Spatial and Temporal Variability Characteristics and Driving Factors of Extreme Precipitation in the Wei River Basin

Abstract

As global climate change intensifies, the global atmospheric circulation process is undergoing significant changes, and the local water vapor pattern has also changed. This study takes the Wei River Basin as the research area. Firstly, an evaluation index system for extreme precipitation was established, and the time-series characteristics of the magnitude, frequency, and duration of extreme precipitation were analyzed. Statistical methods were used to analyze the non-consistency in time-series changes in extreme precipitation indicators. Using spatial heterogeneity analysis methods, the spatial variation differences in extreme precipitation in the Wei River Basin were identified. This study selected the El Niño-Southern Oscillation (ENSO) index, global land-ocean temperature index (LOTI), and land surface temperature (LST) index to quantitatively evaluate the impact of climate change on regional extreme precipitation and analyzed the correlation between temperature and extreme precipitation, identifying the key driving factors of extreme precipitation changes. The conclusions of this study are as follows: (1) The southern region of the Wei River Basin experiences more frequent and intense precipitation events, while the northern region experiences relatively few. (2) From 1981 to 2021, the intensity, frequency, and duration of precipitation events in the Wei River Basin gradually increased, with the most significant increase in extreme precipitation in the Guanzhong Plain. (3) Global climate change has an important impact on precipitation events in the Wei River Basin. The increase in the ENSO, LOTI, and LST indices may indicate an increase in the probability of drought and flood events in the Wei River Basin. The relationships between extreme precipitation and temperature present a peak structure. This conclusion is helpful to better understand the impact of climate change on extreme precipitation in the Wei River Basin and provides some support for the response to extreme meteorological events under the background of future climate change.

1. Introduction

Under the combined influence of climate change and human activities, global and regional precipitation patterns have changed [1,2]. According to the IPCC’s (Intergovernmental Panel on Climate Change) sixth climate change evaluation report, the frequency and intensity of extreme precipitation events on land at the global scale are showing an increasing trend, and the extreme precipitation events in most Asia regions present a rising trend with a medium confidence level or above [3]. The regional extreme precipitation pattern is not only affected by the water vapor cycle and thermodynamic effects caused by global climate change but also by factors such as land use and urbanization, which pose significant uncertainties [4,5,6]. Understanding the changing trends in local extreme precipitation characteristics and identifying the main driving factors of extreme precipitation changes are crucial for more accurately predicting the spatial and temporal pattern changes in future extreme precipitation and for effectively responding to the increasing number of extreme hydrological and meteorological events [7,8].

Many studies have been conducted by scholars on the characteristics of extreme precipitation changes in different regions around the world. Donat et al. [9] analyzed the changes in annual precipitation and extreme precipitation in arid and humid regions around the world and pointed out that in the past 60 years, the total precipitation and extreme precipitation in arid regions as well as the extreme precipitation in humid regions have shown a significant increase, while the total precipitation in humid regions has not changed significantly. Paik et al. [10] further investigated the changes in precipitation trends on a global scale. The results indicate that there was a clear trend in the maximum daily precipitation (Rx1day) and the maximum precipitation for five consecutive days (Rx5day) in the temperate regions of the Northern Hemisphere, while the trend in the Southern Hemisphere had uncertainty. Li et al. [11] selected nine extreme precipitation indices (EPIs) and examined the proportion of extreme precipitation in total precipitation in different regions of the world from the perspectives of intensity, frequency, and duration. They pointed out that the global precipitation intensity and precipitation frequency indices and their proportions showed an overall upward trend, with the most significant upward trend in the Northern Hemisphere and western South America. Gu et al. [12] combined daily precipitation observations from 1857 stations with precipitation reanalysis datasets to analyze the spatial and temporal variation in extreme precipitation in China. The impact of urbanization on precipitation was also systematically analyzed. The results showed that there were significant spatial variations in extreme precipitation in China.

Based on the results of numerous studies, there are significant differences in extreme precipitation changes in different regions. To identify the causes, many scholars have conducted relevant analyses and studies on the driving factors of extreme precipitation. Wei et al. [13] analyzed the formation mechanism of extreme precipitation in Central Asia and attributed the main causes to the strength of the Northern Hemisphere subtropical high index, sea surface temperature anomaly index, Asian circulation index, and Atlantic multi-year oscillation index. Wang et al. [14] used historical meteorological station observations to identify potential controlling factors for extreme precipitation in the Qinling–Daba Mountain region. They pointed out that large-scale atmospheric circulation patterns have a significant impact on the spatial and temporal changes in extreme precipitation, and that changes in extreme precipitation indices are closely related to the El Niño-Southern Oscillation (ENSO) on interannual scales. Some scholars have also conducted similar studies on other regions [15,16,17]. Overall, it can be seen that there are significant differences in the causes of extreme precipitation in different regions.

The Wei River Basin is one of the main tributaries of the Yellow River and is crucial to the water supply and ecological balance of the surrounding areas. The increase in extreme precipitation events will have a serious impact on the ecological and environmental problems in the Wei River Basin. Therefore, understanding the spatial and temporal variation trends in extreme precipitation in the Wei River Basin and identifying its main influencing factors are crucial for developing customer adaptation strategies, water resource management, and flood risk mitigation. This study constructed an evaluation index system for extreme precipitation in the Wei River Basin, based on an analysis of observed precipitation data, to identify the spatial and temporal variability characteristics of extreme precipitation. The correlation analysis method was applied to identify the key meteorological driving factors of extreme precipitation in the Wei River Basin.

2. Data and Methods

2.1. Study Area Description

The Wei River originates from the Niaoshu Mountain in Weiyuan County, Dingxi City, Gansu Province, and mainly flows through Tianshui City, Gansu Province, Baoji, Xianyang, Xi’an, Weinan, and other places in the Guanzhong Plain of Shaanxi Province, before flowing into the Yellow River in Tongguan County, Weinan City. The Wei River is the largest tributary of the Yellow River, with a total river length of 818 km.

The Wei River Basin has a typical arid and semi-arid climate, influenced by the continental monsoon climate, and the spatial and temporal distribution of precipitation in the basin is uneven, showing a decreasing trend from southeast to northwest. The average precipitation in the basin is 564.5 mm, and the average annual natural runoff is 63 × 108 cubic meters. The geographical location and spatial distribution of the basin terrain are shown in Figure 1.

2.2. Data Sources

2.2.1. Observed Precipitation Data

This study selected daily precipitation data from 73 national meteorological stations in the basin from 1981 to 2020. Precipitation data were obtained from the National Meteorological Information Center of the China Meteorological Administration. To ensure the integrity and long-term continuity of the data, the consistency of the measured data was tested. For missing data at meteorological observation stations, the differential method was used to obtain data from neighboring meteorological stations during the same period. Considering that different amounts of missing data can make a huge difference in the accuracy of precipitation interpolation, this study determined that data interpolation was needed when the amount of data was less than 10%.

2.2.2. Climate Change Index Data

To identify the main driving factors of extreme precipitation in the Wei River Basin, the El Niño index (ONI), the global land–ocean temperature index (LOTI), and the local surface temperature were selected as the key indicators to quantify climate change. The ONI is the area of Niño 3.4 (5° N–5° S; 120° W–170° W) sea surface temperature (SST) anomaly quarter running average, which is often used to describe the state of the ENSO [18]; the index is available from the National Oceanic and Atmospheric Administration (http://www.cpc.ncep.noaa.gov, accessed on 23 October 2023). The land–ocean temperature index is the core index of the climate cylinder, which can reflect the global temperature changes in the land and ocean to a certain extent, so as to identify the climate warming index, which is of great significance for reflecting global climate warming [19]. Similarly, the index is also available from the National Oceanic and Atmospheric Administration. To further analyze the impact of temperature on regional extreme precipitation, this study further selected local surface temperature to reflect the trend in the regional temperature change. This index was derived from the ERA5 monthly land climate dataset, which can provide high-resolution global land temperature grid data. To ensure consistency in the data and analysis, this study uses raster data processing, turning it into the value of time series data. The data were obtained from the European Centre for Medium-Range Weather Forecasts (https://cds.climate.copernicus.eu, accessed on 23 October 2023). In order to analyze the correlation between the climate index and extreme precipitation, we ensured that the length of the climate index data series was consistent with that of the precipitation observation data series. The data series is from 1981 to 2020. The spatial resolution of the data is 1 km × 1 km.

2.3. Methods

The specific technical process is shown in Figure 2. First, an evaluation index system for extreme precipitation was constructed. EPIs were calculated based on the observed dataset from 73 precipitation stations, and the indexes were divided according to the occurrence frequency, intensity, and duration. Second, using the sequence non-uniformity statistical analysis method, the spatial and temporal variation in the extreme precipitation index were obtained. Finally, three commonly used climate factors, ENSO, LOTI, and LST, were selected to identify the impact of climate change on extreme precipitation in the Wei River Basin.

2.3.1. Analysis Method for Extreme Precipitation Characteristics

(1)

Extreme precipitation index

This study uses 9 extreme precipitation indicators proposed by the United Nations World Meteorological Organization (WMO) to analyze the changing patterns in extreme precipitation characteristics in the Wei River Basin. The interpretation of relevant evaluation indicators is shown in

Table 1. Definition of the extreme precipitation index.

Type	Index	Define	Units
	R10mm	Total number of days with annual daily precipitation >10 mm	d
	R20mm	Total number of days with annual daily precipitation >1 mm	d
Intensity index	Rx1day	Annual maximum daily precipitation	mm
	Rx3day	Annual maximum 3-day precipitation	mm
	R95p	Annual accumulated precipitation with daily precipitation >95% quantile	mm
	R99p	Annual accumulated precipitation with daily precipitation >99% quantile	mm
	SDII	The ratio of the total amount of precipitation ≥1 mm to the number of days	mm/d
	PRCPTOT	Annual accumulated precipitation with daily precipitation >1 mm	mm
Duration index	CWD	The longest duration of daily precipitation >1 mm	d

. Based on the evaluation characteristics of extreme precipitation indicators, they are divided into three categories: frequency, intensity, and duration [20].

(2)

Non-uniformity test method

To analyze the temporal variation characteristics of extreme precipitation at different stations in the Wei River Basin, the Mann–Kendall test was used to conduct a non-uniformity test on the precipitation data series. M-k is a commonly used climate diagnosis and prediction technique, which has the advantages of not requiring samples to follow a certain distribution and being less susceptible to interference from a few outliers. It is more suitable for categorical and ordinal variables [21]. The mathematical formula and process involved in this method are shown below.

In Formula (1), Z represents the trend determination index; τ represents a sign function for determining a change in adjacent values, which follows the standard normal distribution; and Var($\tau$) represents the variance. For the statistic Z value, if Z > 0, it indicates that the sequence shows an upward trend; if Z < 0, it indicates that the sequence shows a downward trend.

$$Z=\left\{\begin{array}{l}\frac{\tau -1}{\sqrt{\mathrm{Var}(\tau )}} , \tau >0\\ 0 , \tau =0\\ \frac{\tau +1}{\sqrt{\mathrm{Var}(\tau )}} , \tau <0\end{array}\right.$$

(1)

$$\mathrm{Var}(\tau )=\frac{i(i-1)(2i+5)}{18}$$

(2)

(3)

Spatial feature analysis method

To analyze the spatial heterogeneity in extreme precipitation and its driving factors, the distance inverse method (IDW) was used to spatially interpolate precipitation at stations and obtain grid precipitation. Using a statistical analysis of gridded precipitation data, the surface precipitation of different divisions in the Wei River was calculated. For the spatial analysis of extreme precipitation, the Wei River Basin was divided into the Guanzhong Plain, Loess Hills, Jing River Basin, and Northern Luohe River Basin.

2.3.2. Driver Correlation Analysis

This study selected the Pearson product-moment correlation coefficient to analyze the correlation between the ENSO, LOTI, and LST changes and extreme precipitation index sequences, thus revealing their connections. Among them, the impact of global climate change on extreme precipitation is quantified by the global land–ocean temperature index [22,23]. Since EPIs are all annual time series data, three time series of the global land–ocean temperature index, the El Niño index, and the local temperature were treated as annual time series before analysis. These three indicators were processed using the annual average to ensure the unity of the time series.

3. Results

3.1. Spatial Variation in Extreme Precipitation in Wei River Basin

Based on the analysis method proposed in the second section of this paper, the extreme precipitation indicators of the Wei River Basin were calculated and analyzed. The results show that the geographical distribution of the 10 extreme precipitation indicators in the Wei River Basin decreases from south to north. The spatial distribution of the extreme precipitation indicator is shown in Figure 3. Among the four regions of the Wei River Basin, the maximum values of EPIs usually occur in the Guanzhong Plain. Specifically, the extreme precipitation indices in the Jing River Basin and Northern Luohe River Basin are usually smaller than those in the southern Loess Hills and Guanzhong Plain regions. In addition, being affected by terrain, rainfall frequency (R10mm and R20mm), rainfall intensity (Rx1day and Rx3day), and rainfall duration (CWD) in the Loess Hills area often showed a low trend. Specifically, the areas with intensive rainfall frequency are mostly located in the southern region, where the maximum values of R1mm, R10mm, and R20mm are 65 days, 22 days, and 9 days, which are about 40 days, 12 days, and 7 days different from the lowest values in the north, indicating that the southern region experiences precipitation events more frequently. Similarly, R95p, R99p, and prcp, which represent rainfall intensity, are also concentrated in the southern region. The maximum value of R95p and R99p is 99.89 mm in the southwest of the Loess Plateau, while the maximum value of prcp is 626.30 mm in the southwest of the Guanzhong Plain. The difference from the lowest value in the north is about 126.26 mm. In addition, the highest value of CWD, which represents the duration of rainfall, also appears in the southern Guanzhong Plain at a value of 6.12 mm, further showing that the southern region has a significant advantage in precipitation events. However, the highest values of Rx1day, Rx3Day, and SDII, which represent rainfall frequency, appear in the western Northern Luohe River Basin, which are 62.01 mm, 88.39 mm, and 11.31 mm/d, respectively.

The differences in the spatial distribution of EPIs may be affected by a combination of elements, including geographical features, topography, and climatic conditions. There is a strong east–west topographic boundary in Wei Plain, and when warm and wet air passes through this area from the east, the air will be affected by mountain uplift. The rising air cools at higher elevations and condenses into clouds, which form precipitation. This topographic uplift generally leads to more intense precipitation events in the southern and western areas, especially at the border between mountains and plains.

3.2. Temporal Variation Characteristics of the Extreme Precipitation Index

The annual variation trend in extreme precipitation in four different regions of the Wei River Basin is shown in Figure 4. Overall, except for CWD, which showed a certain downward trend, other extreme precipitation indices all showed an upward trend to varying degrees, among which the two precipitation indexes R95p and R99p showed particularly significant growth trends. The analysis results of extreme precipitation indicators show that the intensity and frequency of extreme precipitation events in the Wei River Basin as a whole are gradually increasing, while the longest wet period within a year has decreased. In addition, with the exception of R95p and R99p, other EPIs show significant inter-annual fluctuations, which may be affected by meteorological phenomena (such as El Niño events) and short-term climate changes, resulting in the instability of this precipitation change trend.

On the other hand, the inter-annual variation in EPIs in different regions also showed different trend characteristics. The analysis results in Figure 4 show that Loess Hills has the lowest EPIs overall but shows the most significant upward trend in R95p and R99p. By 2021, the extreme precipitation was predicted to increase by about 50 mm, indicating that even at a low precipitation level, the precipitation intensity in this region is increasing continuously, which may have a greater impact on flood risk and soil erosion. Compared with the hilly areas, the Guanzhong Plain has certain advantages in terms of precipitation intensity, precipitation frequency, and precipitation duration. Precipitation frequency and precipitation intensity also have the most significant increase, which indicates that the meteorological change in the Guanzhong Plain is relatively significant. In particular, the rainfall frequency (R10mm and R20mm) in the Guanzhong Plain shows relatively obvious inter-annual fluctuation characteristics, which indicates that this region may be more susceptible to short-term meteorological changes, resulting in a longer precipitation cycle. EPIs in the Jinghe River Basin and the Northern Luohe River Basin are similar to some extent and have significant inter-annual fluctuation characteristics in precipitation intensity (Rx1day, Rx3day, and SDII). The maximum inter-annual difference in annual precipitation intensity in this region is up to 100 mm, while the maximum inter-annual difference in SDII is about 6 mm/d. This indicates that the precipitation intensity varies significantly from year to year, and further analysis is needed to identify the reasons for this difference.

Figure 4. Temporal variation characteristics of the extreme precipitation index in the Wei River Basin. (subfigure (a) represents the temporal variability of the extreme precipitation indicator CWD; subfigure (b) represents the temporal variability of the extreme precipitation indicator PRCP; subfigure (c) represents the temporal variability of the extreme precipitation indicator SDII; subfigure (d) represents the temporal variability of the extreme precipitation indicator R10mm; subfigure (e) represents the temporal variability of the extreme precipitation indicator R20mm; subfigure (f) represents the temporal variability of the extreme precipitation indicator Rx1day; subfigure (g) represents the temporal variability of the extreme precipitation indicator Rx3day; subfigure (h) represents the temporal variability of the extreme precipitation indicator R95p; subfigure (i) represents the temporal variability of the extreme precipitation indicator R99p; K represents the change trend in the long-term series curve; K > 0 means that the curve shows an upward trend; K < 0 means that the curve shows a downward trend). This study uses the Mann–Kendall (Mann–Kendall) trend analysis method to study the EPI time trend in each site and divides the time series trend into five types according to the calculated significance level. The types are strong negative trend, negative trend, strong positive trend, positive trend, and no trend, respectively, and the results are shown in Figure 5. The results show that the EPI variation trend in most stations has a positive trend. CWD (100%), PRCPTOT (54.79%), R95P (100%), R99P (100%), SDII (59.80%), R1mm (100%), R10mm (100%), R20mm (98.63%), Rx1day (100%), Rx3day (100%) had a strong positive trend. The results indicated that the number of sites with an increasing trend and no significant change trend was greater than the number of sites with a decreasing trend, indicating that the 10 EPI time series in the Wei River Basin have generally shown a positive trend over the past 40 years.

Figure 4. Temporal variation characteristics of the extreme precipitation index in the Wei River Basin. (subfigure (a) represents the temporal variability of the extreme precipitation indicator CWD; subfigure (b) represents the temporal variability of the extreme precipitation indicator PRCP; subfigure (c) represents the temporal variability of the extreme precipitation indicator SDII; subfigure (d) represents the temporal variability of the extreme precipitation indicator R10mm; subfigure (e) represents the temporal variability of the extreme precipitation indicator R20mm; subfigure (f) represents the temporal variability of the extreme precipitation indicator Rx1day; subfigure (g) represents the temporal variability of the extreme precipitation indicator Rx3day; subfigure (h) represents the temporal variability of the extreme precipitation indicator R95p; subfigure (i) represents the temporal variability of the extreme precipitation indicator R99p; K represents the change trend in the long-term series curve; K > 0 means that the curve shows an upward trend; K < 0 means that the curve shows a downward trend). This study uses the Mann–Kendall (Mann–Kendall) trend analysis method to study the EPI time trend in each site and divides the time series trend into five types according to the calculated significance level. The types are strong negative trend, negative trend, strong positive trend, positive trend, and no trend, respectively, and the results are shown in Figure 5. The results show that the EPI variation trend in most stations has a positive trend. CWD (100%), PRCPTOT (54.79%), R95P (100%), R99P (100%), SDII (59.80%), R1mm (100%), R10mm (100%), R20mm (98.63%), Rx1day (100%), Rx3day (100%) had a strong positive trend. The results indicated that the number of sites with an increasing trend and no significant change trend was greater than the number of sites with a decreasing trend, indicating that the 10 EPI time series in the Wei River Basin have generally shown a positive trend over the past 40 years.

For the PRCPTOT index, only two stations showed a strong negative trend, while the other stations showed a positive trend, which was consistent with the positive trend in most stations for R1mm (100%), R10mm (100%), and R20mm (98.63%). The indexes of CWD and R20mm showed no trend at 10.95% and 1.37% stations, respectively, which may be the result of natural geographical factors, meteorological conditions, or other EPIs that had little impact on the overall upward trend in the EPIs in the Wei River Basin. Although the SDII index showed a positive trend on the whole, the changing trend in each station was significantly different, among which 30.17% of the sites showed a significant negative correlation trend, mainly distributed in the western part of the basin and the northern edge of the eastern Wei Plain. Considering that the time series of most stations for R1mm (100%), R10mm (100%), and R20mm (98.63%) showed a positive trend, both a strong negative trend and a strong positive trend existed, which may be caused by the difference in the increasing rate of days of R1mm, R10mm, and R20mm. The analysis results show that nearly 70% of the sites have a strong negative trend in SDII, and about 30% of the sites have a strong positive trend, indicating that in the past 40 years, the areas of extreme precipitation increased in the Wei River Basin are more than the areas decreased.

Figure 5. Significant results of EPIs based on the Mann–Kendall trend in the Wei River Basin. (subfigure (a) represents the trends in spatial variation of the extreme precipitation indicator CWD; sub-figure (b) represents the trends in spatial variation of the extreme precipitation indicator PRCP; subfigure (c) represents the trends in spatial variation of the extreme precipitation indicator SDII; subfigure (d) represents the trends in spatial variation of the extreme precipitation indicator R10mm; subfigure (e) represents the trends in spatial variation of the extreme precipitation indicator R20mm; subfigure (f) represents the trends in spatial variation of the extreme precipitation indicator Rx1day; subfigure (g) represents the trends in spatial variation of the extreme precipitation indicator Rx3day; subfigure (h) represents the trends in spatial variation of the extreme precipitation indicator R95p; subfigure (i) represents the trends in spatial variation of the extreme precipitation indicator R99p).

Figure 5. Significant results of EPIs based on the Mann–Kendall trend in the Wei River Basin. (subfigure (a) represents the trends in spatial variation of the extreme precipitation indicator CWD; sub-figure (b) represents the trends in spatial variation of the extreme precipitation indicator PRCP; subfigure (c) represents the trends in spatial variation of the extreme precipitation indicator SDII; subfigure (d) represents the trends in spatial variation of the extreme precipitation indicator R10mm; subfigure (e) represents the trends in spatial variation of the extreme precipitation indicator R20mm; subfigure (f) represents the trends in spatial variation of the extreme precipitation indicator Rx1day; subfigure (g) represents the trends in spatial variation of the extreme precipitation indicator Rx3day; subfigure (h) represents the trends in spatial variation of the extreme precipitation indicator R95p; subfigure (i) represents the trends in spatial variation of the extreme precipitation indicator R99p).

3.3. Intra-Annual Characteristics of Extreme Precipitation

3.3.1. Intra-Annual Spatial Distribution Characteristics

Based on the daily precipitation data collected from 73 precipitation stations in the study area from 1980 to 2020, representative indicators of extreme precipitation frequency, intensity, and duration were selected to analyze the spatial heterogeneity in extreme precipitation during different seasons of the year. Among them, the precipitation frequency index was selected as R20 and Rx1day, the precipitation intensity index was selected as PRCP and SDII, and the precipitation duration index was selected as CWD.

The spatial variation pattern in extreme precipitation frequency indicators in different seasons is shown in Figure 6. From Figure 6a, it can be seen that the low-value areas of the four seasons’ R20 index are mainly distributed in the western and northern regions, while the high-value areas are mainly distributed in the southeastern region. The spatial distribution of the R20 index in the spring, summer, and autumn is basically the same, and only the southern region has precipitation events greater than 20 mm in the winter. As can be seen from Figure 6b, there are some spatial differences in the precipitation index of Rx1day in different seasons. The high-value areas of Rx1day in the spring, autumn, and winter are distributed in the southern region, but the range of the high-value areas in the winter is significantly smaller than that in the spring and autumn. The high-value areas of Rx1day in the summer are distributed in some areas of the central, eastern, and southern regions.

Figure 7 shows the spatial variation in the precipitation intensity indicators in different seasons. Based on Figure 7a, the precipitation in the Wei River Basin mainly concentrates in the summer and autumn, and there are certain spatial distribution differences in different seasons. In the spring, autumn, and winter, high PRCP values are mainly distributed in the southern region, while low values are mainly distributed in the western and northern regions. In these three seasons, the high-value area in the eastern region is the smallest, while the high-value area in the autumn is the largest, with some high-value areas also existing in the central region. In the summer, high PRCP values are mainly distributed in the central and eastern regions. As can be seen from Figure 7b, the spatial distribution of SDII in different seasons is basically consistent with the distribution of PRCP.

From Figure 8, it can be seen that there are significant spatial differences in the distribution of the rainfall duration index CWD in different seasons. In the spring, the high-value areas of CWD are concentrated in the western and southern parts of the region. In the autumn, the high-value areas of CWD are concentrated in the central–western part of the region. In the winter, the high-value areas of CWD are concentrated in small parts of the northwest and southern regions.

3.3.2. Intra-Annual Temporal Characteristics

To analyze the temporal variation in extreme precipitation, the change patterns in the extreme precipitation frequency, intensity, and duration indicators in different months were calculated. The average monthly changes in five extreme precipitation indicators—Rx1, SDII, CWD, PRCP, and R20—are displayed in Figure 9. From Figure 9, it can be seen that the extreme precipitation processes in the Wei River Basin are concentrated in April–October, in which the high-value areas of the extreme precipitation indicator frequency indexes R1 and Rx1 and the extreme precipitation intensity indexes PRCP and SDII all appear in July and August. The highest values of CWD, an indicator of extreme precipitation duration, occur in September.

3.4. Impact of Climatic Factors on Extreme Precipitation

The correlation between the ENSO index and the EPI calculation results was analyzed, and the findings suggest that the extreme precipitation index and the ENSO index present a negative correlation at most stations. The related analysis is presented in Figure 10. Specifically, EPIs such as R1mm (71.24%), R10mm (49.31%), R95p (5.34%), R99p (75.34%), and Rx1day (32.88%) had a significant negative correlation with the ENSO index. This suggests that with an increase in the ENSO index, EPIs in the Wei River Basin tend to have a downward trend, including precipitation intensity, frequency, and duration. In addition, the responses of EPIs to ENSO were different. Prcp (60%), R10mm (49.32%), Rx3day (52.05%), SDII (41.1%), and EPI indexes showed a strong negative correlation with ENSO events. This reflects the fact that frequent El Niño events can reduce rainfall and suppress extreme precipitation events, which can lead to insufficient rainfall or drought.

In addition, the results further show that the correlation patterns between R10mm, R20mm, Rx1day, Rx3day, and ENSO have obvious spatial variation characteristics. For example, R10mm, R20mm, Rx1day, and Rx3day in the Loess Hills areas are often positively correlated with ENSO, that is, the precipitation intensity and frequency in these areas usually increase during ENSO events, while the Guanzhong Plain and Northern Luohe River Basin located in the east of the Wei River Basin show an opposite trend. This suggests that local topographic features may have an impact on the terrazzo so that some areas show a strong positive correlation with ENSO events. It is noteworthy that, in contrast to other EPIs, CWD does not have a significant correlation with ENSO, indicating that ENSO events have a negligible impact on the duration of precipitation in the Wei River Basin.

Because of the possible lag effect of the climate change factor ENSO on precipitation, this study analyzes the effect of a winter ENSO event on precipitation in the spring and summer of the following year. According to the statistical analysis of historical ENSO events in the Wei River Basin, strong ENSO events occurred in 1988, 1998, 1999, 2007, and 2010. We plotted extreme precipitation indicators in the spring and summer to determine whether ENSO events have a significant impact on seasonal precipitation. Figure 11 shows the spring precipitation departure curve. It can be seen from the figure that except for the 1998 ENSO event, the other four ENSO events caused the extreme precipitation indicators in the second year to be significantly lower than the average level over the long series.

Figure 12 illustrates the summer extreme precipitation indicator departure curves, from which it can be seen that all five strong ENSO events in 1988, 1998, 1999, 2007, and 2010 caused the extreme precipitation indicator in the second year to be significantly lower than the multi-year average.

The global land–ocean temperature index is a meteorological index that measures the change in the earth’s surface temperature and can reflect the trend in the global temperature rise to a certain extent. In general, an increase in LOTI means an increase in global temperature, while a decrease in LOTI means a decrease in temperature. Figure 13 shows that global temperature rise has a strong positive correlation with EPIs. The rainfall frequency and intensity of most stations will increase significantly due to global temperature rises, such as prcp (60%), R1mm (60.27%), R95p (79.45%), and R99p (79.45%). This trend is particularly significant in the Jinghe River Basin. This strong dependence is consistent with the Clausius–Clapeyron equation, which states that global warming theoretically increases the amount of water in the atmosphere and increases the probability of precipitation [7]. However, the CWD index showed a certain negative correlation with the LOTI, with 41.1% of the stations experiencing a trend of shortened rainfall duration due to the rise in the global temperature, indicating that precipitation events caused by global warming tend to be more frequent, more intense, and shorter in duration, which is highly likely to lead to more serious flood events.

The correlation between the land surface temperature (LST) and the regional extreme precipitation indicators was analyzed, and the results of the correlation analysis are shown in Figure 14. The results showed that multiple EPIs in the Wei River Basin showed significant positive correlations at most stations. For example, prcp (80%), R1mm (58.90%), R10mm (64.38%), R20mm (68.49%), R95p (73.97%), R99p (73.97%), Rx1day (47.94%), Rx3day (63.01%), and SDII (47.95%) have a consistent spatial distribution trend, which means that localized temperature increases may lead to more wet and heavy precipitation days. In addition, CWD has a strong negative correlation with LST, meaning that local temperature increases lead to fewer wet days. This correlation suggests that rising temperatures may cause more intense drought and flood events.

The formation of extreme precipitation is affected by the environmental temperature, environmental pressure, and other thermodynamic parameters. According to the C-C relationship in thermodynamic theory, the water vapor storage capacity of the atmosphere shows a growth trend of 7%/°C with an increase in temperature [24,25]. Based on the C-C relationship, the relationship between precipitation and temperature change T can be obtained with an exponential regression of each percentage of precipitation value, as shown in Equation (3) [26], where T_a denotes the starting temperature and P_a represents its corresponding precipitation and T_b denotes a certain ending temperature and P_b represents its corresponding precipitation, representing the rate of change in extreme precipitation.

$$P_b=P_a{\left(1+\alpha \right)}^{(T_b-T_a)}$$

(3)

In order to verify the correlation between extreme precipitation and temperature in the Wei River Basin, this study identified the changes in the extreme daily precipitation at the 99% percentile in the Wei River Basin with temperature changes. The correlation is shown in Figure 15. It can be seen from the figure that when the temperature is between 10 and 25 °C, the precipitation increases with the increase in temperature, and the growth rate is about 6.6%/°C, which is basically consistent with the C-C relationship. However, when the temperature exceeds 25 °C, the 99% percentile of precipitation decreases slightly with the increase in temperature. This is because when the temperature exceeds a certain threshold, humidity will significantly decrease with the increase in temperature, which also inhibits the formation of precipitation. The relationship between extreme precipitation and temperature in the Wei River Basin shows that there is an inflection point structure between them.

In order to further analyze the relationship between air temperature and precipitation, this study analyzed the correlation between air temperature change and precipitation by counting the trends in the multi-year monthly average air temperature and precipitation, and the results are shown in Figure 16. The figure shows the trends in the precipitation and temperature in different regions, respectively. The results show that there is a strong correlation between precipitation increase and temperature change (R² = 0.98). In the Wei River Basin, for every 1 °C increase in temperature, precipitation increases by about 5 mm, which further proves that as global temperatures rise, the Wei River Basin faces strong extreme precipitation and flood risks. Among them, the changing trends in the Loess Plateau, the Jing River Basin, and the Beiluo River Basin are consistent, while the precipitation change in the Guanzhong Plain is relatively smooth, indicating that temperature is not the only factor promoting precipitation increases. Changes in topography, vegetation, etc., can also affect precipitation increases.

In summary, global climate change factors are important driving factors for extreme precipitation events in the Wei River Basin. Among them, the occurrence of ENSO events may lead to a decrease in the risk of extreme precipitation events. The climate factor indicators LOTI and LST have a significant positive correlation with extreme precipitation, with LOTI having the strongest correlation with EPI. A vertex-structured relationship is shown between temperature and extreme precipitation.

4. Conclusions and Discussion

This study systematically analyzed the spatial and temporal variation of extreme precipitation indicators in the Wei River Basin by constructing an extreme precipitation evaluation system, identified key climate factors affecting extreme precipitation, and analyzed the impact of indicators such as ENSO, LOTI, and LST on the spatial and temporal variation in extreme precipitation. The correlation between temperature and extreme precipitation was also systematically elaborated. The main research conclusions include the following four aspects.

(1)

The extreme precipitation events in the southern area of the Wei River Basin are more pronounced, with significantly higher extreme precipitation intensity and frequency indicators than those in the northern region. The maximum difference between the northern and southern regions for the three extreme precipitation indicators R1, R10, and R20 reached 40, 12, and 7 days, respectively.

(2)

The extreme precipitation index in most areas of the Wei River Basin showed an overall upward trend, with the most significant change occurring in the Guanzhong Plain region. The temporal variation characteristics of extreme precipitation factors were identified using the non-parametric Mann–Kendall test method. Specifically, most sites show an upward trend in EPIs and are consistent on empty. Among them, the annual variation in seven extreme precipitation indicators (CWD, R95, R99, R1, R10, Rx1day, and Rx3day) at all stations show an upward trend. The stations with an upward trend in the annual variation of the three indicators of R20, PRCP, and SDII account for 98.63%, 54.79%, and 59.8%, respectively. The overall pattern of extreme precipitation changes in four different seasons is consistent. The high values of extreme precipitation are mainly distributed in the southern or central regions, while the low-value areas are mainly in the western region. Among them, the scope and area of high-value areas in summer are more extensive.

(3)

Climate factors such as ENSO, LOTI, and LST are important driving factors for extreme precipitation, with LOTI and LST having the most significant relationship with extreme precipitation. Among them, ENSO events show a negative correlation with extreme precipitation with a certain lag effect, and strong ENSO events in the winter often lead to a decrease in extreme precipitation in the spring and summer of the following year.

(4)

The rise in temperature often leads to more frequent, more intense, and shorter-duration precipitation events. The relationships between extreme precipitation and temperature present a peak structure.

This study proposes a systematic method for analyzing the evolution and driving factors of extreme precipitation, which reveals the spatial and temporal variation in extreme precipitation and analyzes the impact of climate change factors on extreme precipitation. The spatial and temporal heterogeneity in extreme precipitation characteristics in the Wei River Basin are closely related to changes in atmospheric circulation, global climate change, topography, and human activities. On the one hand, different regional circulation types and topographic features contribute to the spatial characteristics of extreme precipitation in different regions. On the other hand, global climate change factors such as ENSO, LOTI, and LST have a significant impact on regional water vapor characteristics. In addition, climate warming has also significantly changed the regional water vapor content, which has a significant impact on regional extreme precipitation. Nevertheless, this study does not involve the analysis of the formation mechanism of typical extreme precipitation events in the Wei River Basin. We plan to conduct research on this part in future studies.