3. Technical flowchart.
Figure 3. Technical flowchart.
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Figure 4. ROC curve and AUC values of the final MaxEnt model.
Figure 4. ROC curve and AUC values of the final MaxEnt model.
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Figure 5. Permafrost probability (PP) distribution in the study area (a) and the PP distribution of 92 boreholes and 16 investigation points with permafrost (b) and 109 boreholes without permafrost (c).
Figure 5. Permafrost probability (PP) distribution in the study area (a) and the PP distribution of 92 boreholes and 16 investigation points with permafrost (b) and 109 boreholes without permafrost (c).
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Figure 6. Distribution relationship between permafrost probability and topographic parameters. (a) shows the frequency distribution histogram of PP in the whole study area. The relationship between PP and the relative frequency distribution of aspect (b), slope (c), altitude (d), and terrain (e) in different value ranges were also analyzed.
Figure 6. Distribution relationship between permafrost probability and topographic parameters. (a) shows the frequency distribution histogram of PP in the whole study area. The relationship between PP and the relative frequency distribution of aspect (b), slope (c), altitude (d), and terrain (e) in different value ranges were also analyzed.
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Figure 7. Numerical distribution of the characteristic variables in the samples with permafrost and the samples without permafrost.
Figure 7. Numerical distribution of the characteristic variables in the samples with permafrost and the samples without permafrost.
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Figure 8. Scatter diagram between PT and PP (a), PC and PP (b), PT and PC (c) in Arxan.
Figure 8. Scatter diagram between PT and PP (a), PC and PP (b), PT and PC (c) in Arxan.
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Figure 9. Comparison of PP (a) with PT (b) and PC (c) in Arxan. Two places (d,e) were magnified. (d1,e1) are real-color base map; (d2,e2) are PP distribution of (d,e); (d3,e3) are PT distribution of (d,e); (d4,e4) are PC distribution of (d,e).
Figure 9. Comparison of PP (a) with PT (b) and PC (c) in Arxan. Two places (d,e) were magnified. (d1,e1) are real-color base map; (d2,e2) are PP distribution of (d,e); (d3,e3) are PT distribution of (d,e); (d4,e4) are PC distribution of (d,e).
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Guo, Y.; Liu, S.; Qiu, L.; Wang, Y.; Zhang, C.; Shan, W. Permafrost Probability Mapping at a 30 m Resolution in Arxan Based on Multiple Characteristic Variables and Maximum Entropy Classifier. Appl. Sci. 2023, 13, 10692. https://doi.org/10.3390/app131910692

AMA Style

Guo Y, Liu S, Qiu L, Wang Y, Zhang C, Shan W. Permafrost Probability Mapping at a 30 m Resolution in Arxan Based on Multiple Characteristic Variables and Maximum Entropy Classifier. Applied Sciences. 2023; 13(19):10692. https://doi.org/10.3390/app131910692

Chicago/Turabian Style

Guo, Ying, Shuai Liu, Lisha Qiu, Yan Wang, Chengcheng Zhang, and Wei Shan. 2023. "Permafrost Probability Mapping at a 30 m Resolution in Arxan Based on Multiple Characteristic Variables and Maximum Entropy Classifier" Applied Sciences 13, no. 19: 10692. https://doi.org/10.3390/app131910692

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