Evaluation of Freeze–Thaw Erosion Intensity in the Ecological Function Reserve of the Greater Hinggan Mountains Based on Geographic Information Systems and a Geographic Detector

Abstract

Freeze–thaw erosion is one of the three major soil erosions in China, including wind erosion and hydraulic erosion, which leads to the destruction of the natural environment, the imbalance of economic development, a threat to personal safety, and irreversible disaster to the country and people. China’s permafrost area accounts for about one-fifth of the country’s land area, and the seasonal permafrost area accounts for half of China’s land area, mainly concentrated in the Qinghai–Tibet Plateau, Xinjiang Province, Heilongjiang Province, Gansu Province, and other regions. In order to establish an evaluation system for the ecological function reserve of the Greater Hinggan Mountains, nine evaluation indicators were selected from the perspectives of topography, climate, soil, and vegetation conditions. GIS technology, a multiple collinearity test, and principal component analysis were used to comprehensively evaluate the freeze–thaw erosion in the ecological function reserve of the Greater Hinggan Mountains. This study categorized the evaluation results into five intensity levels, from micro to severe. Finally, the degree of influence of different influencing factors on freeze–thaw erosion and the interactions between the factors were analyzed using a geographic detector. The results showed the following: (1) The intensity of freeze–thaw erosion in the study area gradually increased from west to east, and the comprehensive evaluation results were −0.2552 to 0.7581. Overall, moderate, severe, and mild erosion accounted for 29.83%, 25.9%, and 21.54% of the total area of the freeze–thaw zone, respectively. (2) Soil moisture content and the annual range in temperature were the main factors contributing to freeze–thaw erosion. The degree of influence of the two effects on freeze–thaw erosion (q = 0.5997) was better than that of the single-factor effect.

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.

2. Study Area and Data

2.1. Study Area

The ecological function area of the Greater Hinggan Mountains is located in northeast China, spanning the Heilongjiang Province and Inner Mongolia Autonomous Region, and is located at 49°23′–53°55′ N, 119°91′–124°29′ E, as shown in Figure 1. The total domain area is about 87,842.8 km². The terrain gradually rises from northwest to southeast. The study area is located in the high latitude and alpine zone, with a cold temperate continental monsoon climate. The average frost-free period is 80 to 110 days, the extreme temperature reaches −53 °C, the extreme maximum temperature is 37 °C, and the average annual rainfall is 460 mm. The soil layer is barren; the tree production is slow and, once destroyed, cannot be copied.

2.2. Data Source

The research data are shown in

Table 1. Data source.

Data Type		Data Source	Website Connection
Study region		Center for Resource and Environmental Science and Data Science, Chinese Academy of Sciences	https://www.resdc.cn/ (accessed on 13 June 2023)
Meteorological data		NOAA National Environmental Information Center	https://www.ncei.noaa.gov/ (accessed on 15 June 2023)
Terrain data		Geospatial data cloud	https://www.gscloud.cn/ (accessed on 6 July 2023)
Soil data	Soil organic carbon	International Soil Reference and Information Centre (ISRIC)	https://data.isric.org/ (accessed on 26 July 2023)
	Clay content	Harmonized World Soil Database (HWSD)	http://westdc.westgis.ac.cn/ (accessed on 26 July 2023)
	Silt content
Vegetation data		NASA Data Center	https://ladsweb.modaps.eosdis.nasa.gov/ (accessed on 2 August 2023)

.

3. Freeze–Thaw Erosion Zone Determination

The occurrence of erosion may not be accompanied by freeze–thaw erosion [9]; therefore, the first step is to determine the freeze–thaw erosion area.

According to the DEM data, the lower boundary elevation of the longitude and latitude and substitution into the freeze–thaw erosion zone is determined by Formula (1) to obtain the lower boundary elevation of the freeze–thaw erosion zone [28,29]. Finally, the study area layer and land use layer are superimposed, and the factors influencing lakes and glaciers are excluded to determine the freeze–thaw erosion area, as shown in Figure 2.

$$H=\frac{36.552-0.094X-0.515Y+4.5}{0.004}-200$$

(1)

where $H$ is the lower boundary elevation of the freeze–thaw erosion zone (m); $X$ is latitude (°); and $Y$ is longitude (°).

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.

• Annual range of temperature (ARTem)

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).

$$NDVI=\frac{NIR-R}{NIR+R}$$

(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).

$$SSI=\frac{SOC(\%)\times 1.724}{Clay(\%)+Silt(\%)}\times 100\%$$

(3)

where $SOC$ is the soil organic carbon concentration ($\mathrm{g}/{\mathrm{kg}}^{-1}$) in the 0–30 cm soil layer; $Clay$ and $Silt$ 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].

$$I_i=\{\begin{array}{cc}\left(I-I_{min}\right)/\left(I_{max}-I_{min}\right)& \mathrm{Forward} \mathrm{factor}\\ \left(I_{max}-I\right)/\left(I_{max}-I_{min}\right)& \mathrm{Reverse} \mathrm{factor}\end{array}$$

(4)

where $I_i$ is the normalized value of the factor; $I$ is the value of each single factor; $I_{min}$ is the minimum value of the factor; and $I_{max}$ 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. Results of the multicollinearity test.

Evaluating Indicator	Collinearity Statistics
	Tolerance	VIF
Aspect	0.993	1.007
FTDs	0.293	3.409
NDVI	0.876	1.142
SI	0.239	4.186
SSI	0.928	1.077
ARTem	0.299	3.35
Slope	0.308	3.25
Pre	0.3	3.337
SMI	0.306	3.266

. 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. Total variance interpretation.

Components	Initial Eigenvalue			The Sum of the Load Squares Was Extracted
	Total	Variance Percentage	Accumulate (%)	Total	Variance Percentage	Accumulate (%)
1	2.336	25.953	25.953	2.336	25.953	25.953
2	2.18	24.222	50.175	2.18	24.222	50.175
3	1.223	13.588	63.763	1.223	13.588	63.763
4	1.013	11.26	75.023	1.013	11.26	75.023
5	0.917	10.186	85.208
6	0.767	8.52	93.728
7	0.309	3.431	97.159
8	0.139	1.542	98.7
9	0.117	1.3	100

. 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. The total variance explained with the eigenvectors.

Appraise Metric		Component Matrix				Feature Vector
		1	2	3	4	1	2	3	4
$X_1$	temp	−0.892	−0.005	−0.222	−0.093	−0.584	−0.003	−0.201	−0.092
$X_2$	FTDs	0.723	−0.222	−0.523	0.009	0.473	−0.150	−0.473	0.009
$X_3$	Pre	0.085	0.875	−0.227	0	0.056	0.593	−0.205	0
$X_4$	SMI	0.477	0.77	0.104	−0.002	0.312	0.522	0.094	−0.002
$X_5$	SI	−0.501	0.753	0.308	−0.016	−0.328	0.510	0.279	−0.016
$X_6$	NDVI	−0.122	−0.42	0.396	−0.15	−0.080	−0.284	0.358	−0.149
$X_7$	Slope	0.629	−0.023	0.697	0.109	0.412	−0.016	0.630	0.108
$X_8$	aspect	−0.06	0.017	−0.145	0.91	−0.039	0.012	−0.131	0.904
$X_9$	SSI	0.34	0.163	−0.28	−0.376	0.222	0.110	−0.253	−0.374

.

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).

$$\begin{gathered} F_1=-0.584X_1+0.473X_2+0.056X_3+0.312X_4-0.328X_5-0.08X_6+0.412X_7-0.039X_8+0.222X_9 \\ {F}_2=-0.003X_1-0.150X_2+0.593X_3+0.522X_4+0.510X_5-0.284X_6-0.016X_7-0.012X_8+0.110X_9 \\ {F}_3=-0.201X_1-0.473X_2-0.205X_3+0.094X_4+0.279X_5+0.358X_6+0.630X_7-0.131X_8-0.253X_9 \\ {F}_4=-0.092X_1+0.009X_2-0.002X_4-0.016X_5-0.149X_6+0.108X_7+0.904X_8-0.374X_9 \end{gathered}$$

(5)

where $F_1$, $F_2$, $F_3,$ and $F_4$ 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).

$$F=\frac{{\lambda }_1}{{\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4}{F}_1+\frac{{\lambda }_2}{{\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4}{F}_2+\frac{{\lambda }_3}{{\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4}{F}_3+\frac{{\lambda }_4}{{\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4}{F}_4$$

(6)

The final comprehensive strength model for freeze–thaw erosion was obtained, as shown in Formula (7).

$$F=-0.253X_1+0.031X_2+0.173X_3+0.293X_4+0.099X_5-0.077X_6+0.268X_7+0.102X_8+0.011X_9$$

(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).

$$q=1-\frac{{{\displaystyle \sum }}_{h=1}^n{N}_h{\sigma }_h^2}{N{\sigma }^2}=1-\frac{SSW}{SST}$$

(8)

where $h=1,2,3\dots ,n$; $n$ is the number of index categories; $N$ and $N_h$ are the number of the whole region and index type units, respectively; $\sigma$ and ${\sigma }_h$ represent the whole area variance and variance of index type, respectively; $SST$ is the total variance of the whole region; and $SSW$ is the sum of index variance.

6. Results and Analysis

6.1. Evaluation of Freeze–Thaw Erosion Strength

According to Formula (11) and combined with ArcGIS, the freeze–thaw erosion intensity level in this region was calculated (among erosion, it is referred to as E). The freeze–thaw erosion strength results are between −0.2552 and 0.7581. The freeze–thaw erosion intensity results were divided into five grades according to the grading criteria. The grading criteria are detailed in

Table 5. Freeze–thaw erosion strength classification.

Freeze–Thaw Erosion Strength Grade	Micro-E	Mild-E	Moderate-E	Strong-E	Severg-E
Freeze–thaw erosion strength classification standard	−0.2552–0.0746	0.0746–0.1978	0.1978–0.3051	0.3051–0.4164	0.4164–0.7581

. The freeze–thaw erosion grading results were obtained, as shown in Figure 4. The total area of the freeze–thaw erosion area in the Greater Hinggan Mountains ecological function reserve is 81,601.43096 km², accounting for 92.9% of the total area. Among them, the area proportion was 11.93% severe, 25.90% strong, 29.83% moderate, 21.54% mild, and 10.80% micro, as shown in Figure 5.

6.2. Interaction Detector Analysis of Geographic Detector Model

Freeze–thaw erosion is affected by a combination of factors but with varying degrees of influence. According to the nine selected indicators, combined with the intensity of freeze–thaw erosion, the explanatory power of the indicators, in descending order, is the soil moisture index, the annual range of temperature, precipitation, slope, NDVI, freeze–thaw daily cycle days, the sunshine index, the soil structural stability index, and aspect. The q-value of the soil moisture index is the largest, which indicates that the soil moisture index contributes the most to the freeze–thaw erosion in the region. The q-value of the aspect is the smallest, which indicates that the aspect contributes the least to the freeze–thaw erosion in the region, as shown in Figure 6.

After the discretization of the data for each factor [37], the interactions between different factors were calculated using the interactive probe module in the geodetector, and the results showed a two-factor enhancement relationship. It was also found that the spatial heterogeneity of freezing and thaw erosion intensity was mostly greater than that of a single factor, showing a non-linear enhancement relationship. Due to the interaction between the factors, a single influence factor does not fully represent the freeze–thaw erosion of the study area. In the two-factor enhancement, the annual range of temperature and precipitation had the largest interaction (0.5997), and the rest were the annual range of temperature and the soil moisture index (0.5789), precipitation and the soil moisture index (0.49668), and freeze–thaw daily cycle days and the soil moisture index (0.4912), as shown in Figure 7.

7. Discussion

7.1. Relationship between FT Erosion and the Evaluation Index

After normalizing the evaluation indicators, the values are in the range of 0–1. The grading criteria according to the natural discontinuity point method after normalization are shown in

Table 6. Strength grading criteria after normalization of evaluation indicators.

Factors	Micro-E	Mild-E	Moderate-E	Strong-E	Severg-E
ARTem	0–0.2741	0.2741–0.4617	0.4617–0.6333	0.6333–0.7880	0.7880–1
Pre	0–0.2588	0.2588–0.4118	0.4118–0.5451	0.5451–0.7137	0.7137–1
NDVI	1–0.6902	0.6902–0.6275	0.6275–0.5608	0.5608–0.4824	0.4824–0
SSI	1–0.4835	0.4835–0.3868	0.3868–0.3072	0.3072–0.1934	0.1934–0
Slope	0–0.2431	0.2431–0.4275	0.4275–0.6196	0.6196–0.8157	0.8157–1
Aspect	0–0.1984	0.1984–0.3997	0.3997–0.5988	0.5988–0.7975	0.7975–1
SMI	0–0.3490	0.3490–0.4902	0.4902–0.6	0.6–0.7098	0.7098–1
SI	0–0.1647	0.1647–0.3569	0.3569–0.5451	0.5451–0.7294	0.7294–1
FTDs	0–0.2537	0.2537–0.4343	0.4343–0.5767	0.5767–0.7307	0.7307–1

.

Along with the increase in the annual temperature range in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually increases; the area of heavy erosion and severe erosion gradually decreases; and the moderate erosion shows the trend of first increasing and then decreasing. Accompanied by the increase in precipitation in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually decreased, and the proportion was close to zero. The area of heavy erosion and severe erosion gradually increased, and the proportion of severe erosion area was as high as 60.32%. The trend of moderate erosion showed an increase and then a decrease. Accompanied by the increase in NDVI in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually increased. The area of strong erosion and severe erosion gradually decreased. Moderate erosion showed a trend of increasing and then decreasing. Accompanied by the increase in the soil stability index in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually increased. The area of strong erosion and severe erosion gradually decreased. The moderate erosion showed a trend of decreasing first and then increasing. Accompanied by the increase in the slope of the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually decreases; the area of strong erosion and severe erosion gradually increases. The area of moderate erosion shows a trend of first decreasing and then increasing. Accompanied by the increase in the aspect of the freeze–thaw erosion area, the area of micro-erosion, mild erosion, and moderate erosion showed a tendency to increase first and then decrease. The areas of strong erosion and severe erosion showed a tendency to decrease first and then increase. Accompanied by the increase in the soil moisture index in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually decreased, and the proportion tended to be close to zero. The area of strong erosion and severe erosion gradually increased. The area of moderate erosion showed a tendency of increasing and then decreasing. Accompanied by the increase in the sunshine index in the freeze–thaw erosion area, the area of micro-erosion gradually decreases. The area of mild erosion and severe erosion shows a trend of increasing and then decreasing. The area of moderate erosion and severe erosion shows a trend of decreasing and then increasing. Accompanied by the increase in the freeze–thaw daily cycle days in the freeze–thaw erosion area, the area of micro-erosion and mild erosion gradually decreased. Moderate erosion and strong erosion showed a trend of decreasing and then increasing. The area of severe erosion gradually increased, as shown in Figure 8.

7.2. Applicability of Evaluation Model Construction for Freeze–Thaw Erosion

In the selection process of evaluation indexes, we combine the principle of freeze–thaw erosion with domestic and international research results to ensure that it is closely related to the universality of the freeze–thaw erosion evaluation system. The occurrence of freeze–thaw erosion is caused by a variety of factors. In previous studies, most scholars preferred the method of hierarchical analysis to determine the degree of influence of evaluation indicators when constructing freeze–thaw erosion evaluation indicators. The principal component analysis method used in this study and the multiple covariance test enabled a more scientific generalization of the determination of weights. It was shown that the degree of freeze–thaw cyclicity is more accurately a freeze–thaw erosion sensitivity parameter.

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.