Preamble

ARID LAND GEOGRAPHY Vol. 48 No. 7 Jul. 2025

Spatiotemporal Evolution Characteristics of Extreme Precipitation Events on the Loess Plateau from 1960 to 2023

ZHANG Xinhan¹, ZHAO Wenting¹, JIAO Juying¹,², MA Xiaowu¹, YANG Bo², LING Qi¹

¹College of Soil and Water Conservation Science and Engineering (Institute of Soil and Water Conservation), Northwest A&F University, Xianyang 712100, Shaanxi, China
²State Key Laboratory of Soil Erosion and Dryland Agriculture in the Loess Plateau, Institute of Water and Soil Conservation, Ministry of Water Resources, Chinese Academy of Sciences, Xianyang 712100, Shaanxi, China

Abstract: Under global warming trends, extreme climate events have become increasingly frequent on the Loess Plateau. Clarifying the spatiotemporal characteristics of extreme precipitation events in this region is crucial for regional disaster prevention. Based on daily precipitation data from 111 meteorological stations across the Loess Plateau from 1960 to 2023, this study identifies extreme precipitation events using detrended fluctuation analysis (DFA) to determine extreme precipitation thresholds. The characteristics of extreme precipitation events across the entire Loess Plateau and its ecological subregions are analyzed using Mann-Kendall tests and other methods. The results show: (1) Extreme precipitation thresholds at individual stations range from 27.4–89.1 mm, with 54% of stations exceeding the national heavy rain standard (>50 mm). Average thresholds across ecological subregions range from 35.0–59.6 mm, showing a distribution pattern of low values in the northwest and high values in the southeast. (2) The precipitation amount and intensity of extreme events increase from 10.6 mm·a⁻¹ and 33.0 mm·d⁻¹ in the northwest to 71.5 mm·a⁻¹ and 133.0 mm·d⁻¹ in the southeast, respectively. Occurrence frequency increases from 0.3 d·a⁻¹ in the north to 0.8 d·a⁻¹ in the south. Extreme precipitation days more closely resemble heavy rain days, particularly in the loess hilly gully region B2 subregion. (3) The loess tableland gully region, earth-rocky mountainous region, and river valley plain region are high-incidence areas for extreme precipitation events and should be prioritized for disaster prevention. (4) Extreme precipitation events exhibit significant interannual variability, with an overall increasing trend across the region, concentrated in July–August. (5) In the last decade, precipitation amount and frequency of extreme events have increased in the loess tableland gully and loess hilly gully regions. The declining trend in sandy land and irrigated agricultural regions has slowed, while earth-rocky mountainous and river valley plain regions experienced a sudden increase in extreme precipitation events in 2020. These findings provide a reference basis for disaster prevention and mitigation of extreme precipitation events across different ecological subregions of the Loess Plateau.

Keywords: extreme precipitation threshold; extreme precipitation events; spatiotemporal variation; ecological regionalization; Loess Plateau

1 Data and Methods

1.1 Study Area Overview

The Loess Plateau (33°41′–41°16′N, 100°52′–114°33′E) features complex terrain and variable climate, holding significant importance for China's socioeconomic development and ecological protection. With elevations ranging from 300–3000 m, the plateau exhibits an overall topography that is lower in the southeast and higher in the northwest. It is characterized by a typical continental monsoon climate with concurrent rainfall and heat, and severely uneven spatial distribution of precipitation. To investigate regional differences in geography, topography, and climate, this study employs ecological subregions formulated according to National Development and Reform Commission requirements to analyze the distribution characteristics of extreme precipitation events. The ecological subregions include: loess tableland gully region (A), loess hilly gully region (B), earth-rocky mountainous and river valley plain region (D), and sandy land and irrigated agricultural region (C). Due to significant variations in topography and climate within these subregions, region A is further divided into A1 and A2 subregions using the Liupan Mountains as a boundary, while region B is divided into B1 and B2 subregions using the southern edge of the Mu Us Desert as a boundary.

[FIGURE:1]

Figure 1 Ecological regionalizations and distribution of meteorological stations on the Loess Plateau. Note: Based on Loess Plateau spatial extent data from the Resource and Environmental Science Data Platform (https://www.resdc.cn/data.aspx?DATAID=140). A1 represents loess tableland gully region A1 subregion; A2 represents loess tableland gully region A2 subregion; B1 represents loess hilly gully region B1 subregion; B2 represents loess hilly gully region B2 subregion; C represents sandy land and irrigated agricultural region; D represents earth-rocky mountainous and river valley plain region. The same applies below.

1.2 Data Sources and Processing

Precipitation data for this study were obtained from the China Meteorological Science Data Center (http://data.cma.cn). To ensure data completeness, meteorological stations with substantial missing data or insufficient observation periods were excluded. Considering that surrounding areas may influence climate at the Loess Plateau margins, 111 stations across the Loess Plateau and adjacent regions were ultimately selected (Figure 1). Daily precipitation observations were compiled to establish stable and continuous precipitation time series from 1960–2023.

1.3 Methods

1.3.1 Determination of Extreme Precipitation Thresholds

This study employs detrended fluctuation analysis (DFA) to determine extreme precipitation thresholds. The DFA method seeks a critical daily precipitation value that satisfies the condition: when the positions of data points below the threshold remain unchanged, any positional changes of data points above the threshold will not affect the long-range correlation exponent of the entire sequence. For a precipitation sequence {xᵢ} of length n, the DFA calculation proceeds as follows:

First, compute the cumulative deviation series y(k) = Σᵢ₌₁ᵏ (xᵢ - x̄), where x̄ is the mean value. Then divide y(k) into Nₛ = int(N/s) non-overlapping subintervals of length s. Since N may not be divisible by s, the division is repeated from the opposite end to ensure no information loss, yielding 2Nₛ subintervals.

Next, perform polynomial regression on data within each subinterval v (v = 1, 2, …, 2Nₛ) to obtain local trend functions yᵥ(j). Remove trends from each subinterval and calculate the mean variance:

F²(s, v) = (1/s) Σⱼ₌₁ˢ [y((v-1)s + j) - yᵥ(j)]² for v = 1, 2, …, Nₛ, and
F²(s, v) = (1/s) Σⱼ₌₁ˢ [y(N - (v-Nₛ)s + j) - yᵥ(j)]² for v = Nₛ+1, …, 2Nₛ.

The q-th order fluctuation function is then determined as:
F_q(s) = {(1/(2Nₛ)) Σᵥ₌₁²ᴺˢ [F²(s, v)]^{q/2}}^{1/q}

The scaling exponent α is obtained from the relationship F_q(s) ∝ s^α in double-logarithmic coordinates, where α represents the long-range correlation index of the precipitation sequence.

To identify the threshold, we systematically remove data points from the maximum value (x_max) downward or from the minimum value (x_min) upward, creating new sequences Y_J. The DFA exponent D_J is calculated for each new sequence. When the D_J values begin to flatten and converge, the corresponding J value is taken as the threshold for extreme precipitation events.

1.3.2 Screening of Extreme Precipitation Events and Indicator Calculation

When daily precipitation at a station exceeds its extreme precipitation threshold, it is recorded as an extreme precipitation event. Using these thresholds, extreme precipitation events at each station were identified, and annual extreme precipitation amount, days, and intensity were calculated. Additionally, five extreme precipitation indices recommended by the World Meteorological Organization (WMO) were computed using the RClimDex 1.0 software, including consecutive wet days (CWD), heavy rain days (R25mm), rainstorm days (R50mm), maximum 1-day precipitation (RX1day), and maximum 5-day precipitation (RX5day). These indices were compared with the threshold-based extreme precipitation event indicators.

1.3.3 Statistical Analysis

The Sen's slope estimator is a non-parametric trend estimation method that yields the median slope of a time series. For a time series x_j and x_k, the slope between each pair is calculated as S_i = (x_j - x_k)/(j - k). The median of all N(n-1)/2 slopes gives the Sen's slope estimate: S_med = median(S_i). A positive S_med indicates an upward trend, while a negative value indicates a downward trend.

The Mann-Kendall test, widely used for trend and mutation detection in meteorological data due to its distribution-free nature, calculates a test statistic Z to determine significance. The formula is:

S = Σₖ₌₁ⁿ⁻¹ Σᵢ₌ₖ₊₁ⁿ sign(x_i - x_k)
Var(S) = [n(n-1)(2n+5) - Σₜ₌₁ᵐ t(t-1)(2t+5)]/18
Z = S/√Var(S)

where sign is the sign function and t represents the number of tied data values. A positive Z indicates an upward trend, negative Z a downward trend. The test is significant at the 90% confidence level when |Z| ≥ 1.64.

For mutation detection, forward (UF_k) and backward (UB_k) sequences are constructed. Intersection points between UF_k and UB_k curves within critical bounds indicate potential mutation points.

The coefficient of variation (C_v) measures normalized dispersion: C_v = σ/x̄, where σ is the standard deviation and x̄ is the mean. C_v values ≤0.1 indicate weak variation, 0.1–0.2 moderate variation, and >0.2 strong variation.

2 Results

2.1 Extreme Precipitation Thresholds

The spatial distribution of extreme precipitation thresholds across the Loess Plateau from 1960–2023 follows a pattern similar to annual average precipitation, characterized by low values in the northwest and high values in the southeast. Individual station thresholds range from 27.4–89.1 mm, with high values concentrated in the southeastern areas where 54% of stations exceed the national heavy rain standard (50 mm·d⁻¹). At the subregional scale, the loess tableland gully region A2 subregion shows the smallest threshold values, with no stations exceeding 50 mm·d⁻¹. The loess hilly gully region B2 subregion has an average threshold approaching 50 mm (51.6 mm), while the earth-rocky mountainous and river valley plain region exhibits the highest average threshold at 59.6 mm, with a wide range of 35.7–89.1 mm.

[FIGURE:2]

Figure 2 Spatial distributions of extreme precipitation thresholds and annual average precipitation at each station on the Loess Plateau.

Table 1 Extreme precipitation indicators and definitions

Category Indicator Definition Extreme precipitation event indicators Extreme precipitation amount Annual sum of precipitation exceeding the extreme precipitation threshold Extreme precipitation days Annual number of days with extreme precipitation events Extreme precipitation intensity Ratio of extreme precipitation amount to extreme precipitation days Extreme precipitation indices Consecutive wet days (CWD) Longest duration of consecutive days with precipitation ≥1 mm Heavy rain days (R25mm) Annual number of days with daily precipitation >25 mm Rainstorm days (R50mm) Annual number of days with daily precipitation >50 mm Maximum 1-day precipitation (RX1day) Annual maximum daily precipitation Maximum 5-day precipitation (RX5day) Annual maximum 5-day precipitation

Table 2 Extreme precipitation thresholds in different ecological regionalizations

Region Threshold range (mm) Average threshold (mm) A1 27.4–49.1 35.0±1.1 A2 42.4–59.0 51.6±1.5 B1 53.3–61.2 57.1±0.7 B2 41.8–62.6 50.6±2.8 C 34.1–57.2 44.5±1.8 D 35.7–89.1 59.6±2.2

2.2 Spatial Distribution Characteristics of Extreme Precipitation Events

Among the three extreme precipitation event indicators (amount, days, and intensity) derived from thresholds, extreme precipitation amount and intensity show a general increasing trend from northwest to southeast, while extreme precipitation days follow a north-south pattern. The spatial distribution of extreme precipitation amount closely resembles that of annual precipitation, with the 400 mm isohyet serving as a boundary—areas northwest of this line receive less than 25 mm·a⁻¹ of extreme precipitation (Figure 3a). Extreme precipitation days increase from 0.3 d·a⁻¹ in the north to 0.8 d·a⁻¹ in the south, with the fewest days in the northwestern region (Figure 3b). Low extreme precipitation intensity values are located in the western Loess Plateau, while high values concentrate in the southeast (Figure 3c).

Among the five extreme precipitation indices, all except consecutive wet days (CWD) generally increase from northwest to southeast. Heavy rain days (R25mm), rainstorm days (R50mm), maximum 1-day precipitation (RX1day), and maximum 5-day precipitation (RX5day) all show this pattern, with RX1day and RX5day distributions particularly consistent with annual precipitation patterns (Figures 3d–3h). Only 14 stations (12.6% of the total) have R50mm values ≥1 d·a⁻¹, indicating that extreme precipitation events in the Loess Plateau are characterized by large amounts, high frequency, and strong intensity.

Comparison between extreme precipitation event indicators and extreme precipitation indices reveals that all subregions have RX1day values far below extreme precipitation thresholds, with differences exceeding 20 mm. The extreme precipitation days in the loess hilly gully region B2 subregion (0.50 d) are closest to R50mm (0.58 d), suggesting this region's extreme precipitation threshold aligns most closely with national heavy rain standards.

Table 3 Extreme precipitation indicator values in different ecological regionalizations

Region Extreme precipitation amount (mm) Extreme precipitation days (d) Extreme precipitation intensity (mm·d⁻¹) CWD (d) R25mm (d) R50mm (d) RX1day (mm) RX5day (mm) A1 22.83±1.71 0.50±0.03 45.17±1.68 7.22±0.34 1.64±0.19 0.14±0.03 33.81±1.41 54.92±2.58 A2 33.75±2.22 0.49±0.03 68.35±2.11 7.06±0.27 3.59±0.34 0.58±0.06 50.53±1.89 79.56±4.11 B1 35.37±2.18 0.48±0.03 74.99±1.23 6.27±0.18 3.84±0.20 0.70±0.05 54.27±1.27 85.16±3.10 B2 30.09±1.74 0.46±0.03 66.40±4.24 5.73±0.17 2.94±0.15 0.50±0.06 48.30±2.12 74.51±3.18 C 21.08±1.81 0.34±0.02 59.91±2.40 4.35±0.13 1.48±0.19 0.26±0.04 38.10±1.91 52.18±3.25 D 42.94±2.34 0.53±0.02 79.91±3.33 6.80±0.14 4.77±0.29 0.96±0.10 59.64±2.43 95.92±3.83

2.3 Temporal Variation Characteristics of Extreme Precipitation Events

2.3.1 Trend Changes in Extreme Precipitation Events

Extreme precipitation amount, days, and intensity at individual stations show similar trends. At the 90% confidence level, 51 stations (45.9%) exhibit significant upward trends in extreme precipitation amount, while only 5 stations (4.5%) show significant downward trends (Figure 4a). Changes in extreme precipitation days directly reflect frequency variations. Across the region, 46.8% of stations display increasing trends in extreme precipitation events, with 14.4% showing significant increases (Figure 4b). The mean extreme precipitation intensity is 66.9 mm·d⁻¹, exceeding China's heavy rain standard, with more stations showing increases (51.4%) than decreases (48.6%).

The coefficients of variation for extreme precipitation amount and days are 0.87 and 0.88, respectively, indicating moderate variation levels and significant interannual fluctuations (Table 4). Extreme precipitation events concentrate in summer, particularly in July–August (Figure 5). Over 50% of stations show decreasing trends in CWD, with 14 stations significant, at an overall rate of -0.009 d·a⁻¹. R25mm and R50mm show increasing trends at 39.6% and 45.0% of stations, respectively, with R25mm showing more pronounced upward trends. RX1day and RX5day display increasing trends at 45.0% and 42.3% of stations, respectively.

Table 4 Statistical test results of extreme precipitation indicators on the whole Loess Plateau

Indicator Trend (Z value) Significance Mutation year Extreme precipitation amount 0.128 mm·a⁻¹ Non-significant None Extreme precipitation days 0.009 d·a⁻¹ Non-significant None Extreme precipitation intensity 0.009 mm·d⁻¹a⁻¹ Non-significant None CWD -0.009 d·a⁻¹ Non-significant None R25mm 0.036 mm·a⁻¹ Non-significant None R50mm 0.009 d·a⁻¹ Non-significant None RX1day 0.128 mm·a⁻¹ Non-significant None RX5day 0.009 mm·d⁻¹a⁻¹ Non-significant None

2.3.2 Mutation Analysis of Extreme Precipitation Events

Mann-Kendall mutation tests reveal that extreme precipitation amount, frequency, and intensity across the entire Loess Plateau show no significant mutations, with numerous intersection points between UF_k and UB_k curves indicating no clear breakpoints.

At the subregional scale, the loess tableland gully region A2 subregion experienced a decreasing mutation in extreme precipitation amount around 1980, followed by a slowing trend after 2000 and an increasing mutation in 2020. The loess hilly gully region B1 subregion showed mutation phenomena around 1980, with recent trends表现为上升趋势和下降减缓趋势. The sandy land and irrigated agricultural region C experienced fluctuating decreases after a mutation around 1990. The earth-rocky mountainous and river valley plain region D shifted to an increasing trend after a mutation in 2020.

Extreme precipitation days in the A2 subregion have remained in the negative zone since the 1990s, while region C experienced a mutation around 1990. The B1 subregion shifted from decreasing to increasing around the turn of the 21st century, with a significant reduction before 2010. The B2 subregion underwent a mutation from fewer to more events around 2010, while region D has shown an increasing trend since the 1980s with a clear upward mutation around 2020.

Extreme precipitation intensity curves for all subregions show multiple intersections, with the A2 subregion's UF_k and UB_k curves intersecting within critical bounds around 1980, and region D showing a significant upward mutation around 2020.

[FIGURE:3]

Figure 3 Spatial distributions of multi-year average extreme precipitation indicators.

[FIGURE:4]

Figure 4 Variation trends of extreme precipitation indicators at each meteorological station.

[FIGURE:5]

Figure 5 Monthly distribution of extreme precipitation events on the Loess Plateau from 1960 to 2023.

[FIGURE:6]

Figure 6 Mann-Kendall mutation test of extreme precipitation events in different ecological regionalizations.

3 Discussion

3.1 Spatial Distribution of Extreme Precipitation Events

Extreme precipitation events are difficult to predict, and assessment complexity increases on the Loess Plateau due to substantial topographic and climatic differences. This study reveals that southern areas (loess tableland gully region, earth-rocky mountainous region, and river valley plain region) are more vulnerable to extreme precipitation impacts. The loess tableland gully region, particularly its A2 subregion, experiences high-frequency extreme precipitation events with substantial intensity. Combined with fragmented terrain, deep and loose soil layers, and poor erosion resistance, this region constitutes a major source of sediment for the Yellow River. Under extreme precipitation conditions, various erosion processes intensify, generating large sediment yields and triggering severe erosion disasters. Although the earth-rocky mountainous and river valley plain region has relatively good vegetation cover and underlying surface conditions, it records the highest incidence and intensity of extreme precipitation events among all subregions, substantially increasing flood and other natural disaster risks. For example, in October 2021, continuous heavy precipitation caused the Beiluo River to breach its banks at Dali County, Weinan City, affecting 49,000 mu of farmland and 40,000 people. Given that extreme precipitation disasters result from combined natural and anthropogenic factors, systematic risk assessments are needed for each subregion.

Previous studies on extreme precipitation spatiotemporal changes in the Loess Plateau have mostly focused on smaller scales such as provincial domains or soil erosion type zones. For instance, Yang et al. found that extreme precipitation in Gansu's Loess Plateau region showed decreasing trends in many areas, concentrated in the southwestern part. Li et al. reported increasing heavy precipitation in northern Shaanxi with a tendency toward extremization. These findings align with our results for corresponding subregions and periods. Wang et al. found decreasing extreme precipitation amount and days but increasing intensity on the Loess Plateau from 1970–2020, differing from our results—likely due to variations in precipitation data, spatial resolution, and threshold selection methods.

International extreme precipitation indices may facilitate regional comparisons, but some indices cannot characterize extreme events. For example, CWD reflects precipitation persistence but may not meet extreme event standards. Our comparison reveals that annual RX1day values across all subregions are below extreme precipitation thresholds, indicating extreme events do not occur in most years. This corresponds to results showing annual extreme precipitation days below 1 d·a⁻¹. The extreme precipitation days in the loess hilly gully region B2 subregion closely match R50mm, suggesting this region's threshold aligns best with national heavy rain standards, allowing simple description using extreme precipitation indices.

3.2 Temporal Variation of Extreme Precipitation Events

Unlike widespread temperature increases, long-term evolution of extreme precipitation shows more complex spatiotemporal patterns. All ecological subregions experienced decreasing extreme precipitation trends during the 1980s, with region C showing fluctuating decreases after a mutation around 1990. Since large-scale ecological projects were implemented in 1999, vegetation coverage on the Loess Plateau has increased significantly, affecting intra-annual precipitation distribution and potentially influencing extreme precipitation events indirectly—though the relationship requires comprehensive consideration of multiple factors and long-term research.

Since the 21st century, most subregions have begun showing increasing trends, likely due to massive greenhouse gas emissions causing warming and humidification of the Loess Plateau climate, affecting seasonal water resource cycles and increasing extreme precipitation probability. Overall, extreme precipitation changes primarily result from recent climate warming and human activity interference.

This study examines spatiotemporal variations from 1960–2023 based on historical data. However, how future extreme precipitation events will evolve on the Loess Plateau and how climate change and human activities will influence them requires further investigation.

4 Conclusions

This study analyzes spatiotemporal evolution characteristics of extreme precipitation events on the Loess Plateau from 1960–2023, yielding the following conclusions:

1. Extreme precipitation thresholds show a spatial pattern of low values in the northwest and high values in the southeast. At the station scale, thresholds range from 27.4–89.1 mm, with 54% of stations exceeding 50 mm. At the subregional scale, the loess tableland gully region A1 subregion has the lowest average threshold (35.0 mm), while the earth-rocky mountainous and river valley plain region has the highest (59.6 mm).

2. Spatial distribution of extreme precipitation events: Among three extreme precipitation indicators, amount and intensity increase from northwest to southeast, while extreme precipitation days show a south-high, north-low pattern. Significant differences exist among subregions, with the loess tableland gully region and earth-rocky mountainous and river valley plain region identified as high-incidence areas requiring prioritized disaster prevention.

3. Comparison with extreme precipitation indices: All extreme precipitation indices except CWD show increasing trends from northwest to southeast. RX1day and RX5day distributions align with annual precipitation patterns. The loess hilly gully region B2 subregion's extreme precipitation days closely match R50mm, allowing simple description using extreme precipitation indices.

4. Temporal variation: Extreme precipitation events show significant interannual fluctuations, with an overall increasing trend across the region. Extreme precipitation amount and intensity are increasing at rates of 0.128 mm·a⁻¹ and 0.009 mm·d⁻¹a⁻¹, respectively. Events concentrate in July–August. In the last decade, the loess tableland gully and loess hilly gully regions have seen increased precipitation amounts and frequencies, while region C's declining trend has slowed. Regions D experienced sudden increases in extreme precipitation events in 2020.

These findings provide scientific support for disaster prevention and mitigation strategies targeting extreme precipitation events across different ecological subregions of the Loess Plateau.

References

[1] Jiang Zhihong, Ding Yuguo, Chen Weilin. Projection of precipitation extremes for the 21st century over China[J]. Climate Change Research, 2007, 3(4): 202-207.

[2] Yuan Wende, Zheng Jiangkun, Dong Kui. Spatial and temporal variation in extreme precipitation events in southwestern China during 1962–2012[J]. Resources Science, 2014, 36(4): 766-772.

[3] Liu B J, Chen J F, Chen X H, et al. Uncertainty in determining extreme precipitation thresholds[J]. Journal of Hydrology, 2013, 503: 1-12.

[4] Watters P A, Martin F. A method for estimating long range power law correlations from the electroencephalogram[J]. Biological Psychology, 2004, 66(1): 79-89.

[5] Yang Ping, Hou Wei, Feng Guolin. Determining the threshold of extreme events with detrended fluctuation analysis[J]. Acta Physica Sinica, 2008, 57(8): 5333-5342.

[6] Liu Bingjun, Wu Lili, Lu Wenxiu. Researches on DFA based extreme precipitation threshold in the Pearl River Basin[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2013, 52(1): 136-141.

[7] Zheng Zuofang, Zhang Xiuli, Cao Hongxing, et al. Characteristics of long-term climate change in Beijing with detrended fluctuation analysis[J]. Chinese Journal of Geophysics, 2007(2): 420-424.

[8] Zheng Tengfei, Guo Jianmao, Yin Jifu, et al. DFA based research on spatiotemporal distribution of extreme precipitations in Jiangsu Province[J]. Journal of Natural Disasters, 2012, 21(4): 76-83.

[9] Chi X X, Yin Z E, Wang X, et al. Spatiotemporal variations of precipitation extremes of China during the past 50 years (1960–2009)[J]. Theoretical and Applied Climatology, 2016, 124(3-4): 739-755.

[10] Wang L Y, Chen S F, Zhu W B, et al. Spatiotemporal variations of extreme precipitation and its potential driving factors in China's north-south transition zone during 1960–2017[J]. Atmospheric Research, 2021, 252: 105429.

[11] Xinhua News Agency. Severe floods and waterlogging in Shanxi have affected more than 1.75 million people[EB/OL]. [2021-10-10]. http://www.xinhuanet.com/local/2021-10/10/c_1127942989.htm.

[12] Alexander L V, Tapper N, Zhang X, et al. Climate extremes: Progress and future directions[J]. International Journal of Climatology, 2009, 29(3): 317-319.

[13] Mass C, Skalenakis A, Warner M. Extreme precipitation over the west coast of North America: Is there a trend?[J]. Journal of Hydrometeorology, 2011, 12(2): 310-318.

[14] Lu Shan, Hu Zeyong, Wang Baipeng, et al. Spatiotemporal patterns of extreme precipitation events over China in recent 56 years[J]. Plateau Meteorology, 2020, 39(4): 683-693.

[15] Gao Tao, Xie Lian. Study on progress of the trends and physical causes of extreme precipitation in China during the last 50 years[J]. Advances in Earth Science, 2014, 29(5): 577-589.

[16] Jiang Zhihong, Ding Yuguo, Chen Weilin. Projection of extreme precipitation events in China based on regional climate model CCLM[J]. Journal of Natural Resources, 2017, 32(2): 266-277.

[17] Zhang J J, Gao G Y, Fu B J, et al. A universal multifractal approach to assessment of spatiotemporal extreme precipitation over the Loess Plateau of China[J]. Hydrology and Earth System Sciences, 2020, 24(2): 809-826.

[18] Lu Shan, Hu Zeyong, Fu Chunwei, et al. Characteristics and possible causes for extreme precipitation in summer over the Loess Plateau[J]. Plateau Meteorology, 2022, 41(1): 241-254.

[19] Li Zhi, Zheng Fenli, Liu Wenzhao. Analyzing the spatial temporal changes of extreme precipitation events in the Loess Plateau from 1961 to 2007[J]. Journal of Natural Resources, 2010, 25(2): 291-299.

[20] Zhao Anzhou, Zhu Xiufang, Pan Yaozhong. Spatiotemporal variations of extreme precipitation events in the Loess Plateau from 1965 to 2013[J]. Journal of Beijing Normal University (Natural Science Edition), 2017, 53(1): 43-50.

[21] Wang Wanzhong, Jiao Juying, Wei Yanhong, et al. Spatial temporal differentiation characteristics of erosion sediment yield on the Loess Plateau during the recent half century[J]. Journal of Sediment Research, 2015, 40(2): 9-16.

[22] Zhang Guanghui. Understanding sediment connectivity from soil erosion perspective[J]. Advances in Water Science, 2021, 32(2): 295-308.

[23] CCTV Network. Continuous rainfall in Dali, Shaanxi Province has caused 491,000 mu of farmland to be flooded and urgently evacuated over 18,000 people[EB/OL]. [2021-10-10]. http://m.news.cctv.com/2021/10/10/ARTIeQrDBFBOzW8M3tAe4HE7211010.shtml.

[24] Sen P K. Estimates of the regression coefficient based on Kendall's Tau[J]. Journal of the American Statistical Association, 1968, 63(324): 1379-1389.

[25] Hirsch R M, Slack J R. A nonparametric trend test for seasonal data with serial dependence[J]. Water Resources Research, 1984, 20(6): 727-732.

[26] Jing Le, Li Jianping, Zhang Yi, et al. Study on dry soil layers under different land use systems in the Loess Plateau[J]. Pratacultural Science, 2018, 35(8): 1829-1835.

[27] Yang Yanfen, Wang Bing, Wang Guoliang, et al. Ecological regionalization and overview of the Loess Plateau[J]. Acta Ecologica Sinica, 2019, 39(20): 7389-7397.

[28] Du Shixiong, Wu Ruiying, Sun Huaiwei, et al. Analysis of extreme precipitation events along the China-Pakistan economic corridor[J]. Transactions of the Chinese Society of Agricultural Engineering, 2022, 38(Suppl. 1): 152-160.

[29] Pei Hongze, Zhao Yachao, Zhang Tinglong. Analysis of spatial and temporal patterns and drivers of local regional NEP in the Loess Plateau from 2000 to 2020[J]. Arid Zone Research, 2023, 40(11): 1833-1844.

[30] Liu Guobin, Shangguan Zhouping, Yao Wenyi, et al. Ecological effects of soil conservation in Loess Plateau[J]. Chinese Academy of Sciences, 2017, 32(1): 11-19.

[31] Yang Dong, Cheng Junqi, Li Xiaoya, et al. The variation characteristic of different levels of precipitation and extreme precipitation in Loess Plateau of Gansu Province region in recent 52 years[J]. Ecology and Environmental Sciences, 2012, 21(9): 1539-1547.

[32] Li Shuangshuang, Kong Feng, Han Lu, et al. Spatiotemporal variability of extreme precipitation and influencing factors on the Loess Plateau in northern Shaanxi Province[J]. Geographical Research, 2020, 39(1): 140-151.

[33] Wang Guozhen, Yan Hong, Liu Chengcheng, et al. Spatiotemporal evolution of extreme precipitation in Loess Plateau from 1970 to 2020 and its response to atmospheric circulation changes[J]. Journal of Earth Environment, 2023, 14(5): 588-602.

[34] Zhou Xiaohong, Zhao Jingbo. Climatic change and vegetation restoration on the Loess Plateau[J]. Arid Zone Research, 2005, 22(1): 116-119.

[35] Zhang Baoqing, Tian Lei, Zhao Xining, et al. Study on the feedback effect of vegetation restoration on local precipitation on the Loess Plateau[J]. Science China (Earth Sciences), 2021, 51(7): 1080-1091.

[36] An Bin, Xiao Weiwei, Liu Yufeng, et al. Temporal and spatial evolution of relative humidity in the Loess Plateau during 1955–2021[J]. Arid Land Geography, 2023, 46(12): 1939-1950.

[37] Li Heng, Zhu Bingbing, Bian He, et al. Temporal and spatial changes in extreme precipitation and its driving factors in the water-wind erosion crisscross region of the Loess Plateau from 1960 to 2017[J]. Arid Land Geography, 2024, 47(4): 539-548.

[38] Tabari H. Climate change impact on flood and extreme precipitation increases with water availability[J]. Scientific Reports, 2020, 10(1): 13768.

[39] Lu Yan. Unbearable changes in global climate in 2021[J]. Green China, 2021(23): 16-21.