Spatiotemporal Trends and Variation of Precipitation over China’s Loess Plateau across 1957–2018

Abstract

Better understanding of the spatiotemporal characteristics of precipitation is essential in developing the best management practices for ecological restoration and soil erosion control on China’s Loess Plateau, an arid and semiarid region with severe soil erosion. This study aimed to explore the spatiotemporal trends of precipitation using long-term precipitation data from 1957 to 2018 from the 100 national standard meteorological stations across the Loess Plateau. The nonparametric Mann–Kendall statistical test and geospatial interpolation were used to detect the trends and to analyze spatial patterns of annual and seasonal precipitation. Wavelet analysis was applied to examine periodical variation across the plateau. The results reveal that regional annual precipitation over the Loess Plateau decreased during the 62 years of the study at a mean rate of −1.05 mm/10 years (p > 0.1). The changes in annual precipitation showed a periodical fluctuation with an increasing trend from 1957 to 1969, a decreasing trend from 1970 to 1999, and an increasing trend again in the first 18 years of the 21st century. The annual precipitation decreased in all eight sub-annual periods except for winter. Spatially, a decreasing trend occurred in the southern and eastern parts of the Loess Plateau, whereas a slight increase existed in the northwest in all periods. The decrease in six stations was statistically significant (p < 0.05), and a significant increase occurred in four stations (p < 0.1). These changes can be explained by an evident southward shift of the precipitation isohyets especially for 350 mm, 450 mm and 550 mm from the 1960s to the 1990s, and a clearly northward shift after the 1990s. Findings from this study facilitate an understanding of the spatial temporal trends of precipitation so appropriate countermeasures can be developed for effective vegetation restoration and soil erosion control across the Loess Plateau.

1. Introduction

With global warming, precipitation in China over the past 50 years has been well documented to have a slightly increasing trend, but the climatic variables show considerable spatial variation and uncertainty [1,2]. Global warming can simultaneously intensify the hydrological cycle at local and regional scales, especially in arid and semi-arid regions such as the Loess Plateau in northern China [3,4]. The distribution of precipitation can be consequently altered and may have great impacts on the regional ecosystems [5]. Understanding the trend and the periodic variation of precipitation have important implications to ecological restoration, soil erosion assessment and water resource regulation in the arid and semi-arid area.

Numerous studies on precipitation have been implemented on the Loess Plateau [6,7,8,9,10,11,12,13,14,15]. Ref. [16] showed that a signal of climate transition from warm-dry to warm-humid was detected in northwest China, and the transformation may be on a century time scale, but it was not yet possible to determine the speed and extent of its change. Ref. [9] analyzed the annual precipitation across the Loess Plateau using 214 meteorological stations revealing that about 83% of the total stations had a decreasing trend. Ref. [17] reported that the annual rainfall decreased gradually from southeast to northwest with great spatial variability over the Loess Plateau. Ref. [11] reported that annual precipitation showed a decreasing trend from 1961 to 2014 (p > 0.05) and the region with the largest decreasing rate was in the southeastern Loess Plateau, whereas the changes in the northwestern Loess Plateau were not obvious. Ref. [18] found that there was no significant trend of annual precipitation on the Loess Plateau and the climate tended to be humid in the western part (approximately 7.98% of the total area) from 1901 to 2014 by using the delta downscaling method. Ref. [14] found the annual extreme precipitation from seven indices (including maximum one-day precipitation, maximum five-day precipitation, erosive precipitation, heavy precipitation, rainstorm, very wet day precipitation and extremely wet day precipitation) all exhibited decreases on the Loess Plateau. These previous studies were useful to understand the large-scale change in precipitation of the Loess Plateau before 2010. However, in the last 10 years, several extreme rainstorms with a return period of once in a century occurred in some places on the Loess Plateau (e.g., 2012, 2013 and 2017), which resulted in serious flooding and soil erosion and consequently catastrophic disasters for the local residents. Thus, it is urgent and important to know the new patterns and trends of precipitation changes over the Loess Plateau using longer and more recent data.

In the study of climate change, the nonparametric Mann–Kendall (MK) method is widely used to detect the significance of monotonic trends in climatological time series [19,20]. Due to its fine structure in precipitation time series, the application of wavelet transform for climate variability assessment and ecological pattern analysis has been widely studied [21,22]. Ref. [23] analyzed the correlation between the time series of temperature in Tomsk and solar activity using the wavelet transform method and found a significant correlation between the periodicities in the time series of temperature and individual solar activity indexes. Ref. [24] used the wavelet transform method to study the temporal variability of precipitation of five precipitation series in northern California, U.S.A. in the past 96 years and found that the dominant period is about 16 years in the area. Additionally, this method was used to study the characteristics of precipitation changes in Northeast China [25]. The trends of precipitation, especially its periodic variation, are of great significance for understanding the interaction among atmosphere, vegetation, soil and hydrology on the Loess Plateau.

Water resources are scarce in the Loess Plateau, most of which covered arid and semi-arid area, with the most severe soil erosion in the world [26]. To reduce the source of sediment in the downstream Yellow River, many soil and water conservation practices have been introduced since 1949 including the conversion of slope farming land to forest and grassland or ‘Grain for Green’ project implemented since 1999, resulting in changes in surface hydrology [27]. The change of precipitation in space and time is expected to affect the water discharge and sediment yield by influencing the vegetation distribution and community composition [28]. The spatiotemporal trend of precipitation especially for the last 60 years over the Loess Plateau can help in understanding the regional vegetation restoration and sediment reduction, however, there is still a knowledge gap in understanding these recent trends [29]. Therefore, we conducted this study to (1) assess the trend and spatial distribution of annual and eight sub-annual precipitation series over the Loess Plateau, (2) determine how precipitation isohyets shift on the Loess Plateau during the study period, and (3) identify the period characteristics of annual precipitation on the Plateau. The findings from this study will help us to understand the climate impact on the local ecological environment and develop adaptation measures to these changes.

2. Study Site and Data Source

2.1. Study Site

The Loess Plateau is bounded by 100.8°–114.6° E, 33.7°–41.3° N, covering approximately 6.24 × 10⁵ km². Most parts of the Loess Plateau range from 800 to 2000 m a.s.l. (Figure 1a,b). The soil is mainly wind-deposited loess with an average thickness of approximately 100–200 m [30]. Precipitation on the Loess Plateau shows a clear zonal variation with a high value in the southeast and a low value in the northwest, about 440 mm per year on average (Figure 1c). However, the variation coefficient ($C_v$) of annual precipitation in this area is characterized by an opposite change trend compared to the precipitation, and the $C_v$ in the northwestern part of the Loess Plateau is approximately two times greater than that in the southeast (Figure 1d).

The precipitation is highly uneven in seasons affected by the East Asian monsoons. About 70–80% of the precipitation was concentrated from June to September, and the intense rainfall is the main cause of runoff and soil erosion in this area. The total area affected by soil erosion was 4.3 × 10⁵ km² and 65% of that area (2.8 × 10⁵ km²) suffered severe erosion [26,31]. More than 90% of the sediment in the lower reaches of the Yellow River was sourced from the Loess Plateau. The area with the mean annual soil erosion modulus between 5000 and 10,000 t·km⁻²·a⁻¹ is generally covered by the annual precipitation of 350–450 mm due to the intense rainstorms and wind erosion there [26].

2.2. Data Source and Processing

In accordance with the data in [29], a total of 100 meteorological stations comprising 62 years of monthly precipitation recordings in the period of 1957–2018 were analyzed. The Loess Plateau and the adjacent areas cover 68 and 35 national standard meteorological stations, respectively. The monthly precipitation observation data of stations that were obtained from the China meteorological data sharing network (http://data.cma.cn/, accessed on 10 November 2022) were checked and compiled to the seasonal and annual total.

In this study, the basic information of the meteorological stations (station name, longitude and latitude coordinates, elevation and precipitation data) was input into ArcGIS to create a point shape file with attribute information. The annual precipitation data of most meteorological stations passed the normal distribution test (p < 0.05); therefore, the ordinary kriging interpolation method was applied for spatial interpolation. The missing values of annual and monthly precipitation at partial meteorological stations were interpolated and extended to 1957 using the regression analysis method. Simultaneously, the anomalous values were detected and eliminated.

The regional precipitation estimated from the 100 meteorological stations for each year and the long-term average over the Loess Plateau during 1957–2018 were obtained by the ordinary kriging interpolation method. The isohyets of 250 and 450 mm were widely used to divide the climate zones, such as the arid, semi-arid and semi-humid regions over the Loess Plateau by considering annual, seasonal distribution of rainfall as well as actual evapotranspiration and drought index [29]. Therefore, the shifts of isohyets including 250 and 450 mm were examined in decadal scale by using surface analysis and resampling tools.

The East Asian summer monsoon index (EASMI) is a good indicator of climate change and can reflect the phased characteristics of climate change in China. Previous research [32] found that EASMI began to decline in the late 1960s and again increased in the late 1990s. Accordingly, three stages were identified, namely stage Ⅰ from 1957 to 1969, stage Ⅱ from 1970 to 1999, and stage Ⅲ from 2000 to 2018.

We further separated each year into eight periods to better detect and describe the trends of precipitation based on [29]. These periods are listed in

Table 1. The eight sub-annual periods used in this study.

Number	Name of Periods	Range of Periods
1	Spring	March to May
2	Summer	June to August
3	Autumn	September to November
4	Winter	December to the following February
5	Wet season	May to October
6	Dry season	November to the following April
7	Early flood period (EFP)	May to July
8	Late flood period (LFP)	August to October

.

3. Methods

3.1. Mann–Kendall Trend Test

The nonparametric MK method was chosen [19,20] to detect the significance of monotonic trends in hydrological and climatological time series considering its simplicity, reliability and ability to handle missing values and extreme values. It is one of the most appropriate time series trend analysis methods extensively used in the world [33,34].

The null hypothesis $H_0$ is the observed sample data. The values $x_i$($i=1,2,3......n$) are independent of each other and identically distributed. The alternative hypothesis $H_1$ indicates a monotonic trend in $x_i$. The Mann–Kendall test statistic $S$ is derived as follows:

$$S={\displaystyle \sum _{k=1}^{n-1}{\displaystyle \sum _{j=k+1}^n\mathrm{sgn}(x_j-x_k)}}$$

(1)

$$\mathrm{sgn}(x_j-x_k)=\{\begin{array}{ll}1& x_j-x_k>0\\ 0& x_j-x_k=0\\ -1& x_j-x_k<0\end{array}$$

(2)

where $x_j$ and $x_k$ are the statistical values ($j>k$), respectively. The n indicates the record length of the data series and $\mathrm{sgn}(x_j-x_k)$ is the return function. For the cases where $n\ge 10$, the statistic $S$ denotes normal distribution and $E(S)=0$. The variances are calculated based on the following formula:

$$VAR(S)=\frac{1}{18}\left[n(n-1)(2n+5)-{\displaystyle \sum _{p=1}^q{t}_{}(t-1)(2t+5)}\right]$$

(3)

where $q$ and $t$ are the number of tied groups and data values, respectively. The standard test statistic $Z$ is calculated as:

$$Z=\{\begin{array}{ll}\frac{S-1}{\sqrt{VAR(S)}}& \mathrm{if} S>0 \\ 0& \mathrm{if} S=0 \\ \frac{S+1}{\sqrt{VAR(S)}}& \mathrm{if} S<0 \end{array}$$

(4)

where the statistical value $Z$ possesses the characteristics of standard normal distribution. The $H_0$ will be rejected if $\left|Z\right|$$\ge Z_{1-\alpha /2}$ at the level of significance in bilateral trend detection. A positive $Z$ value denotes an upward trend and a negative $Z$ value denotes a downward trend. When the $\left|Z\right|$ ≥ 1.28, 1.64, and 2.32, it means passing the significance tests of 90%, 95%, and 99%.

3.2. Sen’s Slope Estimator

The Sen’s estimator can be used to estimate the slope of detected data under the condition that the meteorological and hydrological elements exhibit a linear trend [35]. Fortunately, the estimator is insensitive to abnormal values and can accurately calculate the magnitude of a trend in time series [36]. The $f(t)$ is given by:

$$f(t)=Qt+B$$

(5)

In the given Equation (5), $Q$ indicates the magnitude of the trend and $B$ denotes a constant. Estimated slope $Q$ of all detected data are calculated using the following formula:

$$Q_i=\frac{x_j-x_k}{j-k}; i=1, 2, ···, N$$

(6)

where $x_j$, $x_k$ denote the data values ($j>k$). In case there are n values, $x_j$ during the study period, then $N=n(n-1)/2$ and slope estimates, $Q_i$ will be calculated. The median $Q_i$ of slope depends on the following situation:

$$Q_i=\{\begin{array}{ll}{Q}_{\frac{N+1}{2}}& \mathrm{if} N \mathrm{is} \mathrm{odd}\\ \frac{1}{2}\left(Q_{\frac{N}{2}}+Q_{\frac{N+2}{2}}\right)& \mathrm{if} N \mathrm{is} \mathrm{even}\end{array}$$

(7)

3.3. The Variation Coefficient of Annual Precipitation

The variation coefficient ($C_v$) of annual precipitation is an index used to denote the volatility of the precipitation at the annual scale which has a high relation with annual precipitation and elevation [2,37]. The greater the $C_v$, the more obvious the fluctuation of annual precipitation with a smaller annual precipitation. The $C_v$ is determined as follows:

$$C_v=\frac{S}{\overline{x}}\times 100\%$$

(8)

where $S$ and $\overline{x}$ denote the standard deviation and the mean value of selected data series, respectively.

3.4. The Wavelet Analysis

The Morlet wavelet in Matlab wavelet analysis toolbox was used as the generating function to analyze the periodic variations of annual precipitation over the Plateau. Its advantages in both the local time and frequency domain showing the fine structure of precipitation time series are noticeable [21]. It provides a new way to analyze the multiple time scales variation of hydrological and meteorological elements. The function is:

$$\psi (t)=e^{ict}{e}^{-t^2/2}$$

(9)

where $i$ denotes unreliable number and $c$ is a constant.

Wavelet transformation is essential to wavelet analysis. The characteristics of wavelet change in the wavelet change domain are acquired by analyzing wavelet transformation parameter graph. The wavelet transformation of time series of detected data $f_t\in L^2(R)$ is determined as:

$$W_f(a,b)={\left|a\right|}^{-\frac{1}{2}}{\displaystyle \int \begin{array}{l}+\infty \\ -\infty \end{array}}f(t)\overline{\psi }(\frac{t-b}{a})dt$$

(10)

where $W_f(a,b)$ means wavelet transformation coefficient, $a$ indicates the length of wavelet period and $b$ denotes the transformation time [23,38].

Wavelet variance shows the distribution of signal fluctuating energy in precipitation series and each significant period can be detected in each peak value. The existing main period can be conveniently diagnosed in the process of precipitation change to the typical meteorological stations. Wavelet variance can be calculated as follows [22].

$$Var(a)=\frac{1}{n}{\displaystyle \sum _{b=1}^n{\left|W_f(a,b)\right|}^2}$$

(11)

where $n$ denotes the number of sample data and ${\left|W_f(a,b)\right|}^2$ means module square of wavelet transformation coefficient.

4. Results

4.1. Trend of Annual Precipitation over the Loess Plateau

The mean annual precipitation over the Loess Plateau during 1957–2018 was 440 mm, which was slightly greater than 434 mm from 1957 to 2009 [29]. The annual precipitation over the Loess Plateau showed an extremely slight decreasing trend (p > 0.1) and possessed a declining rate of −1.05 mm/10 a, which approximately accounted for 0.024% of the mean annual precipitation on the Loess Plateau. The trend of annual precipitation was consistent with the results of previous research [9,11,29,39], but with some differences in magnitude of decrease.

The annual precipitation showed a significant fluctuation with 470, 441, 430, 411, 419, and 465 mm corresponding to the periods of 1957–1969, 1970s, 1980s, 1990s, 2000s and 2010–2018, respectively. Based on the fluctuation characteristics, annual precipitation can be divided into three stages (

Table 2. The stage variation of annual precipitation across the Loess Plateau, China during 1957–2018.

Stage	Period	Mean (mm)	Maximum (mm)	Minimum (mm)	${\mathit{C}}_{\mathit{v}}$
I	1957–1969	470	647	304	0.20
II	1970–1979	441	513	330	0.12
	1980–1989	430	504	334	0.13
	1990–1999	411	483	315	0.12
III	2000–2009	419	559	375	0.12
	2010–2018	465	512	403	0.07

). Stage Ⅰ (1957–1969): the mean annual precipitation reached the maximum value and the variation coefficient in this stage was also the largest, 0.20, implying a high fluctuation rate of annual precipitation. Stage Ⅱ (1970–1999): precipitation began to decline since 1970s and fell to the lowest level in the late 1990s. The variation coefficient is significantly lower than that of the first stage. Stage Ⅲ (2000–2018): an increasing trend occurred in recent 20 years of the 21st century. In this stage, the fluctuation range of annual precipitation was the lowest with $C_v$ of 0.07. Table 2 also shows that the annual precipitation during 1957–2018 exhibited a periodic fluctuation of increasing-decreasing-increasing pattern, while $C_v$ exhibited a stable decreasing trend due to the expansion of the range between maximum precipitation and minimum precipitation on the Loess Plateau.

Figure 2 shows the spatial trend of annual precipitation across the Loess Plateau. During 1957–2018, there were 65 meteorological stations within and around the Plateau exhibiting a negative trend, and six of them were statistically significant (p < 0.05). Nevertheless, 38 meteorological stations covering the Plateau and the adjacent areas exhibited a positive trend with four stations statistically significant on the Plateau (p < 0.1). From Figure 2, the area with an increasing rate of 0.8–5 mm/10 a during the study period was primarily situated in the northwestern part of the Plateau. However, a much greater increasing rate of 5–15 mm/10 a was detected in northeastern Qinghai Province that would lead to a more obvious ecological restoration process. The areas with a significant decreasing trend (p < 0.05) are mainly located at places like Wutai Mountain station and Hua Mountain station, where the annual precipitation was detected with a decreasing rate of −30 to −44 mm/10 a. Overall, 34% of the total area of the Plateau (about 2.18 × 10⁵ km²), including 45 stations, exhibited an increasing trend. Nevertheless, the area covered by a decreasing trend was mainly situated in the eastern and southeastern part of the Plateau, approximately 66% of the total area of the Plateau or 4.06 × 10⁵ km² (Figure 2). The area with an increasing trend increased by 1.25 × 10⁵ km², which mainly covered the northwestern part of the Plateau.

4.2. Trend of Seasonal Precipitation over the Loess Plateau

Table 3. The mean annual change trend of seasonal rainfall (mm/a) over the Loess Plateau, China.

	Spring	Summer	Autumn	Winter	Wet Season	Dry Season	EFP	LEP
Sen’s slope	−0.04	−0.28	−0.03	0.05	−0.11	−0.16	−0.14	−0.29
Significance	no	no	no	no	no	no	no	no

Note: ‘no’ indicates that the trend of sub-annual precipitation is not significant.

and

Table 4. The seasonal precipitation (mm) and C_v in different time periods over the Loess Plateau.

Period	Spring		Summer		Autumn		Winter
	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$
1957–1969	85.5	0.38	247.1	0.23	119.5	0.32	10.1	0.44
1970–1979	70.1	0.17	271.2	0.34	106.4	0.28	13.6	0.31
1980–1989	78.1	0.27	234.9	0.16	95.5	0.3	10.6	0.61
1990–1999	81.1	0.42	231.6	0.19	81.4	0.2	9.8	0.6
2000–2009	66.8	0.31	219.2	0.13	108.1	0.22	14.0	0.26
2010–2018	81.2	0.15	266.6	0.36	119.4	0.25	13.4	0.39
Period	Wet season		Dry season		EFP		LFP
	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$	Mean (mm)	${\mathit{C}}_{\mathit{v}}$
1957–1969	393.8	0.22	68.8	0.22	187.9	0.21	205.9	0.3
1970–1979	369.6	0.15	60.6	0.24	177.7	0.16	191.9	0.24
1980–1989	367.7	0.16	57.2	0.4	189.3	0.18	178.5	0.21
1990–1999	341.0	0.15	56.1	0.33	184.6	0.16	156.5	0.26
2000–2009	357.3	0.12	52.9	0.24	170.8	0.16	186.5	0.18
2010–2018	388.3	0.11	64.2	0.29	199.3	0.24	189.0	0.15

show the seasonal precipitation and the change intensities. A non-significant decreasing trend was detected in all the sub-annual periods except winter (Table 3). There were noticeable differences in the mean annual change rates among different periods. The mean annual change rates of summer, and LFP were relatively higher than that of spring, autumn, winter, wet season, EFP, and dry season by nearly 2–10 times.

The variation of the seasonal precipitation (mm) in different periods reveals that $C_v$ of annual precipitation was generally lower than that of the eight sub-annual series (Table 2 and Table 4). The $C_v$ of precipitation in winter, dry season, spring and autumn was greater than that of other sub-annual series during 1957–2018, which showed the climatic nature of the arid region. The $C_v$ of precipitation in seven out of eight sub-annual seasons showed a decreasing trend in decadal scale (Table 4), which resulted in the same change direction in $C_v$ as of annual precipitation (Table 2).

Overall, the precipitation in summer, wet season, dry season and LFP showed a decreasing trend from 1957 until 2018 on the Loess Plateau, but the precipitation demonstrated an increasing trend in winter, particularly in the western Loess Plateau (Figure 3). Moreover, the areas with a tendency of increasing and decreasing in precipitation were basically consistent in spring, autumn and EFP. As shown in Figure 3, the areas with a decreasing trend account for orderly 47%, 72%, 46%, 11%, 65%, 75%, 49.6% and 85% of the total area of the Plateau from spring to LFP, respectively.

Figure 3 also shows that the decreasing trend in precipitation mainly covered the eastern and southern parts of the Loess Plateau. However, the area with an increasing trend in precipitation mainly included the western part of the Plateau. Further analysis indicated that an increasing trend always occurred in the western part of the Plateau for all the sub-annual periods. Similarly, the decreasing trend appeared in the local meteorological stations, such as Wutai Mountain and Hua Mountain for the entire period, which is consistent with that in Figure 2 and Table 2.

4.3. Shifts of Isohyets across the Loess Plateau

In this section, shifts of the isohyets (e.g., 150, 250, 350, 450 and 550 mm) in terms of a decadal scale were examined to estimate the variation of the annual precipitation across the Loess Plateau. As shown in Figure 4, the movement of all isohyets was generally along the direction from northwest to southeast before the 1990s, but the opposite direction after the 1990s. In general, the 150, 250 and 350 mm isohyets experienced no obvious shifts and moved less than 30 km except for the 150 mm isohyet from the 1980s to the 2000s (Figure 4a,b,e). Nevertheless, the 450 and 550 mm isohyets witnessed more significant shifts (Figure 4c–e). The centroids of the 450 and 550 mm isohyets moved nearly 105 and 60 km eastward, 95 and 70 km southward from 1957 to the 1990s, respectively. After the 1990s, they reversed by almost 141 and 105 km westward, 107 and 106 km northward, respectively (Figure 4e). Figure 5 indicates that the areas covered by annual precipitation less than 150, 350–450, and 450–550 mm over the Loess Plateau exhibited an increasing trend, and 150–250 mm remained the same, while the area covered by 250–350 mm and larger than 550 mm had a downward trend.

Generally, the areas covered by annual precipitation of less than 250 mm kept steady along the decades with the mean rate of only 0.06%/10 a. The area covered by 250–450 mm showed a faster decreasing trend with a rate of −0.22%/10 a, which is due to the much faster decreasing trend (−0.47%/10 a) of the areas covered by 250–350 mm, and simultaneously increasing trend (0.25%/10 a) by 350–450 mm. The areas covered by annual precipitation of greater than 450 mm kept an increasing trend by 0.16%/10 a, which resulted from the fairly quick increasing trend of the areas covered by 450–550 mm with the rate of 0.65%/10 a and dramatic decreasing rate of −0.49%/10 a in the areas covered by greater than 550 mm (Figure 5). The changes for these isohyet areas, especially the isohyets of greater than 350 mm, could be well explained by the southeast moving trend of 450 mm and 550 mm in the previous 40 years and the greater northwest moving back in the later 20 years as shown in Figure 4. The results derived from this study are consistent with the findings in [29], and confirms the humidifying trend after 2000 on the Loess Plateau.

The spatial variation patterns of precipitation in China’s Loess Plateau were mainly affected by the annual fluctuation of the East Asian monsoon [40]. [32] found that the EASMI began to decline in the late 1960s and remained at a lower level in 1980s. In general, the climate of the Loess Plateau has been characterized by a dry trend from the 1960s to the end of 1990s, but precipitation increased again in the 21st century. The areas bounded by the isohyets of 450 and 550 mm increased significantly from 2010 to 2018, whereas the areas covered by the isohyets of 150–250, 250–350 and 350–450 mm retreated northwestward and decreased evidently, particularly in the 350–450 mm. These findings implied that rainfall conditions were generally favorable to vegetation restoration on the Loess Plateau after the 2000s.

4.4. Periodical Analysis of Annual Precipitation

To better understand the periodic feature across the Loess Plateau, we chose and analyzed precipitation data from five typical stations at Taiyuan, Lanzhou, Wugong, Etuokeqi and Wuqi stations representing east, west, south, north, and the center, respectively (Figure 1).

The Taiyuan, Wuqi and Lanzhou are three typical meteorological stations representing the eastern, central and western Loess Plateau in the longitude direction, respectively. There were stable period variations of 4–7 years, 2–6 years and 3–9 years at Taiyuan station, Wuqi station and Lanzhou station, respectively, with quasi-eight oscillations in the annual precipitation during the study period (Figure 6a–c). The results illustrate that the three typical stations generally had a significant period at 2–7 years scale, which indicates that precipitation exhibited a short and consistent period variation over the Loess Plateau from east to west.

Additionally, the Wugong, Wuqi and Etuokeqi stations represent the southern, central, and northern parts of the Plateau in the latitude direction by turn. Complex-value Morlet wavelets showed there was obvious period variation in the three typical stations, but the difference existed between each station. Shorter period variation of annual precipitation was detected at Wugong, Wuqi and Eketuoqi stations at the 4–8 years, 2–6 years, and 4–8 years scales, respectively, but Etuokeqi station had a longer period of 9–14 years (Figure 6). The intensity of oscillation of shorter period scale in the annual precipitation gradually decreased for the entire study period. Moreover, these findings suggest that the period variation scale of annual precipitation on the Loess Plateau possibly exhibited the characteristic of the higher the latitude, the longer the period. The periodic variation of precipitation at typical stations on the Loess Plateau is mainly in short scale.

5. Discussion

5.1. Causes of Spatiotemporal Variation in Precipitation

In this paper, the spatiotemporal trends of precipitation were analyzed across 1957–2018 over the Loess Plateau. The causes of change in precipitation across the Loess Plateau have been the focus of widespread attention in the past several decades. Numerous studies pointed out that natural climate variability was the dominant driving force for the change in precipitation across the Loess Plateau, but the effects of human activities should be further analyzed [41].

From a natural perspective, the coupling effect of oceanic evaporation and atmospheric circulation played a critical role in climate change in large scale areas. The decreasing trend in annual precipitation on the Loess Plateau was affected by atmospheric circulation systems [42]. Ref. [32] pointed out that EASMI began to decline in the late 1960s, with the lowest value in the late 1990s, and increased again after 2000. It was found that the trend of annual precipitation and the moving characteristics of precipitation isohyets across the Loess Plateau in different decades were intrinsically related to the change of EASMI in the past half century. The decreasing rate of annual precipitation was tested to be −1.05 mm/10 a (p > 0.1) across the Loess Plateau from 1957 to 2018, while the average rates of −11.5 mm/10 a (p < 0.1) between 1957 and 2009 and −7.51 mm/10 a (p > 0.05) during 1961–2014 on the Plateau have been reported by [11] and [29]. The difference indicates that the annual precipitation in the study area witnessed an obvious increasing trend in the last 10 years. Ref. [43] reported that the Yellow River experienced severe drought from 1983 to the late 1990s, which caused a decrease in runoff and sediment transportation to the Yellow River Delta. This also explains the fact that annual precipitation decreased in stage Ⅱ on the Loess Plateau.

In the past half century, the decreasing trend of the summer precipitation may be attributed to the weakened southeast monsoon and reduced water vapor transport capacity in regions [44]. Furthermore, a decreasing trend of $C_v$ detected in annual precipitation in seven of eight sub-annual series on the Plateau was cause by the decrease of the maximum value of precipitation and the increase of the minimum value at decadal scales from 1957 to 2018.

In the past decades, we found that the variations of precipitation were characterized by an increasing trend in the western margin of the Loess Plateau, but a decreasing trend in central and eastern regions. The average wind speed near the ground in mainland China has decreased significantly [12,45,46,47], and the enhanced North wind in eastern China weakened the transportation of water vapor from the northwest Pacific Ocean, which was likely to be one of the reasons for detected variations of precipitation over the Loess Plateau [16]. The increase of net water vapor budget accounts for the obvious increases of annual precipitation in the Northwest dry area [41]. In addition, the increasing of annual and seasonal precipitation in the western Loess Plateau may be related to increased water vapor content from atmosphere and intensified water cycle driven by global climate warming [3,4,48]. Ref. [49] revealed that North Atlantic oscillation (NAO) and El Niño-Southern Oscillation (ENSO) are the main reasons for affecting precipitation change in northeast Qinghai Province. The shift of climate pattern from warm-dry to warm-humid was preliminarily verified in Northwest China [16], but a non-uniformity of trend in spatial scale was revealed [12]. Moreover, the strong extent of decreasing trend in annual and seasonal precipitation always occurred in the meteorological stations, such as Wutai Mountain and Hua Mountain, which was probably affected by the local topographical factors and atmospheric circulation condition due to the high elevation of 2000 m a.s.l. at these stations.

In addition, it cannot be ignored that increasing human activities have intensified greenhouse gas and aerosol concentrations, and altered land use and land cover conditions on the underlying surface, which probably have a certain impact on the climate system, rainfall intensify and its spatiotemporal distribution pattern [41,50,51,52].

Similar to previous research results in [53], the quasi-period of 2–7 a in the five typical stations of this paper may be affected by the ENSO and quasi-biennial oscillation (QBO) [54]. Ref. [11] reported period variations of 5–7 a and 12–14 a for annual precipitation on the Loess Plateau. Ref. [55] also pointed that the annual precipitation has a dry and wet change of 2–4 a and 11–18 a on the Loess Plateau. Two obvious periods were detected in these studies, among which the shorter period is basically consistent with this study. However, the longer period, as discovered in Etuokeqi station, can be affected by solar activity [56].

5.2. The Implication of Precipitation Variation on Soil Erosion

The annual precipitation on the Loess Plateau generally showed a slightly decreasing trend (−1.05 mm/10 a) while an evident increasing trend occurred after 2000. It was expected that the rainfall erosivity of the Loess Plateau would fluctuate at the same pace [57]. However, a terrace and wrap dam can hold water and sediment directly and restored vegetation can actively enhance evapotranspiration and increase soil infiltration capacity by improving soil physical and chemical properties [58], which can result in an evident reduction in the runoff and sediment generation in the catchment and the Plateau [59].

An increasing trend of precipitation in the 21st century was detected, especially with an accelerated increasing rate since 2010. The increasing precipitation does not mean sediment transportation increases into the Yellow River. The results showed that the areas covered by 250–450 mm and greater than 450 mm with a faster decreasing trend (−0.22%/10 a) and an increasing trend (0.17%/10 a), respectively, which demonstrated that the climatic conditions on the Loess Plateau are basically conducive to local vegetation restoration. It is reported that the total vegetation cover increased significantly on the Loess Plateau from 56% to 76.8% during 2001–2017 [60]. Compared to the 1952–1979 period, average annual runoff and annual sediment transportation from the Loess Plateau decreased from 171.46 × 10⁸ m³ and 14.99 × 10⁸ t to 81.75 × 10⁸ m³ and 2.37 × 10⁸ t during 2000–2015, respectively [61]. The soil erosion area on the Loess Plateau decreased from 4.3 × 10⁵ km² in the early 1980s [26] to 2.14 × 10⁵ km² in 2018 [62]. A great number of studies proved that soil erosion control measures implemented by the nation exert a major role in the reduction of runoff and sediment in the different regions, such as the catchments and the Loess Plateau [59,63,64,65,66,67,68,69,70,71,72].

However, it is well known that soil erosion on the Loess Plateau is mainly caused by heavy rainfall, especially extreme rainstorms. Changes in extreme precipitation across the Loess Plateau have been deeply discussed by [73]. Flood events with a return period of 10 years or more and extreme precipitation events were proposed to be the dominant erosion risk factors on the Loess Plateau [71]. For instance, the model of rill erosion on slope farmland was up to 20 × 10³ t/km² in the extreme rainstorm with a return period of once in 200 years in Suide, Shaanxi Province in 2017, resulting in road damage and the town being inundated [74]. This suggests that the impact on soil erosion caused by extreme rainfall events over the loess plateau cannot be ignored.

The variation coefficient of annual precipitation is helpful to the analysis of regional flood and drought disasters [75]. For areas with severe soil erosion, $C_v$ of the precipitation well explains the impact of extreme precipitation on the ecological environment. The $C_v$ of annual precipitation and seven of eight sub-annual series on the Plateau showed a decreasing trend in decadal scales, indicating that the change amplitude of precipitation was weakened and its distribution is more uniform. As presented in Table 2 and Table 4, the precipitation of annual and wet season on the Plateau have been increasing since 2000. The $C_v$ of annual precipitation and precipitation in most sub-annual seasons showed a decreasing trend, indicating that the fluctuation magnitude of precipitation exhibited a decreasing trend on the Loess Plateau, especially in the wet season. Overall, favorable climate conditions can promote vegetation restoration and availably play its role in conserving soil in this area.

The obvious periodical change in the typical stations helps to understand the variation characteristics of vegetation cover, runoff discharge and sediment transportation from a climatological point of view [76]. For instance, there was a return period of 4 a in annual precipitation from 1957 to 2018 at Wuqi station, the hinterland of the Loess Plateau, which had similar characteristics with the vegetation cover variability during 2001–2017 [77]. Further research was conducted and discovered that annual rainfall erosivity approximately possesses a return period of 4 a at this station throughout the study period. However, a return period of 6 a in runoff discharge and sediment transportation was detected from 1969 to 1996 and no obvious return period after the mid-1990s. There were basically consistent return periods of annual precipitation, annual rainfall erosivity, runoff discharge and sediment transportation before 1996. Since the late 1990s, runoff discharge and sediment transportation have reduced sharply in Wuqi hydrological station. Therefore, it was the effect of vegetation construction and restoration on soil and water loss since 1998.

6. Conclusions

This study used the monthly precipitation data of 100 meteorological stations within and around the Loess Plateau and analyzed the spatiotemporal trends of precipitation between 1957 and 2018 using the nonparametric Mann–Kendall method, Sen’s slope estimator and kriging interpolation method.

Temporally, a slightly decreasing trend in annual precipitation was detected for the entire period (p > 0.1), with a mean decreasing rate of −1.05 mm/10 a. Along the decades the trends were different, and three stages were classified: an increasing trend from 1957 to 1969, a decreasing trend from 1970 to 1999, and an increasing trend again in the 21st century, especially with an accelerated increasing rate since 2010. The precipitation in the sub-annual periods except for winter decreased slightly, whereas the winter increased slightly over the 62 years. The $C_v$ of annual precipitation was generally lower than that of the eight sub-annual series. Like the trend of annual precipitation, the $C_v$ of precipitation in seven of eight sub-annual seasons also showed a decreasing trend in decadal scale. The annual precipitation in the typical stations of four directions and the center generally exhibited a period of 2–7 years.

Spatially, the annual precipitation was characterized by a decreasing trend from southeast to northwest, but the trend of variation coefficient was opposite. Noticeably, a decreasing trend in annual precipitation and eight sub-annual series except for winter was detected in the southern and eastern parts of the Plateau. Additionally, there was an obvious southward shift for the 450 and 550 mm isohyets from the 1960s to the 1990s, while there was a faster northward shift after 1990s. However, the shifts of isohyets, such as the 150, 250 and 350 mm were not evident between the decades. The area covered by 250–450 mm showed a faster decreasing trend followed by a rate of −0.22%/10 a. Nevertheless, the areas covered by the annual precipitation of greater than 450 mm kept an increasing trend by 0.17%/10 a.

In summary, better understanding the spatiotemporal distribution characteristics of precipitation in annual and seasonal periods is greatly helpful for comprehensive watershed management and ecological construction. The effective and reasonable measures adapting to local conditions such as engineering measures (terracing, check dams as well as reservoirs), tillage measures (adjusting crop types, agricultural planting structures, and tillage measures) and biological measures (afforestation and pasture improvement) were expected to be given more attention by local governments to reduce the threat of soil erosion during flooding season. Simultaneously, the management and maintenance of implemented measures in the treated area were suggested to be strengthened. Understanding the spatiotemporal characteristics and variations of precipitation over the Loess Plateau assists the development of cost-effective soil erosion control practices to reduce soil loss and other adverse effects at specific locations and times across the region.