1. Introduction
In recent years, more and more scholars have studied the theories and characteristics of freeze–thaw erosion and analyzed the effects of different factors on the degree of freeze–thaw erosion. The area where the freeze–thaw acts violently on the rock soil and forms the landform characteristics of the freeze–thaw erosion is called the freeze–thaw erosion area [
1]. In 1988, some scholars proposed that freeze–thaw erosion was classified as permafrost erosion and glacier erosion because of the effect of freeze–thaw erosion on different erosion substances [
2]. Freeze–thaw refers to the physical process in which the temperature of the soil surface layer increases from below 0 °C to more than 0 °C and then decreases from above 0 °C to below 0 °C [
3]. Soil and rock mass change their physical characteristics in the freeze–thaw cycle, which affects the internal corrosion resistance, stability, shear resistance, hydraulic conductivity, and so on [
4,
5,
6,
7,
8]. In 2003, Jing Guochen summarized [
9] that freeze–thaw erosion is subject to freezing and thawing processes through water changes, changing the physics of the rock mass and soil characteristics, and thus promoting the occurrence of freeze–thaw erosion. In other words, freeze–thaw erosion is the intrusion of the rock mass by water, which expands the internal cracks, in the continuous cycle, into a rock mass composed of fragments; the internal results are extremely unstable [
10,
11]. To summarize, freeze–thaw erosion can be explained as the final result of physical and chemical weathering [
12].
At present, scholars have extensively explored the influencing factors of freezing and thawing erosion. The analytic hierarchy process (AHP) and the comprehensive evaluation index method have become relatively mature methods for evaluating freezing and thawing erosion. In 2005, Zhang et al. selected the temperature, terrain, vegetation, soil, and precipitation to evaluate the freeze–thaw erosion intensity in Sichuan Province, China [
13]. Shi et al. selected poor annual temperature, precipitation, slope, solar radiation, and vegetation coverage, evaluated the intensity of freeze–thaw erosion in the Three-River-Source Area using AHP, and found that the freeze–thaw erosion area was mainly concentrated at the source of the Yangtze River [
14]. Chen et al. analyzed the poor annual temperature accumulation, precipitation, vegetation coverage, slope, and aspect as evaluation factors and used the AHP method and comprehensive evaluation index method to evaluate the freeze–thaw erosion intensity in the Dadu River basin [
15]. Li et al. used AHP and the comprehensive evaluation index method to evaluate the intensity of freezing and thawing erosion in Gansu Province, China, and selected the annual poor temperature, annual precipitation, slope, vegetation coverage, average rainfall during the thawing period, and average lowest temperature during the freezing period as evaluation factors [
16]. According to the results of Bartczak A, the number of freeze–thaw cycles can more accurately express the degree of freeze–thaw erosion [
17]. Wang et al. found that the freeze–thaw cycle and soil moisture affect the size and stability of soil aggregates, which are more likely to lead to erosion [
18]. Taskin Oztas found that soil stability was accompanied by increased water content during freezing [
19]. Lu et al. used the hierarchical analysis method to score the annual range of temperature, annual precipitation, slope, vegetation cover, and elevation to determine the weight and the evaluation intensity of freeze–thaw erosion using the comprehensive evaluation index method [
20].
Chen et al. used principal component analysis to evaluate the groundwater quality in Liaocheng City in order to provide technical support for the development of groundwater management strategies [
21]. Fu et al. used principal component analysis to analyze the spatial and temporal evolution of the water quality of Guangli River by combining water quality monitoring data from 2015 to 2017 [
22]. Zhang et al. used principal component analysis to assess the effectiveness of ecological civilization construction in Shanxi Province through 35 index evaluation indicators [
23]. Zhai et al. individually analyzed the spatial and temporal evolution of water quality in the Zuli River basin through the data of 17 water quality indicators from 2016 to 2020, using the principal component analysis method, among others [
24]. Lu et al. evaluated the freeze–thaw erosion intensity of the China–Mongolia–Russia economic corridor by selecting eight influence factors [
25]. By integrating soil moisture and temperature, Krzeminska et al. conducted a field investigation of freeze–thaw erosion in southeast Norway [
26]. Sadeghi et al. conducted an analysis of the impact of freeze–thaw cycles in regions prone to soil erosion located in the mountainous areas of northern Iran [
27].
At present, there are a variety of weight assignment methods, and in the study of freeze–thaw erosion, hierarchical analysis is the most common. However, the hierarchical analysis method receives a greater degree of subjective influence, so this study selects the principal component analysis and, using the multiple collinearity test, screens out the indicators with strong interdependency to deduce the comprehensive assessment model of freeze–thaw erosion.
The ecological function reserve of the Greater Hinggan Mountains is a Water conservation ecological function protection zone in China. The frequency of natural disasters like landslides brought on by freeze–thaw erosion is gradually increasing in relation to the changing global climate. Therefore, based on previous studies, this study comprehensively considered the evaluation indexes of freeze–thaw erosion in the ecological function reserve of the Greater Hinggan Mountains, explored the spatial distribution of freeze–thaw erosion in the area, and analyzed its evaluation indexes. It provides a certain reference value for the prevention and control of freeze–thaw erosion and ecological environmental protection in the ecological function reserve of the Greater Hinggan Mountains and its neighboring areas.
4. Freeze–Thaw Erosion Strength Evaluation Factors
The formation process of freeze–thaw erosion is complex and is affected by certain climate, soil, terrain, geology, and hydrological conditions. The schematic diagram of the standardized evaluation index is shown in
Figure 3.
Temperature is the first driving force of freeze–thaw erosion, which has a significant influence on the freezing and melting of rocks [
30]; the annual range of temperature is an important indicator of temperature change. The results of the relationship between temperature and freeze–thaw erosion show that the annual range of temperature increases with latitude and decreases with altitude [
31]. And, in high north latitude areas, the soil active layer was increased [
32]. The depth of the frozen rock and melting layers is changed by the temperature range, which is proportional to the duration and the possibility of freezing and thawing erosion. The greater the temperature difference, the greater and more serious the damage to the soil rock aggregate [
33]; therefore, the annual range of temperature plays an indispensable role in the occurrence of freezing and thawing erosion.
- 2.
Precipitation (Pre)
Precipitation is the key factor affecting the freezing and thawing erosion process, which mainly affects the freezing and thawing process by changing the water content of the cracks and pores in the rock mass of the slope [
34,
35]. The process of liquid water becoming solid ice during the freezing period destroys the structure of soil or rock. The precipitation is directly proportional to the freezing and thawing speed. The greater the rainfall, the greater the rock water content and the faster the freezing and thawing speed [
36].
- 3.
Vegetation cover index
Since vegetation is beneficial to stabilize the internal characteristics of the soil, vegetation coverage plays a slowing role in reducing the degree of freeze–thaw erosion [
37]. Generally, the normalized vegetation coverage index (
NDVI) is used to quantify the difference between the near-infrared (vegetation strong reflection) band and red (vegetation absorption) band. The value range is between −1 and 1, and when the value is less than or equal to 0, no vegetation coverage is indicated [
20], as shown in Formula (2).
where
R stands for the red band’s reflectance and
NIR for the near-infrared band.
- 4.
Soil structural stability index (SSI)
Freeze–thaw will change the physical and chemical characteristics of soil, mainly affecting the stability of soil aggregates, leading to a change in soil corrosion resistance [
3]. It can change the size of the aggregate, affect the physical and chemical properties of the soil, cause damage to the soil’s mechanical structure, and, therefore, cannot recover naturally, increasing the corrosion of the soil. During freezing, the volume expands and increases the soil volume, while the loss of water shrinks the soil volume. In the body surface, the porosity may decrease, but its absorption and permeability will increase [
38,
39], which further changes the soil etchability, thus affecting the change in the degree of freezing and thawing erosion. In addition, the soil bulk density will also change with the downward distance of the seasonal freezing–thaw cycle, with a larger distance and the pore ratio, leading to more prone to freeze–thaw erosion [
40], as shown in Formula (3).
where
is the soil organic carbon concentration (
) in the 0–30 cm soil layer;
and
are the clay and silt content (%) obtained in the 0–30 cm soil layer; and 1.724 corresponds to the van Beuren transformation variable for soil organic matter.
- 5.
The slope and aspect
Changes in elevation cause a change in the ground slope. As the slope increases, the steeper it becomes, the transport transfer of material increases, and as the distance moved increases, the erosion intensity increases [
20]. The greater the slope, the more likely the soil and water will be lost, and the less likely it is to recover the ecological environment and vegetation. It has strong stability and good anti-interference ability in places with gentle slopes due to the reclamation and building activities to a greater extent.
Aspect makes the rock mass differentially exposed to light and produces discrepancies in the value of solar radiation received [
41]. Sunny aspects and shady aspects cause temperature differences in the rock mass, which destroys the structure of the rock mass and has an impact on the degree of erosion [
42,
43].
- 6.
Soil moisture index (SMI)
The soil moisture index is the moisture content in the soil, which describes the richness or dryness of the moisture in the soil. Water content has important effects on soil stability and erosion processes [
44,
45]. Appropriate amounts of water can increase the adhesion between soil particles and enhance the adhesion and erosion resistance of the soil, thus reducing the risk of soil erosion.
- 7.
Sunshine index (SI)
The sunshine index is the statistical value of the average sunshine hours of the region over a period of time. A higher sunshine index can increase the temperature difference between day and night and freeze–thaw cycle frequency, aggravating the occurrence of freeze–thaw erosion. At the same time, it may also increase the occurrence of the frost swelling force and further damage the soil structure. However, vegetation growth and cover can mitigate the effects of freeze–thaw erosion by regulating water and temperature. Therefore, the sunshine index should be considered for freeze–thaw erosion evaluation in freeze–thaw areas.
- 8.
Freeze–thaw daily cycle days (FTDs)
A freeze–thaw cycle day is a day in which the maximum soil temperature is greater than 0 °C and the minimum temperature is less than 0 °C. Freeze–thaw erosion refers to the freezing and thawing process, which leads to the fragmentation, movement, and reorganization of soil particles, which triggers soil erosion [
46]. Freeze–thaw daily cycle days are an important indicator of the freeze–thaw cycle, which is closely related to the soil freeze–thaw process.
At low temperatures, water in the soil freezes, forming a freezing zone or frozen frost. When the water in the soil is free, the water volume expands, creating a freezing force and applying pressure on the soil particles. As the daily temperature rises, the frozen soil begins to thaw, and the frozen water is converted into liquid water. The formation of liquid water during the thawing process will change the arrangement and structure of soil particles, making the soil uneven and increasing the soil fluidity. Repeated freezing and thawing, this freezing force will cause the fragmentation and movement of soil particles, increasing the loosening degree of the soil [
47]. Overall, the more freeze–thaw daily cycle days will exacerbate the frequency and intensity of the freeze–thaw cycles, thus increasing the vulnerability and erosiveness of the soil.
5. Study Method
The evaluation of freeze–thaw erosion intensity is based on multiple indicators, and the weights of the indicators are determined according to their importance or contribution. The most common weight determination method in the study of freeze–thaw erosion is hierarchical analysis, but it is more subjective, so this study selects the principal component analysis method, which is more considerable to evaluate the intensity of freeze–thaw erosion.
In this study, firstly, ArcGIS was used to generate 100 × 100 random points in the range of the freeze–thaw erosion area and crop out the points in the range of the freeze–thaw erosion area, which are the statistical points. Secondly, the attribute values of the annual difference in temperature, annual precipitation, slope, slope direction, vegetation cover, sunshine index, soil structure stability index, soil moisture, and days of freeze–thaw daily cycle were extracted to the statistical points, and the number of principal factors, contribution rate, and cumulative contribution rate were determined using principal component analysis in SPSS. Finally, through each principal component corresponding to the eigenvalues, the comprehensive principal component model was obtained, from which the freeze–thaw erosion intensity was calculated.
5.1. Standardization Method
The standardization method is a common data processing method used to convert data of different dimensions or scales into comparable forms. The raw data are transformed to have similar scale, scope, or directly comparable properties for better data analysis and decision making. In this study, because the factors affecting freeze–thaw erosion have different dimensions and units, in the calculation process, the factors that promote freeze–thaw erosion are positively normalized, the inhibition selection is inversely normalized, and are then followed by the superposition comprehensive calculation. The standardized calculation method is shown in Formula (4). The method scaled the data to [0, 1] or any other specified range by subtracting the minimum value and dividing by the difference between the maximum and minimum values [
48,
49].
where
is the normalized value of the factor;
is the value of each single factor;
is the minimum value of the factor; and
is the maximum value of the factor.
Due to the different meanings of the evaluation indexes, there are differences in units and resolution. Therefore, this study firstly unifies the coordinate system of evaluation indexes as Krasovsky_1940_Alber and resamples the image element size as 30 × 30. To ensure the scientificity of the data and the reliability of the experimental results, the Z-score method in SPSS 26 software is used to standardize the values of the attributes of the evaluation indexes.
5.2. Multiple Collinearity Test
The multiple collinearity test is a statistical method used to detect linear relationships between independent variables. This method performs the test by calculating the variance inflation factor (VIF) for each independent variable. If the VIF of an independent variable is greater than 10, it means there is multicollinearity. And, if the VIF is greater than 100, it means that there is a serious multicollinearity between the variables [
50].
In order to avoid the problem that the covariance of the evaluation indicators leads to inaccurate results of the model assessment, firstly, the multiple covariance test is carried out on the evaluation indicators, and it is found that the VIF is less than 10, as shown in
Table 2. Therefore, it is judged that the evaluation indicators do not have covariance and can be used for model building.
5.3. Principal Component Analysis
Principal component analysis (PCA) is a sophisticated statistical technique that uses a deft orthogonal transformation to convert a set of possibly correlated variables into a set of linear, uncorrelated variables. We call this transformed variable the principal component. These principal components not only maintain the information of the original variables but also greatly reduce the complexity of the data, facilitating our deep understanding of the data. Principal component analysis plays an important role in the analysis of multivariate data. It can help us reveal the hidden structure in the data, extract the main features, and make the complex data set concise and clear. Simultaneously, it can efficiently decrease the quantity of calculations and enhance the effectiveness of analysis [
51].
In analyzing the results, the principal components were determined based on the eigenvalues of the principal factors, and the principal components were determined based on the principle of eigenvalue greater than 1. According to the calculation results, the first four principal components are selected, and their eigenvalues are 2.336, 2.18, 1.223, and 1.013, respectively. The cumulative contribution rate reaches 75.023%, as shown in
Table 3. It shows that four principal components can be used to replace the nine original indicators.
According to the loaded sum of squares and the component matrix, the eigenvectors of each evaluation indicator in each principal component are obtained using the values of the component matrix of the evaluation indicators and the corresponding initial eigenvalues after opening the root sign, as shown in
Table 4.
In the comprehensive evaluation of freeze–thaw erosion, the four principal component values were obtained by multiplying and calculating the eigenvectors obtained from
Table 2 with the standardized values of the evaluation indicators, as shown in Formula (5).
where
,
,
and
are the principal component scores of 1–4, respectively. Using the percentage of the variance of the initial eigenvalue as the corresponding principal component weight value, the principal component integrated model
F was calculated, as shown in Formula (6).
The final comprehensive strength model for freeze–thaw erosion was obtained, as shown in Formula (7).
5.4. The Geographic Detector
The geographic detector mainly consists of four parts: the interactive detector, the risk detector, the factor detector, and the ecological detector. It is measured by calculating the q-value by detecting the driving force of the dependent variable for each factor [
52,
53], as shown in Formula (8).
where
;
is the number of index categories;
and
are the number of the whole region and index type units, respectively;
and
represent the whole area variance and variance of index type, respectively;
is the total variance of the whole region; and
is the sum of index variance.
8. Conclusions
In this study, we selected nine factors, namely, the annual range of temperature, precipitation, NDVI, the soil structural stability index, slope, aspect, soil moisture content, the sunshine index, and freeze–thaw daily cycle days, to evaluate the freeze–thaw erosion intensity of ecological function reserve. The following conclusions were obtained in this paper:
The total area of freeze–thaw erosion is 81,601.43096 km2, accounting for 92.9% of the total area of the ecological function reserve of the Greater Hinggan Mountains. The area of moderate erosion, strong erosion, and mild erosion is larger, accounting for 29.83%, 25.9%, and 21.54% of the total area of freeze–thaw erosion, respectively. This is followed by severe erosion accounting for 11.93% of the total area of freeze–thaw erosion. The area of micro-erosion is the least, accounting for 10.8% of the total area.
There are significant differences in the spatial pattern of the distribution of freeze–thaw erosion intensity in the ecological function reserve of the Greater Hinggan Mountains. From west to east, the intensity of freeze–thaw erosion gradually strengthens. Strong erosion and severe erosion are mainly concentrated in the eastern and central parts of the ecological function area of the Greater Hinggan Mountains. Micro-erosion and mild erosion are mainly distributed in the western part of the ecological function reserve of the Greater Hinggan Mountains and a small part of the southern part.
Within the study area, a comprehensive evaluation model for the area was derived, and the intensity of freeze–thaw erosion in the ecological function area of the Greater Hinggan Mountains was calculated by means of the multiple collinearity test and principal component analysis method. The severely eroded and intensely eroded areas were dominant, with the total area accounting for more than 50% of the eroded area. Soil moisture content and the number of freeze–thaw daily cycle days were the two indicators with the highest degree of influence, and the interaction effect was greater than the degree of influence of any factor. At present, it is difficult to collect some data on the selection of influencing factors for the ecological function area of the Greater Hinggan Mountains, and the selection of indicators needs to be further improved.