Temporal and Spatial Variation in Rainfall Erosivity in the Rolling Hilly Region of Northeast China

Abstract

The Rolling Hilly Region of Northeast China (RHRNEC) is a critical grain production area in China, and soil erosion is a major problem in this region. To determine spatial and temporal changes in rainfall erosivity (RE) in the RHRNEC and generate information useful for soil and water conservation, agricultural management, and ecological protection efforts, a RE index consisting of nine erosivity indices based on normal and extreme precipitation was established. The normal RE index (NREI) comprised annual RE (ARE), wet season RE (WRE), dry season RE (DRE), typical wet-month RE (TWRE), and typical dry-month RE (TDRE), and the extreme RE index set (EREI) comprised maximum one-day RE (RE × 1 day), maximum five consecutive days RE (RE × 5 day), storm RE (RE50), and maximum continuous RE (CRE). ARE, WRE, and TWRE decreased at relative rates of 2.5%, 2.9%, and 4.1%, respectively. By comparison, DRE increased at a non-significant relative rate of 6.3%, and all extreme RE indices decreased at a non-significant rate relative to 1981–2015 mean values. The future trends for all RE indices were predicted to be opposite to historical trends. The future trends and historical trends of all indices exhibited opposite patterns. RE gradually increased from north to south, and WRE, DRE, and all extreme RE indices were significantly negatively correlated with longitude, latitude, and altitude (p < 0.05). ARE, WRE, and TWRE showed increasing trends in the north and south and decreasing trends in the center. The findings are useful for soil and water conservation, especially for agricultural management and ecological protection.

1. Introduction

Soil erosion is a critical threat to global food security and the sustainability of ecosystems [1]. Unfortunately, this problem has been on the rise in recent years [2]. Soil erosion affects soil health and productivity by removing highly fertile topsoil and exposing the remaining soil, reducing crop yields and threatening food security [3]. Additionally, soil erosion is responsible for a significant decrease in the amount of organic carbon (OC) and nitrogen (N) that is associated with aggregates in agricultural soils, thereby accelerating soil degradation and GHG emissions from soil into the atmosphere to affect the global climate [4,5,6]. Soil erosion also degrades soil hydraulics and physical properties, which may increase the risk of drought for agroecosystems [7].

Rainfall erosion is the main type of soil erosion in the black soil area of northeastern China [8]. Rainfall erosivity (RE) refers to the potential capacity for rainfall-induced soil erosion, and it can comprehensively characterize the effect of rainfall, rainfall intensity, duration, and kinetic energy on soil erosion [9,10]. RE is a constituent factor of the universal soil loss equations USLE (Universal Soil Loss Equation) and RUSLE (Revised Universal Soil Loss Equation) and was initially formulated as the product of the total kinetic energy of a single rainfall event, E, and the intensity of that event’s maximum 30 min rainfall event, I30 [11,12,13,14]. This method permits accurate calculations of rainfall erosive power at a fixed location over a short period. To obtain RE over a larger area for a longer period, long-term experiments are needed to obtain long-term sequences of rainfall data. Due to the difficulty of obtaining these data [15], some researchers have proposed specific algorithms for RE, wherein regular precipitation data from meteorological stations are used to estimate RE; for example, RE can be calculated based on annual precipitation data [16], monthly precipitation data [17], both annual and monthly precipitation data [18,19], and daily precipitation data [20]. Zhang Wenbo’s daily RE model was used in this study [21]; this model has been widely used in China to calculate RE in different locations. Previous studies have shown that the results obtained by this model are highly correlated with actual RE and are highly accurate [22].

To clarify the effect of rainfall on soil erosion, several researchers from various countries have studied RE at a local scale. Due to climate warming, RE is increasing in the United States and some countries in Europe [23,24,25]; RE is expected to increase in the northeastern and southern regions of Brazil and decrease in the southeastern, central, and northwestern regions [26,27]. RE in the Alpine region of Australia is expected to increase during 2020–2039 and 2060–2079 by 2% and 8%, respectively [28]; Central Asia has experienced a non-significant increase in RE and higher rainfall is the main factor affecting spatial and temporal variability in RE [29]. Annual RE has decreased in Bangladesh, but it has increased during the monsoon season. The spatial and temporal distribution of RE in China varies. Average RE on the Tibetan Plateau decreases from the southeast to the northwest, and the average RE has significantly increased [30,31], which is associated with the recovery of vegetation in recent years and reduction in sand transport on the Loess Plateau [32]. The degree of rainfall erosion in South China varies from season to season, and the erosivity of annual and seasonal rainfall has increased [33]. The results of these studies provide important references for regional soil and water conservation.

Analysis of the daily precipitation in the northeast region from 1960 to 2011 has shown that the total rainfall in this region significantly varies; a non-significant decrease has been observed over the entire region [34]. Also, droughts and floods have increased in frequency after 2006, and precipitation events have become more extreme. The distribution of precipitation has become more uneven, which might lead to more frequent and stronger flooding and harm agricultural production in the northeast region [35]. The RE in the warm season of northeast China has decreased [8]; however, precipitation is expected to increase in the future, and the increase in RE in the northern part of the region is larger than that in the southern part of the region [36]. Studies on the spatial and temporal distribution of rainfall erosivity are often carried out on annual and monthly scales [37,38]. This paper analyses the rainfall erosivity in the northeast region on annual, wet and dry seasonal, monthly, and daily scales, as well as on heavy rainfall conditions, with a view to providing some theoretical basis for soil and water conservation work and agricultural farming measures in different scenarios. Several studies have examined patterns of precipitation, RE and soil erosion across the northeast region [35,39,40]. However, few studies have deeply investigated spatial and temporal variation in RE in the Rolling Hilly Region of Northeast China (RHRNEC) which is the core of the Northeast Black Soil Region and an important grain production base in China. The agricultural land in this region mainly includes sloped arable land with the following characteristics: long and slow slopes, undulating terrain, large catchment areas, concentrated runoff, and loose soil. The severity of soil erosion has been increasing because of the use of inappropriate cultivation practices. The middle parts of the slopes are mainly affected by erosion by water, which leads to the formation of a large number of scouring ditches and degrades fertile land [41]. The lower parts of the hillslopes are largely affected by sedimentation. This results in increases in the elevation of the riverbed and the siltation of reservoirs and dams, which poses safety risks.

Rainfall erosion in the RHRNEC mainly occurs during the wet season. Erosion is nearly always caused by heavy rainfall during the wet season; a RE index was developed in this study to describe erosion events caused by various rainfall events. The index comprises the normal RE index (NREI) and extreme RE index (EREI). The NREI includes annual RE (ARE), wet season RE (WRE), dry season RE (DRE), typical wet month RE (TWRE), and typical dry month RE (TDRE); the EREI includes four indices: maximum one-day RE in one year (RE × 1 day), maximum five consecutive days RE in one year (RE × 5 day), total storm rainfall (daily precipitation ≥ 50 mm) erosivity in one year (RE50), and maximum continuous RE in one year (CRE).

In this study, the daily rainfall from 1981 to 2015 at 79 meteorological stations in the study area and its neighborhood was used to calculate the RE index of the stations based on the daily RE model, and the climate tendency rate, Mann–Kendall (M-K) test model, sliding t-test, Hurst exponent, Pearson’s correlation, and inverse distance interpolation were used; the aim of this study was to characterize temporal and spatial variability in the RE index of the RHRNEC and explore the effects of factors due to location on soil and water conservation and ecological protection. Our objectives were to clarify spatial and temporal variability in the RE index, explore the effects of different location factors on RE, and provide information that could aid soil and water conservation, agricultural management, and ecological protection in the RHRNEC.

2. Materials and Methods

2.1. Study Area Description

The RHRNEC is located in the premontane terrace (42°9′–51°0′ N, 122°45′–128°40′ E) extending from the Greater and Lesser Xing’anling Mountains and the Changbaishan Mountains, and it encompasses most of the Songnen Plain and the northern part of the Liaohe Plain, which spans the three provinces Heilongjiang, Jilin, and Liaoning. The region experiences a temperate continental monsoon climate, with an average annual precipitation of approximately 500 mm, and most precipitation is concentrated in the summer months. The region’s landscape is defined by undulating hills, featuring gradual and extensive slopes, with slope lengths ranging from 500 to 2000 m and slope gradients varying between 1° and 6° [42,43].The distribution of black soil and black calcium soil in the region is concentrated, the terrain is undulating, the reclamation coefficient is high, the vegetation cover of farmland is low, and the frequent occurrence of heavy rainfall in summer leads to intense gully erosion, which degrades high-quality arable land and threatens food production [44].

2.2. Data Collection

The scope of the study area was obtained from the “National Soil and Water Conservation Plan (2015–2030)” issued by the Ministry of Water Resources, PRC. Vector boundary data for administrative districts were obtained from the 1:1000.000 version of the Basic Geographic Information Data (2021)” (https://www.webmap.cn, (accessed on 15 July 2023)). Daily precipitation data from 79 meteorological stations for 1981–2015 were obtained from the China National Meteorological Science Data Center (http://data.cma.cn, (accessed between 10 July 2023 and 19 July 2023)). The spatial distribution of the study area and meteorological data stations is shown in Figure 1. The exact longitude, latitude, elevation, and annual precipitation have been collected in Appendix A.

2.3. RE Indices

Rainfall in May–September was higher than that in all other periods according to 1981–2015 monthly average rainfall (45.1 mm); this period was thus classified as the wet season. Rainfall for January–April and October–December was less than that in other periods; this period was thus classified as the dry season. Rainfall was highest in July, which was considered a typical wet month; rainfall was lowest in January, which was considered a typical dry month (Figure 2). Annual rainfall erosivity (ARE), wet season rainfall erosivity (WRE), dry season rainfall erosivity (DRE), typical wet month rainfall erosivity (TWRE) and typical dry-month rainfall erosivity (TDRE) were used in this study to describe normal erosive rainfall events. According to the Chinese daily precipitation classification [45], daily precipitation data were classified into seven levels according to the amount of rainfall (

Table 1. Classification of daily rainfall.

Level	Daily Rainfall Amount
Drizzle	<0.1
Light rain	0.1~9.9
Moderate rain	10.0~24.9
Heavy rain	25.0~49.9
Torrential rain	50.0~99.9
Downpour	100.0~249.9
Heavy downpour	≥250.0

). Based on the extreme precipitation indices such as maximum 1-day precipitation (R × 1 day), maximum consecutive 5-day precipitation (R × 5 day), Annual count of days when PRCP>=nn mm (Rnn), and Maximum number of consecutive days with RR>=1 mm (CWD) defined by the Expert Team on Climate Change Detection and Indices (ETCCDI) [46], maximum one-day rainfall erosivity in a year (RE × 1 day), maximum consecutive five-day rainfall erosivity in a year (RE × 5 day), the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year (RE50), and maximum continuous rainfall erosivity in a year (CRE) were used in this study to describe extreme erosive rainfall events. The definitions of all indices are shown in

Table 2. Definition of normal and extreme rainfall indices.

Category	Index	Definition
Normal	ARE	Annual rainfall erosivity
	WRE	Wet season rainfall erosivity
	DRE	Dry season rainfall erosivity
	TWRE	Typical wet month rainfall erosivity
	TDRE	Typical dry-month rainfall erosivity
Extreme	RE × 1 day	Maximum one-day rainfall erosivity in a year
	RE × 5 day	Maximum five-day rainfall erosivity in a year
	RE50	The sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year
	CRE	Maximum continuous rainfall erosivity in a year

.

2.4. RE Calculation Procedure

We used the Richardson erosive agent model revised by Zhang [21,47].The equation is as follows:

$$R_i=\alpha \sum _{j=1}^k{\left(P_j\right)}^{\beta }$$

(1)

$$\beta =0.8363+\frac{18.144}{P_{d12}}+\frac{24.455}{P_{y12}}$$

(2)

$$\alpha =21.586{\beta }^{-7.1891}$$

(3)

where $R_i$ is the RE ($\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$) in the $i$th half-month; the annual RE value is obtained by the summation of all half-month RE values in a year; $k$ represents the total days in each $i$th half-month; the first 15 days of each month are used as the one half-monthly period and the remainder as the other half-monthly period, with the year divided into 24 periods. $P_j$ is the daily amount of erosive rainfall (>12 $\mathrm{m}\mathrm{m}$) on the $j$th day in the period of a half-month, and the $P_j$ value is effective when the rainfall is greater than 12 mm, otherwise, it is zero. $\alpha$ and $\beta$ are the parameters; $P_{d12}$ is the average daily amount of erosive rainfall ($\mathrm{m}\mathrm{m}$); and $P_{y12}$ is the average annual amount of erosive rainfall ($\mathrm{m}\mathrm{m})$. The daily RE values are summed to obtain monthly, seasonal, and annual RE for each station.

2.5. Data Statistics

2.5.1. Linear Regression

Magnitudes of long-term trends in the RE indices on an annual scale were calculated using linear regression.

$$x_i=a+b{t}_{i}i=\mathrm{1,2},\dots ,n$$

(4)

where $x_i$ represents the erosive power of rainfall for a sample size of $n$, $a$ denotes the regression constant, $b$ denotes the regression coefficient, and $10a$ denotes the climate trend rate.

2.5.2. C_v Value

$C_v$ represents the coefficient of variation, a metric that indicates the extent to which RE is altered. It can be calculated as follows:

$$C_v=\frac{\sigma }{\overline{x}}$$

(5)

where $\sigma$ is the standard deviation of RE, and $\overline{x}$ is the mean RE.

2.5.3. Mutation Point Detection

The Mann–Kendall (M−K) test and sliding t-test were used to identify abrupt changes in annual RE. The advantages of the Mann–Kendall (M−K) test include the lack of manual intervention and its high performance in quantitative analyses; however, these methods is not suitable for cases with multiple variants or variants at multiple scales. To ensure the accuracy of mutation tests, both the sliding t-test and M-K test were used to determine the year of occurrence of each mutation. The relevant literature contains information on the specific calculations for both tests [47,48,49].

2.5.4. Hurst Exponent

The Hurst exponent can provide insights into future trends of time series [50]. The computational steps have been described exhaustively in previous studies [51,52]. When H is equal to 0.5, the time series is a random sequence and is not sustainable in the future. However, when H is greater than 0.5, it implies positive sustainability, and the time series will continue to follow the current trend in the future. By contrast, when H is less than 0.5, it indicates negative sustainability, and the time series will follow the opposite trend in the future. The classification of the index is shown in

Table 3. Classification of the Hurst exponent.

Classification	H Range	Classification	H Range
Ⅰ	0.50 < H ≤ 0.55	−Ⅰ	0.45 < H ≤ 0.50
Ⅱ	0.55 < H ≤ 0.65	−Ⅱ	0.35 < H ≤ 0.45
Ⅲ	0.65 < H ≤ 0.75	−Ⅲ	0.25 < H ≤ 0.35
Ⅳ	0.75 < H ≤ 0.80	−Ⅳ	0.20 < H ≤ 0.25
Ⅴ	0.80 < H ≤ 1.00	−Ⅴ	0.00 < H ≤ 0.20

.

2.5.5. Pearson’s Correlation Analysis

Pearson correlation coefficients (R) were used to determine the correlations between the RE index and geographic factors. This technique assigns correlation values between −1 and 1, where −1 is a total negative correlation, 0 is no correlation, and 1 is a total positive correlation. The formula is as follows:

$$r=\frac{\sum _{i=1}^n \left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}{\sqrt{\sum _{i=1}^n \left(x_i-\overline{x}\right)\sum _{i=1}^2 {\left(y_i-\overline{y}\right)}^2}}$$

(6)

where $r$ is the correlation coefficient between the geographic factor and RE index; $x_i$ and $y_i$ are the RE index and geographic factor of the $i$th station, respectively; $\overline{x}$ is the mean value of the RE index; $\overline{y}$ is the mean value of the factor related to location; and $n$ is the number of weather stations.

2.5.6. Interpolation

Because inverse distance weighting (IDW) is more suitable for areas with low precipitation than other methods like Ordinary Kriging, Global Poynomial [53], this study utilized ArcGIS 10.2 (ESRI, Louisville, CO, USA) to perform inverse distance weighting on the individual indices of 79 stations, subsequently extracting the continuous distribution map of rainfall erosivity indices for the study area.

3. Results

3.1. Temporal Variation in RE Indices

3.1.1. Temporal Changes in RE

The annual RE in the RHRNEC decreased by −46.9 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h}·10\mathrm{a})$, with an average annual rainfall erosive power of 1870.9 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$.The trend in the regional annual rainfall erosive power and annual precipitation was basically the same, but the extreme value in annual rainfall erosive power and the extreme value of precipitation were observed in different years. The maximum value of annual rainfall erosive power in the RHRNEC was 3349.3 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$ in 1994 and the total precipitation in that year was 686.1 mm. The maximum precipitation was 693.4 mm in 2013, and the rainfall erosive power was 2652.6 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$. The main reason for the above finding is that although the total annual precipitation was small, the precipitation on a particular day or days in the year was large, which results in a large annual RE.

According to the 5a sliding average curve (Figure 3a), the trend in ARE generally consisted of two phases: a fluctuating downward trend before 2003 and a fluctuating upward trend after 2003. The WRE contributed 95% of the ARE, and WRE and ARE were highly correlated (

Table 4. Correlations between NREI. NREI, normal rainfall erosivity indices; ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity.

	ARE	WRE	DRE	TWRE	TDRE
ARE	1 *	0.9 *	0.8 *	0.9 *	0.6 *
WRE	0.9 *	1 *	0.8 *	0.8 *	0.4 *
DRE	0.8 *	0.8 *	1 *	0.7 *	0.6 *
TWRE	0.9 *	0.8 *	0.7 *	1 *	0.6 *
TDRE	0.6 *	0.4 *	0.6 *	0.6 *	1 *

* p ≤ 0.05.

). The trend in WRE was the same as that of ARE, but the decrease in WRE was greater than that in ARE, which was −52.4  $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h}·10\mathrm{a})$. Rainfall erosion was lower and freeze-thaw erosion was higher in the dry season [54]. With the exception of 1983 and 2012 when the DRE exceeded 250 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, the DRE of the other years ranged from 16.9 to 172.3 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, but the DRE showed a weak increasing trend. The $C_v$ was 0.7 and 4.6 for DRE and TDRE, respectively, and 0.3, 0.4, and 0.4 for ARE, WRE, and TWRE, respectively, suggesting that variation in RE was higher in the dry season than in the wet season. In Heilongjiang, all the rainfall erosivity indices showed a weakening trend except TDRE; in Jilin, only DRE showed an increasing trend, and both ARE and WRE showed a weakening trend; and the observed changes in ARE and WRE in Liaoning were opposite to those in Jilin. The above patterns were significant (

Table 5. Trends and $C_v$ values of NREI in Heilongjiang, Jilin, and Liaoning. $C_v$, the coefficient of variation; NREI, normal rainfall erosivity indices; ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity.

Index	Heilongjiang		Jilin		Liaoning
	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$
ARE	−43.9	0.3	−71.9	0.3	14.3	0.4
WRE	−38.5	0.3	−82.6	0.3	−32.5	0.5
DRE	−5.4	0.8	10.7	0.8	46.8	0.9
TWRE	−15.2	0.4	−78.8	0.5	44.5	0.8
TDRE	0.0	0.0	0.0	4.4	0.0	4.7

).

.

The correlation coefficients between the extreme RE indices were greater than 0.95 (p < 0.05) (

Table 6. Correlations between EREI. EREI, extreme rainfall erosivity indices; RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

	RE × 1 day	RE × 5 day	RE50	CRE
RE × 1 day	1 *	0.97 *	0.9 *	0.98 *
RE × 5 day	0.97 *	1 *	0.98 *	0.99 *
RE50	0.95 *	0.98 *	1 *	0.97 *
CRE	0.98 *	0.99 *	0.97 *	1 *

* p ≤ 0.05.

); the inter-annual changes were similar (Figure 3b), and the overall trend was decreasing. The change was divided into three stages. The first stage was observed from 1981 to 1996, and the EREI showed a fluctuating upward trend. The second stage was from 1996 to 2006, and the EREI showed a fluctuating downward trend. The third stage was from 2006 to 2015, and the EREI showed a fluctuating upward trend. The highest EREI values were observed in 1994. The $C_v$ of RE50 was 0.5, which was higher than that of RE × 1 day, RE × 5 day, and CRE, and changes in RE50 were more pronounced than changes in RE × 1 day, RE × 5 day, and CRE. The EREI of Heilongjiang and Jilin showed a decreasing trend, and the EREI of Liaoning showed an overall increasing trend; however, none of the trends were significant, and the fluctuations were large (

Table 7. Trends and $C_v$ values of EREI in Heilongjiang, Jilin, and Liaoning. $C_v$, the coefficient of variation; EREI, extreme rainfall erosivity indices, RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

Index	Heilongjiang		Jilin		Liaoning
	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$	Trend $\mathbf{M}\mathbf{J}·\frac{\mathbf{m}\mathbf{m}}{{\mathbf{h}\mathbf{m}}^2·\mathbf{h}·10\mathbf{a}}$	${\mathit{C}}_{\mathit{v}}$
RE × 1 day	−8.1	0.3	−16.6	0.4	31.0	0.6
RE × 5 day	−17.3	0.3	−28.7	0.3	31.0	0.6
RE50	−11.0	0.5	−30.2	0.7	56.9	0.9
CRE	−8.9	0.3	−23.2	0.4	53.3	0.7

).

3.1.2. Identification of RE Index Mutation Points

The M-K mutation test and sliding t-test were used to jointly analyze the year-by-year ARE indices in RHRNEC (Figure 4 and Figure 5). ARE and WRE were mutated in the late 1980s and weakened after the mutation point; DRE and TERE were mutated in 2002 and strengthened after the mutation point.

No significant mutation point was observed for RE × 1 day; RE × 5 day and CRE were mutated in the late 1990s; RE50 was mutated in 1988, and it exhibited a fluctuating upward trend prior to the mutation point and a fluctuating downward trend thereafter.

3.1.3. The Hurst Exponent of RE Indices

The R/S method was used to analyze the trend persistence of RE indices in the RHRNEC from 1981 to 2015 to obtain the Hurst exponent of each index. The Hurst exponent of each RE index was less than 0.5 (

Table 8. The Hurst exponent of REI. REI, rainfall erosivity indices; NREI, normal rainfall erosivity indices; ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity; EREI, extreme rainfall erosivity indices, RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

Category	Index	Hurst Exponent	Classification
NREI	ARE	0.33	−Ⅱ
	WRE	0.33	−Ⅱ
	DRE	0.44	−Ⅲ
	TWRE	0.41	−Ⅲ
	TDRE
EREI	RE × 1 day	0.38	−Ⅲ
	RE × 5 day	0.39	−Ⅲ
	RE50	0.39	−Ⅲ
	CRE	0.38	−Ⅲ

); the future and historical trends in ARE showed opposite patterns. The Hurst exponents of ARE and WRE were lower than 0.35, indicating that their future trends are expected to be opposite historical trends and that the intensity of antipersistence is higher. The future trends of DRE, TWRE, and EREI were weakly antipersistent. The ARE, WRE, and EREI in Heilongjiang and Jilin showed strong inverse persistence and are about to show an increasing trend (

Table 9. The Hurst exponent of REI in Heilongjiang, Jilin, and Liaoning. REI, rainfall erosivity indices; NREI, normal rainfall erosivity indices; ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity; EREI, extreme rainfall erosivity indices, RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

Category	Index	Heilongjiang	Jilin	Liaoning
NREI	ARE	0.30	0.33	0.31
	WRE	0.30	0.32	0.32
	DRE	0.42	0.40	0.44
	TWRE	0.39	0.34	0.40
	TDRE
EREI	RE × 1 day	0.35	0.32	0.32
	RE × 5 day	0.33	0.34	0.35
	RE50	0.35	0.34	0.30
	CRE	0.29	0.31	0.35

); the EREI index in Liaoning has strong inverse persistence and is predicted to show a weakening trend in the future with a high degree of persistence in light of its increasing trend based on historical precipitation data (Table 7 and Table 9).

3.2. Characteristics of Spatial Variation in REI

3.2.1. Spatial Distribution of REI

The spatial distribution of REI in the region was obtained using inverse distance interpolation and the REI of each site in RHRNEC from 1981 to 2015 (Figure 6 and Figure 7). All the REI increased from the northeast to southwest, and large spatial differences were observed. REI were significantly negatively correlated with latitude (p < 0.05), with correlation coefficients around −0.7. With the exception of ARE, TWRE, and TDRE, significant negative correlations (p < 0.05) of other indices with longitude and elevation were observed, with correlation coefficients ranging from −0.43 to −0.21 (

Table 10. Correlations between REI and geographic factors. ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity; RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

	ARE	WRE	DRE	TWRE	TDRE	RE × 1 Day	RE × 5 Day	RE50	CRE
Lat	−0.7 *	−0.7 *	−0.7 *	−0.5 *	−0.4 *	−0.7 *	−0.7 *	−0.7 *	−0.7 *
Lon	−0.2	−0.4 *	−0.4 *	−0.2	−0.2	−0.4 *	−0.4 *	−0.3 *	−0.4 *
Alt	−0.1	−0.3 *	−0.3 *	0	0.1	−0.3 *	−0.3 *	−0.3 *	−0.3 *

* p ≤ 0.05.

). The centers of the highest NERI were all located in Liaoning. The centers of the lowest values were located at Songyuan and Qianguo stations in Jilin. The range of the erosive power of the average annual rainfall was 1306.4–2800 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, and the ranges of WRE and TWRE were 1227.9–2687.6 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$ and 502.2–1006.3 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, respectively. WRE and TWRE were the main components of ARE because precipitation in the northeast occurs mainly during the wet season, and extreme precipitation events were frequent in July, when susceptibility to extreme soil erosion is high.

3.2.2. Spatial Distribution of Trends in REI

To analyze trends in RE in the RHRNEC, the climatic propensity rate of each RE index was calculated for all stations from 1981 to 2015, and the climatic propensity rate of each RE index was interpolated using ArcGIS 10.2; its spatial distribution was plotted (Figure 8). In the RHRNEC, the number of sites showing increases was slightly larger than that of the number of sites showing decreases, with the exception of DRE, and the number of sites showing increases was lower than the number of sites showing decreases for each of the other indices. Spatial variation in ARE, WRE, and TWRE was similar; specifically, increases in these variables were observed in the north and south, and decreases were mainly observed in the center. Soft black soil was predominant in the north, and extreme rainfall was the main cause of erosion.

In Heilongjiang, 68.2% of the sites had decreasing DRE, and the decreases in DRE were significant (p < 0.05) at three of these sites (

Table 11. Percentage of sites with upward and downward trends in each rainfall erosivity index. NREI, normal rainfall erosivity indices; ARE, annual rainfall erosivity; WRE, wet season rainfall erosivity; DRE, dry season rainfall erosivity; TWRE, typical wet month rainfall erosivity; TDRE, typical dry-month rainfall erosivity; EREI, extreme rainfall erosivity indices, RE × 1 day, rainfall erosivity maximum one-day rainfall erosivity in a year; RE × 5 day, maximum five-day rainfall erosivity in a year; RE50, the sum of storm (precipitation ≥ 50 mm) rainfall erosivity in a year; CRE, maximum continuous rainfall erosivity in a year.

Category	Index	RHRNEC		Heilongjiang		Jilin		Liaoning
		Increase	Decrease	Increase	Decrease	Increase	Decrease	Increase	Decrease
NREI	ARE	40.5	59.5	47.7	52.3	26.1	73.9	50.0	50.0
	WRE	39.2	60.8	50.0	50.0	26.1	73.9	25.0	75.0
	DRE	51.9	48.1	31.8	68.2	69.6	30.4	100.0	0.0
	TWRE	43.0	57.0	50.0	50.0	17.4	82.6	87.5	12.5
	TDRE	5.1	7.6	0.0	0.0	8.7	13.0	12.5	12.5
EREI	RE × 1 day	46.8	53.2	45.5	54.5	43.5	56.5	62.5	37.5
	RE × 5 day	45.6	54.4	50.0	50.0	34.8	65.2	75.0	25.0
	RE50	46.8	53.2	52.3	47.7	39.1	60.9	62.5	37.5
	CRE	48.1	51.9	50.0	50.0	39.1	60.9	87.5	12.5

); the number of sites with increasing and decreasing indices was basically the same. The RE indices in the central region were mainly increasing, whereas those in the northwestern and southeastern regions were mainly decreasing. The stations with the largest changes in ARE, WRE, and EREI in the RHRNEC were all located in Heilongjiang (Table 11). The ARE in Jilin showed a decreasing trend, except Yushu. The DRE in Jilin Province showed a decreasing trend in the northwestern part of the province, and the DRE in the south-central part of the province showed an increasing trend. The station with the largest decrease in TWRE in the study area was observed at Gongzhuling Station in Jilin Province, and the rainfall erosive power in a typical wet month was 905.0 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, with a decrease of −266.9 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h}·10\mathrm{a})$. An increasing trend in the DRE was observed for all stations in Liaoning Province (Table 11). The station with the largest increase was Kangping Station in Liaoning Province; the annual mean DRE was 150.4 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h})$, and the increase in annual mean DRE was 57.3 $\mathrm{M}\mathrm{J}·\mathrm{m}\mathrm{m}/({\mathrm{h}\mathrm{m}}^2·\mathrm{h}·10\mathrm{a})$. A significant (p < 0.05) increase was observed for one station. TWRE showed a decreasing trend in eastern Liaoning, and other areas showed an increasing trend. In Liaoning Province, there are more sites with increasing trends in EREI than those with decreasing trends.

4. Discussion

Erosive precipitation in the RHRNEC affected by the monsoon mainly occurs from May to September, which is classified as the wet season in this paper [55], and the ARE and WRE of the RHRNEC showed non-significant decreasing trends [8]; according to R/S analysis, rainfall erosive power is expected to increase in the future, which is consistent with changes predicted through multiple meteorological scenario models [56]. Due to warm winters, the DRE erosive power in the dry season showed an increasing trend, which is consistent with the results of a previous study [57]. One problem that cannot be overlooked is the low density of meteorological stations in the north, which poses a challenge for detailed analyses of RE. The spatial distribution of EREI gradually increased from northwest to southeast and decreased with elevation, longitude, and latitude [34], and the EREI showed a weakening trend across the whole region. However, the number of stations with an increasing trend and the number of stations with a decreasing trend were basically the same in each subregion. The overall trend is derived from averaging the meteorological data of each station, and the presence of a few stations with relatively large changes in amplitude can affect the overall trend.

Several studies have aimed to analyze the effect of precipitation data on RE calculations at different time scales [58,59]. These studies have revealed that the accuracy of RE calculations from precipitation data is more accurate at smaller time scales. However, when the study area is vast, precipitation data are often incomplete at short time scales, which leads to a larger margin of error in RE calculations. The use of daily rainfall as a calculation factor is appropriate for the following reasons. (1) It provides insights into the overall erosion trend. Although daily precipitation data do not fully reflect the spatial and temporal distribution of rainfall intensity [22,58], daily precipitation data over a longer period can shed light on the overall erosive power of rainfall in a certain region, thus providing insights into the overall erosion trend. This information is important for assessing the degree of erosion in different areas, quantifying geographical variability, and comparing precipitation erosion risks [60,61]. (2) Precipitation is a widely used parameter in meteorological observations, and it is one of the most common measurement parameters. Relevant precipitation data can be obtained globally with ease, and they are highly reliable and available [62]. This makes it practically feasible and useful for establishing a RE index based on daily precipitation.

The causes of soil erosion can be categorized as natural or anthropogenic factors. Extreme rainfall represents a primary natural factor leading to severe soil erosion. In contrast, anthropogenic factors such as unsustainable over-farming and over-grazing have emerged as prevailing concerns due to expanding populations and heightened demands for food production [1]. These activities contribute to long-term soil degradation and exhaustion, resulting in reduced fertility, water retention, and nutrient content, ultimately impacting plant growth [63]. The development of a rainfall erosivity index holds significant importance for local soil and water conservation, agricultural management, and ecological protection. It serves as a valuable tool for assessing the potential extent and spatial distribution of rainfall erosion, aiding in the formulation of appropriate conservation measures, such as constructing terraces, restoring vegetation, and establishing shelter belts to minimize soil erosion and safeguard soil resources [64,65]. Additionally, it facilitates rational farmland utilization, crop cultivation methods, and farming practices, consequently reducing the risk of soil erosion and enhancing farmland productivity and sustainability [66]. Furthermore, this index provides a foundation for identifying the ecological impacts of soil erosion, promoting vegetation growth, and restoring soil and water conservation functions within ecosystems affected by severe erosion [20,67].To effectively prevent and control soil erosion, several measures can be implemented. These measures will also continue to be refined in the future to make the prevention and control of soil erosion more effective: (1) Vegetation restoration: planting trees, herbaceous plants, and shrubs can bolster soil organic matter, improve soil structure, enhance erosion resistance, and augment water retention capacity, thereby reducing the impacts of wind and water erosion [68]. (2) Land consolidation: modifying the shape, slope, and direction of the land through the construction of terraces, ditches, and dams lowers water flow velocity, diminishes impulse, and amplifies water infiltration and utilization [69,70]. (3) Farming management: implementing sustainable farming practices, including strategic crop planting, harvesting, and rotation, helps maintain soil fertility and activity while minimizing bare and damaged soil, for example, intercropping, such as using ridges with groundnuts, is the most effective method to reduce erosion in cocoa land use in Krueng Sieumpo, Indonesia [71]. Conservation tillage measures and intercropping can enhance soil coverage and aeration, as exemplified by China’s “Lishu Model” [72]. (4) Legislation and Regulation: enacting and enforcing laws and regulations effectively regulate and supervise land use and protection. They serve to penalize and prevent unreasonable land reclamation, mining, and grazing, as evidenced by China’s black land protection law aimed at safeguarding black land from detrimental activities.

5. Conclusions

We made several findings based on the 1981–2015 daily rainfall data from 79 meteorological stations in the RHRNEC and the spatial and temporal variability in ARE. The ARE, WRE, and TWRE in the RHRNEC showed a weakening trend with gentle fluctuations and ARE and WRE experienced a sudden change in the late 1980s from an upward to a downward trend. The DRE showed an increasing trend with more dramatic fluctuations; a sudden change from a decreasing to an increasing trend was observed in 2002. The EREI all showed a weakening trend with fewer fluctuations; a mutation point of RE × 5 day was identified in the 1990s, and a mutation point of RE50 was identified in 1988; changes from an upward to a downward trend were observed for both RE × 5 day and RE50. The results of this study are similar to previous studies on rainfall erosivity in the northeast, but there are some differences from existing studies due to the time period of the study and the resolution of the data [8,36]. In Heilongjiang, all RE indices showed a decreasing trend; in Jilin, RE indices showed a decreasing trend in all cases, with the exception of DRE. In Liaoning, WRE showed a decreasing trend, and ARE, DRE, TWRE, and all EREI showed an increasing trend. Future trends were opposite to historical trends, and strong antipersistence was observed in ARE, WRE, and EREI.

The NREI in the RHRNEC showed an increasing trend from north to south; the center of low values was located in the western part of Jilin, and the center of high values was located in Liaoning. All EREI were significantly negatively correlated with latitude; the EREI of extreme rainfall gradually increased from northwest to southeast, and the RE × 5 day was significantly negatively correlated with latitude, longitude, and altitude. The DRE showed a decreasing trend in the northern part of the RHRNEC and an increasing trend in the south-central part, and ARE, WRE, TWRE, and EREI showed an increasing trend in most parts of Heilongjiang and Liaoning and a decreasing trend in Jilin.