1 Introduction

In recent years, affected by climate change, extreme precipitation events have occurred frequently around the world (Huang et al. 2021; Lei et al. 2021; P. Wang et al. 2021a, b). Extreme precipitation events have caused serious impacts and huge losses on many aspects such as society, economy, and people’s life safety (Huang et al. 2021; Luo et al. 2016; P. Wang et al. 2021a, b). The global climate has been in a stage of continuous warming in the past 100 years (Ergin et al., 2021; X. Liu et al. 2021a, b; Mandal et al. 2022). From 1880 to 2012, the global average surface temperature increased by 0.85 °C (Hu et al. 2021; Zhao et al. 2021). The research on the changes of extreme precipitation under the background of global warming is the focus in recent years (Luo et al. 2016; Ogorodnikov and Sereseva 2015; Wang et al. 2019). The intensity and frequency of extreme precipitation events have changed significantly, and this change has strong regional and local characteristics (Dar et al. 2021; Luo et al. 2016; Zhang et al. 2014). Many studies have shown that as global warming intensifies, extreme precipitation generally shows an increasing trend (X. Li et al. 2021a, b, c; Ren et al. 2021; Zhang and Zhou 2020). In the mid-high latitudes of the northern hemisphere, even if the annual precipitation decreases, the extremeness of precipitation has increased significantly (Sun et al. 2016; Wang et al. 2020).

Temperature and precipitation are the two most commonly used variables in climate change research and have important instructions to the natural environment of an area (Patra et al. 2021; Yao et al. 2021). Water vapor is the link between extreme precipitation and temperature. Changes in temperature will change the water vapor content in the atmosphere, increasing the uncertainty of the occurrence of extreme precipitation (Vázquez et al. 2020; Wang et al. 2017). Global warming increases the uncertainty of regional extreme precipitation, and extreme precipitation events have occurred frequently in China in recent years (Lu et al. 2021; Wu et al. 2021). Studies have shown that under representative concentration pathway (RCP) 4.5 and RCP8.5 scenarios, for every 1 °C increase in regional average temperature in China, extreme precipitation defined by the 95th percentile increases by 11.9% and 11.0%, respectively (Gao et al. 2021; Hu et al. 2021; Zhu et al. 2021). The anomaly of temperature, especially the anomaly of sea temperature, is an important factor that induces extreme precipitation (Cai et al. 2021; Carvalho et al. 2021; Mondal et al. 2021). There are different processing methods to define extreme precipitation event (Schauwecker et al. 2021; Xu et al. 2019; Zhu et al. 2021). According to the time resolution of the precipitation series, precipitation events with different time steps can be defined (Sadeghi et al. 2021; Wei et al. 2021). In previous studies, the daily precipitation that exceeds a certain threshold is often regarded as an extreme precipitation event, but this is often not a complete precipitation process, because heavy precipitation process may last for more than one day (Breugem et al. 2020; Cao et al. 2021; Douluri and Chakraborty 2021; Lu et al. 2021).

The occurrence of extreme precipitation events has strong regional characteristics (Cheng et al. 2021; Luo et al. 2016; Nguyen et al. 2020). Therefore, the study of extreme precipitation from a regional perspective is an important supplement to the study of large areas, and the characteristics of extreme precipitation events can be found on a smaller spatial scale (Ergin et al. 2021; Michel et al. 2021; P. Wang et al. 2021a, b). This study selected the Huaihe River Basin (HRB), which is located in the climate transition zone between north and south of China, as the research object (Cheng et al. 2021). In recent years, frequent extreme precipitation events have caused huge losses of life and property in this area (Cheng et al. 2021; Xu et al. 2019). This study extracted extreme precipitation events in the HRB based on precipitation amount and precipitation intensity and further analyzed the causes of extreme precipitation from the perspective of abnormal temperature and atmospheric circulation. It provides a certain reference value for the analysis of the background causes of extreme precipitation in the HRB.

2 Study area

The HRB (110°22′–121°52′E, 29°27′–36°12′N) (Fig. 1) is located in eastern China, across Jiangsu, Anhui, Henan, and Shandong provinces, between the Yellow River and the Yangtze River, with a drainage area of about 2.7 × 105 km2 (Cheng et al. 2021; Xu et al. 2019). The HRB is located in the north–south climate transition zone of China, and the southern part of the HRB belongs to the subtropical humid monsoon climate zone, while the northern part belongs to the semi-humid monsoon climate zone (Chen et al. 2020). The weather and climate in the basin are complex and changeable, and floods are prone to occur. This may be related to its location in the north–south climate transition zone and plus the impact from land and marine.

Fig. 1
figure 1

Topography and station location distribution in the HRB

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The annual average precipitation in the HRB is about 900 mm, but the inter-annual variation is large, mostly concentrated in June to September, and the spatiotemporal distribution during the year is also extremely uneven. Precipitation gradually decreases from south to north, with more in mountainous areas than in plain areas, and more in coastal areas than in inland areas. The variability of climate and the complexity of topography determine the uniqueness of the spatiotemporal distribution of precipitation in the HRB. The variability of climate and the complexity of topography have led to the difference in the spatiotemporal distribution of precipitation in the HRB. Influenced by the global warming, the distribution characteristics of precipitation in the HRB have also changed in recent years. Heavy precipitation in large areas can easily induce floods, cause the lives and property of the people in the HRB to be lost, and hinder social and economic development.

3 Data and methodology

3.1 Data

The precipitation data for this study comes from the China Meteorological Data Service Center (CMDSC) of China Meteorological Administration (CMA) (http://data.cma.cn/dataService/) (Shi et al. 2020). We selected the daily precipitation data of 30 meteorological stations in HRB from 1960 to 2018, and a small amount of missing data was filled by linear interpolation. The CMA evaluated the quality of the data to ensure the reliability and continuity of the data (Zhai et al. 2005). The extreme precipitation events were extracted from the precipitation sequence based on the specific precipitation threshold in this study. However, although the amount of precipitation in an extreme precipitation event is large, the precipitation intensity may not large, so we further extracted the extreme precipitation event based on the precipitation intensity. This can ensure the identification of all forms of extreme precipitation events. The detailed information of the stations is shown in Table 1. The last three columns of the table are the annual average amount of precipitation (PRE), extreme precipitation (EP), and intensity-based extreme precipitation (IBEP).

Table 1 Attribute information of meteorological stations in the HRB
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The reanalysis dataset used in this study comes from global atmospheric reanalysis data jointly developed by the National Center for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) (R. Li et al. 2021a, b, c). The meteorological variables used in this study were geopotential height, wind speed, specific humidity, and surface pressure. The data can freely available from the National Oceanic and Atmospheric Administration (NOAA) Physical Sciences Laboratory (PSL) (https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html). This study used monthly timescale data from January 1960 to December 2018. The data has a spatial resolution of 2.5° × 2.5° and a total of 144 × 73 grids. These data were used to analyze circulation anomalies when extreme precipitation occurs.

Further, we selected 20 circulation indicators to analyze the correlation between extreme precipitation and circulation anomalies; their details are shown in Table 2. These data were provided by the National Climate Center (NCC) of CMA (https://cmdp.ncc-cma.net/Monitoring/). In addition, four indicators, Nino 1 + 2, Nino 3, Nino 3.4, and Nino 4, which characterize the El Niño Southern Oscillation (ENSO) event, were selected to analyze the relationship between the occurrence of extreme precipitation and the sea surface temperature (SST) anomaly in the Pacific Ocean (Muñoz et al. 2021). Other climate variables include the Atlantic multidecadal oscillation (AMO), Arctic Oscillation (AO) Index, Dipole Mode Index (DMI), North Atlantic Oscillation (NAO), North Pacific Index (NPI), Pacific Decadal Oscillation (PDO), and Southern Oscillation Index (SOI). The data were also provided by the NOAA (https://psl.noaa.gov/).

Table 2 Atmospheric circulation index information table
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3.2 Data process

In this study, three indicators, PRE, EP, and IBEP, were selected to extract precipitation characteristics. Among them, PRE is the total annual precipitation amount. Precipitation was counted according to the continuity to obtain precipitation events, and then the largest precipitation event was selected as EP among the annual precipitation events, a schematic diagram of the extraction of extreme precipitation events based on continuity is shown in Fig. 2. The IBEP was selected based on the precipitation intensity, that is, the precipitation event with the highest precipitation intensity was selected. Their calculation formula is as follows:

$$PRE=\sum \nolimits_{i}^{n}{P}_{i}$$
(1)
$$EP=\mathrm{max}\left\{{P}_{1}, {P}_{2}, \cdots {P}_{n}\right\}$$
(2)
$$Int=P/D$$
(3)
$$IBEP=\mathrm{max}\{\left({P}_{1}, {Int}_{1}\right),({P}_{2}, {Int}_{2})\cdots ({P}_{n},{Int}_{n})\}$$
(4)

where PRE is the total annual precipitation (mm), P is the precipitation amount of each precipitation event (mm), n is the number of precipitation events in a year, EP is the annual maximum extreme precipitation (mm), Int is the precipitation intensity of the precipitation event (mm/day), D is the duration of a precipitation event (day), IBEP is the precipitation amount of the precipitation event with the highest precipitation intensity (mm).

Fig. 2
figure 2

Schematic diagram of extraction of annual extreme precipitation events based on continuity

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3.3 REOF

Rotational empirical orthogonal function (REOF) is obtained by orthogonal rotation with maximum variance based on empirical orthogonal function (EOF) decomposition (X. Li et al. 2021a, b, c; Zambreski et al. 2018). The principal component contribution rate after rotation is more average than EOF method, which simplifies the structure of the feature vector (Mo et al. 2021). The spatial modes decomposed by rotation can more clearly reflect the climate characteristics. The calculation process is to first standardize the element field matrix to obtain the standardized matrix X and calculate the cross-product of the matrix X and its transposed matrix XT to obtain the correlation number matrix A. Then use the Jacobi method to find the eigenvalue λ, feature vector V, and time coefficient Z of the matrix (Mandal et al. 2022). Take the feature vector V that has passed the significance test to perform the maximum variance rotation. When the difference between the current two rotations and the variance meets the accuracy requirements (such as variance difference value/initial variance < 0.01), then stop the rotation. In this way, the variance and variance contribution rate of each factor, the rotated feature vector B, and the rotated time coefficient G are obtained:

$$X=B\times G$$
(5)

where X is the standardized matrix, B is the rotated feature vector, and G is the rotated time coefficient.

3.4 SVD

Singular value decomposition (SVD) is essentially a mathematical matrix operation, that is, for any real matrix, it is decomposed into the product of two unit orthogonal matrices and diagonal matrices (Liu et al. 2017). In meteorology, this method is often used to study the spatial relationship of the time–domain correlation between two fields and to find the key areas of the two fields with each other (Sadeghi et al., 2019). Suppose there are two fields, X and Y, called the left field and the right field, which contain m and n spatial grid points or stations, respectively, and the time length is k. The matrix is expressed as follows:

$$X=\left[\begin{array}{ccc}{x}_{11}& \cdots & {x}_{1k}\\ \vdots & \ddots & \vdots \\ {x}_{m1}& \cdots & {x}_{mk}\end{array}\right], Y=\left[\begin{array}{ccc}{y}_{11}& \cdots & {y}_{1k}\\ \vdots & \ddots & \vdots \\ {y}_{n1}& \cdots & {y}_{nk}\end{array}\right]$$
(6)

Find the cross-covariance matrix XYT of X and Y. If the data in the matrix all belong to the real number domain, then perform SVD decomposition transformation on it; two orthogonal linear transformation matrices L and R can be obtained when their covariance is the largest. They satisfy the following properties:

$${L}^{T}X=U, {R}^{T}Y=V$$
(7)

where the qth column vector of L and R is called the qth left and right singular vector or the qth left and right mode respectively. U is called the left field time coefficient matrix, V is called the right field time coefficient matrix, and the qth row vectors of U and V are called the qth left and right modal time coefficients, respectively.

The matrix after SVD transformation has the following advantages: (1) the left field only has a high correlation with the corresponding mode of the right field and is not related to other modes. (2) The first N pairs of modes can explain most of the relevant characteristics of the two fields. (3) When the correlation coefficients of the two modes are positive, the area with the same sign of the correlation coefficient of the left and right fields indicates a positive correlation, and the opposite area indicates a negative correlation and vice versa. Through the SVD decomposition, the analysis of the numerous relationships between the left field and the right field variables over time becomes a simple relationship between the time coefficients of the N pairs of modes, which simplifies the problem and highlights the research focus.

3.5 Water vapor flux and divergence calculation

Water vapor flux represents the water vapor content flowing through a unit cross-sectional area per unit time and is divided into horizontal water vapor flux and vertical water vapor flux (MacDonald et al. 2018; Zhang and Zhou 2020). It reflects the transport path and intensity of the water vapor in the atmosphere carried by the airflow from one area to another. This study only analyzes the horizontal transportation flux, mainly studying the path and intensity of water vapor transportation. The calculation formula is as follows:

$$\overrightarrow{F}={g}^{-1}{\int }_{{p}_{z}}^{{p}_{s}}q\overrightarrow{V}dp$$
(8)

where \(\overrightarrow{V}\) is the wind speed vector, which can be decomposed into zonal wind speed \(u\) and meridional wind speed \(v\). It is stipulated that \(u\) is positive to the east, negative to the west, \(v\) is positive to the north, and negative to the south. \(q\) is the specific humidity, \({p}_{s}\) is the surface pressure, \({p}_{z}\) is the pressure at the altitude \(z\), and \(g\) is the acceleration due to gravity. \(\overrightarrow{F}\) is the water vapor transport flux; its conveying direction is consistent with the wind direction.

The water vapor transport flux divergence indicates the convergence and divergence of water vapor in a region (Yin et al. 2020). Since the NECP/NCAR reanalysis data is stored in the form of grids, it is more appropriate to use the latitude and longitude grid method when calculating the plane divergence. The formula for calculating the water vapor flux divergence is as follows:

$$D=\frac{1}{g}\nabla \left(Vq\right)=\frac{\partial }{\partial x}\left(\frac{1}{g}uq\right)+\frac{\partial }{\partial y}(\frac{1}{g}vq)$$
(9)

where D is the water vapor flux divergence, g represents the acceleration due to gravity, u represents the zonal wind speed, v represents the meridional wind speed, and q is the specific humidity.

3.6 Multivariate wavelet coherence (MWC)

Multivariate wavelet coherence (MWC), developed from binary wavelet coherence (BWC) and ternary wavelet coherence (TWC), is an effective method to study multivariate correlations (Hu and Si 2016). MWC is more powerful than BWC and TWC due to its ability to handle cross-correlated variables. MWC has demonstrated excellent performance in unraveling scale-specific and local multivariate relationships in geosciences. The magnitude of the correlation between variables was evaluated by average coherence and percent area of significant coherence (PASC).

4 Results

4.1 PRE, EP, and IBEP spatiotemporal distribution

The annual average PRE presents a cascade change in the basin, with more in the south and less in the north (Fig. 3a1). The spatial trend of PRE shows an increase in the southwest and a decrease in the northeast (Fig. 3a2). The multi-year average EP shows decreasing from south to north in the basin, and the source area in the southwest of the HRB is the high-value area (Fig. 3b1). The EP from west to east shows a decreasing, increasing, and then decreasing trend in the HRB (Fig. 3b2). The multi-year average IBEP shows a trend of being more in the southwest and southeast and less in the northeast, northwest, and central part of the basin (Fig. 3c1). The IBEP trend change shows a decreasing trend in most parts of the basin, especially in the northeast, but there is a certain increasing trend in the southwest and southeast of the basin (Fig. 3c2). This shows that precipitation amount in the HRB is greatly affected by latitude, and the western mountainous area and eastern coastal area are more prone to extreme precipitation.

Fig. 3
figure 3

Annual average spatial distribution and trend changes of PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2) (Note: * indicates a significant trend, and the significance level is 5%, the same below)

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The average PRE, EP, and IBEP variation curves of the whole basin are shown in Fig. 4. The average PRE of the whole basin has a slight increasing trend (Fig. 4a), while EP (Fig. 4b) and IBEP (Fig. 4c) have no obvious changing trend. It is worth noting that years with a large PRE may not necessarily produce extreme EP and IBEP. The occurrence years of larger EP and IBEP were similar.

Fig. 4
figure 4

Average trend change curve of PRE (a), EP (b), IBEP (c) in the HRB

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PRE has a main cycle of about 15 years, but in recent years (after 1984), this main cycle has been divided into a small cycle of about 10 years and a major cycle of about 20 years (Fig. 5a1, a2). EP has three obvious periodic characteristics, which are about 5-year, 12-year, and 25-year cyclical changes (Fig. 5b1, b2). However, after about 1980, the 12-year cycle disappeared, the 5-year cycle gradually increased to about 10 years, and the 25-year cycle gradually decreased to about 20 years. Similar to the EP cycle change, IBEP had about 5-year, 12-year, and 27-year cycle changes before about 1984, but after 1984, the 5-year and 12-year cycles gradually merged into a major cycle of about 10 years, and the intensity of the 27-year cycle gradually weakened (Fig. 5c1, c2). In summary, it can be seen that the extreme precipitation cycle of the HRB has changed since the 1980s, and the uncertainty has increased.

Fig. 5
figure 5

The contour map and the variance map of the real part of wavelet coefficients for PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2)

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Mann–Kendall (MK) test is one of the most commonly used mutation and trend testing methods for time series (Chong et al. 2022; Güçlü, 2020; Nyikadzino et al. 2020). It can determine the mutation point and change trend by analyzing the changes of the statistics \({UF}_{k}\) and \({UB}_{k}\). The PRE fluctuates significantly in the HRB (Fig. 6a). Although there were many mutation points around 2000, the trend of PRE after the mutation did not change significantly. EP had a mutation point around 1967, but the downward trend after mutation did not reach the 5% significance level (Fig. 6b). Around 2000, EP had a mutation point and then showed an upward trend, but the trend was also not significant. IBEP had a mutation point around 1992 and then showed an upward trend, but the trend was also not significant (Fig. 6c). These show that both PRE, EP, and IBEP have an increasing trends in recent years (after around 2000), although the trends are not significant.

Fig. 6
figure 6

MK mutation analysis of PRE (a), EP (b), IBEP (c)

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The variance contribution rates of the first mode (REOF1) and the second mode (REOF2) of PRE are 41% and 16%, respectively, which represent the main spatial distribution characteristics of PRE in the HRB. In the first mode, PRE presents the same state in the whole basin, that is, the whole basin shows the same increase or decrease mode (Fig. 7a1). In the second mode, PRE presents an opposite trend from southeast to northwest in the HRB, that is, the PRE is large in the southeast and small in the northwest, or the PRE is small in the southeast and large in the northwest (Fig. 7a2). The variance contribution rates of the first mode and the second mode of EP are 18% and 13%, respectively. This shows that in addition to the first and second modes of EP in the HRB, other modes also account for a large proportion. The first mode presents the opposite of EP in the eastern and western regions of the HRB (Fig. 7b1). The second mode presents the opposite situation of EP in the southern and northern parts of the HRB (Fig. 7b2). The variance contribution rate of the IBEP first mode accounted for 17%, and the second mode accounted for 11%. The first mode of IBEP shows the opposite situation in the north and south of the HRB (Fig. 7c1), while the second mode shows the same situation in the whole basin, but the low-value areas are mainly concentrated in the middle of the basin (Fig. 7c2). This shows that the spatial distribution characteristics of EP and IBEP are more complicated than PRE.

Fig. 7
figure 7

The spatial distribution of the first and second modes (REOF1 and REOF2) of PRE (a1, a2), EP (b1, b2), IBEP (c1, c2)

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The time coefficient variation curves of the first mode and the second mode of PRE, EP, and IBEP are shown in Fig. 8. It can be seen from the figure that except for the second mode time coefficient of PRE which showed an insignificant upward trend (Fig. 8 a2), the time coefficients of other modes did not change significantly. This shows that the spatial distribution characteristics of EP and IBEP in the HRB are relatively stable.

Fig. 8
figure 8

The time coefficient variation curve of the first and second modes of PRE (a1, a2), EP (b1, b2), IBEP (c1, c2)

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4.2 Correlation analysis of PRE, EP, IBEP, and temperature

The abnormal temperature will cause the fluctuation of the atmospheric circulation, and then the fluctuation of the atmospheric circulation will cause the weather and climate system to fluctuate, making extreme precipitation easier to produce (Räisänen, 2021). Therefore, the influence of abnormal temperature on the global climate has become a research hotspot in meteorology, oceanography, and hydrology. The HRB is located in the East Asian monsoon region, and one of the main driving forces for the formation of the monsoon is the thermal difference between the sea and land (Y. Xu et al. 2021a, b). Therefore, changes in temperature can affect the strength of the East Asian monsoon, which in turn affects the intensity of water vapor transport and further affects the precipitation amount in the HRB (J. Wang et al. 2021a, b).

PRE is positively correlated with the temperature in the Bering Sea and the Norwegian Sea, and the correlation is significant, while it is negatively correlated with the temperature in the South China Sea and the southern Indian Ocean, though the correlation is not significant (Fig. 9a). EP is positively correlated with the temperature of the Northeast Pacific but negatively correlated with the southern Indian Ocean and the eastern part of the Tibetan Plateau, and the correlations are significant (Fig. 9b). Similar to the correlation between EP and temperature, IBEP is positively correlated with the northeast Pacific temperature, but the correlation is no longer significant but still has a significant negative correlation with the southern Indian Ocean and the east of the Qinghai–Tibet Plateau (Fig. 9c). This shows the regions that have a major impact on PRE, EP, and IBEP in the HRB are the North Pacific, the South Indian Ocean, and the Qinghai–Tibet Plateau.

Fig. 9
figure 9

The spatial distribution of the correlation coefficients between PRE (a), EP (b), and IBEP (c) with temperature (Note: + indicates that the significance level exceeds 5%)

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The distribution of the SVD first mode heterogeneous correlation coefficient between PRE and global temperature is shown in Fig. 10 (a1 and a2. The contribution rate of the squared covariance of the first mode reaches 50%, which shows that the first mode can basically represent the impact of global temperature on PRE in the HRB. The spatial distribution of the heterosexual correlation coefficient of PRE in the HRB is from positive to negative from southwest to northeast. However, the spatial distribution of the global temperature heterogeneous correlation coefficient is mostly positive, and the negative regional correlation is not significant. This indicates that the global temperature rises, the precipitation in the southwest regions of the HRB will increase while the precipitation in the northeast regions will decrease. The contribution rate of the squared covariance of the first mode of SVD between EP and global temperature is 31%. The heterosexual correlation coefficient of EP shows positive correlation, negative correlation, and positive correlation in the HRB from southwest to northeast (Fig. 10b1). However, the heterosexual correlation coefficient in the southeast is a significant negative correlation. The global temperature field shows a uniform negative distribution, especially in the central Indian Ocean, the central and western Pacific, the central and western Atlantic, and the Tibetan Plateau (Fig. 10b2). This indicates that lower temperatures in these areas will contribute to the production of EP in the southwest and northeast of the HRB. The contribution rate of the squared covariance of the first mode of SVD between IBEP and global temperature is 39%. The heterogeneous correlation coefficient of IBEP is positive in most areas of the basin while in a small part areas of the southwest and southeast is negative (Fig. 10c1). The heterogeneous correlation coefficients of temperature fields show negative distributions in most regions, and the most significant correlation regions are located in the Indian Ocean, the central eastern Pacific Ocean, the central Atlantic Ocean, and the Qinghai–Tibet Plateau (Fig. 10c2).

Fig. 10
figure 10

The spatial distribution of the SVD first mode heterogeneous correlation coefficients between PRE (a1, a2), EP (b1, b2), IBEP (c1, c2) and global temperature (Note: * indicates that the significance level exceeds 5%)

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The first mode time coefficient curves of PRE, EP, IBEP, and temperature are shown in Fig. 11. From this, it can be clearly seen that the time correlation coefficient between temperature and PRE shows a significant upward trend, which indicates that PRE will increase in the southern part of the HRB and decrease in the northeast (Fig. 11a). The time correlation coefficients of temperature with EP and IBEP all show a downward trend (Fig. 11b, c), which indicates that extreme precipitation in the northeast and southwest of the HRB will have an increasing trend, while the southeast will have a decreasing trend. It can be seen that although PRE increased in the southern part and decreased in the northern part of the HRB, EP and IBEP in the northern part showed an increasing trend, which is consistent with the frequent occurrence of extreme precipitation in the northern part of the HRB in recent years.

Fig. 11
figure 11

Time coefficient curve of SVD first mode heterogeneous correlation coefficient of PRE (a), EP (b), and IBEP (c)

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4.3 Background analysis of extreme precipitation events

According to the provisions of the World Meteorological Organization (WMO), an event with an anomaly of 1.3 times the standard deviation (\(\sigma\)) of a climate indicator is called an abnormal climate event, and an event with an anomaly of 2 times the standard deviation is called a severe climate event. In this study, the years with more than ± 1.3σ are selected as the years with abnormally high and low precipitation.

It can be seen from Fig. 12 that the changing trends of PRE, EP, and IBEP are basically the same, but the high-value years of PRE do not necessarily make EP and IBEP also high-value years. Generally, the high-value and low-value years of EP and IBEP are basically the same. Table 3 lists the high- and low-value years of PRE, EP, and IBEP. It can be seen from the table that the high-value years of EP and IBEP are basically similar, but the extreme years of other indicators are not the same.

Fig. 12
figure 12

Extraction of extreme events from PRE, EP, and IBEP by \(\pm 1.3\sigma\)

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Table 3 Statistics on the years of extreme events of PRE, EP, and IBEP
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In the high-value year of PRE, the annual average temperature in the HRB is relatively low, and the annual average temperature is also relatively low in the Qinghai–Tibet Plateau (Fig. 13a1). In the low-value year of PRE, the annual average temperature in the HRB is relatively high, and the annual average temperature is also relatively high in the northern Indian Ocean and the South China Sea (Fig. 13a2). The annual average temperature in the HRB is relatively high in the high-value year of EP, while the annual average temperature in the Qinghai–Tibet Plateau is relatively low (Fig. 13b1). In the low-value year of EP, the annual average temperature of HRB is lower, and the annual average temperature of the northern Indian Ocean and the South China Sea is also lower (Fig. 13b2). In the high-value year of IBEP, the average annual temperature of HRB is higher, while the annual average temperature of Qinghai–Tibet Plateau, Siberia, and Southern Indian Ocean is lower (Fig. 13c1). In the low-value year of IBEP, the average annual temperature of HRB is lower, but the annual average temperature of Qinghai–Tibet Plateau, Siberia, and the Southern Indian Ocean is higher (Fig. 13c2). It can be seen that when extreme PRE, EP, and IBEP appear in HRB, there are significant differences in temperature in Siberia, the Tibetan Plateau, and the Indian Ocean, which has an important impact on the occurrence of extreme PRE, EP, and IBEP in HRB.

Fig. 13
figure 13

The abnormal distribution of global temperature in high-value and low-value years of PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2)

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The El Niño indicator is an important means to show abnormal changes in the Pacific Ocean temperature. Anomalies in sea temperature will further cause anomalies in atmospheric circulation, which in turn will induce extreme weather events (Xu et al. 2019). Table 4 lists the average values of the four El Niño indicators in the high-value and low-value years of PRE, EP, and IBEP. It is obvious showed from the table that PRE, EP, and IBEP have higher El Niño index values in high-value years than that in low-value years. This indicates that the year of high sea surface temperature in the Pacific contributes to the production of extreme heavy precipitation in the HRB. The El Niño indicator can be used to predict the extreme precipitation in the HRB.

Table 4 The average El Niño indicator of PRE, EP, and IBEP in the high-value and low-value years (Note: average represents the overall average during the study period (1960–2018))
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Wind has an important influence on the transmission of water vapor, especially the water vapor transport between sea and land. The strong southerly wind in the high-value year of PRE brings sufficient water vapor from the sea to the HRB (Fig. 14a1), while in the low year of PRE, the northerly wind prevails in the basin, which reduces the water vapor entering the HRB (Fig. 14a2). In the high-value EP year, the strong northerly wind and the strong East Asian monsoon meet over the HRB, which is conducive to the production of extreme precipitation (Fig. 14b1). In the low-value EP year, although the northerly wind is stronger, the East Asian monsoon is weaker, which makes the water vapor coming to the HRB less, leading to a small precipitation (Fig. 14b2). In the high-value year of IBEP, similar to the wind field in the high-value year of EP, the strong northerly wind and the strong East Asian monsoon meet in the HRB, which is conducive to the occurrence of heavy precipitation (Fig. 14c1). In the low-value year of IBEP, although the southerly wind is strong, the northerly wind is weak, so that the water vapor only passes through the HRB and it is difficult to form precipitation in the HRB (Fig. 14c2).

Fig. 14
figure 14

The average wind field distribution of PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2) in high-value years and low-value years

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From the high-value year and low-value year 500 hPa height composite field of the PRE, EP, and IBEP, the 500 hPa height field is stronger in the high-value year and is weaker in the low-value year (Fig. 15). In the strong year of the subtropical high, the HRB is affected by the warm and humid airflow along the slope of the subtropical high. The airflow is rich in water vapor, and the upward movement is strong, so there are more extreme precipitation events.

Fig. 15
figure 15

The average 500 hPa synthetic height field of PRE, EP, and IBEP in the extremely high and low years

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The 500 hPa anomaly field in the high-value year of PRE is relatively high throughout China, the Indian Ocean, and the Pacific (Fig. 16a1). However, in the low-value year of PRE, the 500 hPa anomaly height field in the North Pacific is relatively low, and it is also relatively low in most areas of the Indian Ocean and the Pacific Ocean (Fig. 16a2). In the high-value year of EP, the 500 hPa anomaly height field showed positive anomalies in most areas of the North Pacific and Indian Ocean (Fig. 16b1), while in the low-value year of EP, in the North Pacific, the Indian Ocean, and Northwest China all showed negative anomalies (Fig. 16b2). In the high-value year of IBEP, the 500 hPa anomaly height field still has a positive anomaly in the North Pacific, but it shows a negative anomaly in most of the Indian Ocean and the Pacific (Fig. 16c1). In the low-value year of IBEP, the 500 hPa anomaly height field in most areas of China is at positive anomalies, and in most areas of the Indian Ocean and the Pacific, it is also at positive anomalies (Fig. 16c2). At this time, the air pressure in Siberia was low, making the northerly wind weaker, which was not conducive to the formation of heavy precipitation in the HRB. On the whole, the increase in the 500 hPa height field in Siberia and the Northwest Pacific will contribute to the occurrence of extreme precipitation in the HRB.

Fig. 16
figure 16

The 500 hPa height anomaly field of PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2) in high-value and low-value years (unit: hPa)

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Circulation anomalies are the main cause of extreme weather events, and they can be identified through the circulation index (Y. Xu et al. 2021a, b). Table 5 lists the average values of 20 circulation indices of PRE, EP, and IBEP in high-value and low-value years. It can be clearly seen from the table that the value of the circulation index in the high-value year of PRE is significantly higher than that in the low-value year. Similarly, most of the circulation indices in the high-value year of EP and IBEP are greater than those in the low-value year. This indicates that the year when the circulation is abnormally strong is more likely to cause extreme strong precipitation in the HRB, and the numerical value of the circulation index can be used to predict the occurrence probability of extreme precipitation in the HRB.

Table 5 The average circulation indices of PRE, EP, and IBEP in the high-value and low-value years (Note: average represents the overall average during the study period (1960–2018))
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The water vapor transport flux anomalies and water vapor flux divergence anomalies of the whole layer in high-value year and low-value year of PRE, EP, and IBEP are shown in Fig. 17. During the high-value year of PRE, a large amount of water vapor continuously enters the HRB from the South China Sea, resulting in a large amount of precipitation in the HRB (Fig. 17a1). In the low-value year of PRE, the water vapor in the HRB was in a state of divergence, and precipitation was mainly formed in southern China (Fig. 17a2). In the high-value year of EP, water vapor from the Indian Ocean was continuously imported into the HRB, and violent convergence occurred, forming relatively large precipitation (Fig. 17b1). In EP low-value year, the water vapor in the HRB mainly comes from the South China Sea, but the water vapor convergence occurs in the north rather than over the HRB (Fig. 17b2). In IBEP high-value year, water vapor from the Indian Ocean continuously enters the HRB and converges in the HRB, resulting in relatively large precipitation (Fig. 17c1). In the IBEP low-value year, the water vapor in the HRB mainly comes from the South China Sea, but the water vapor is mainly transit water vapor and does not converge in the HRB (Fig. 17c2). In IBEP low-value year, the water vapor in the HRB mainly comes from the South China Sea, but the water vapor is mainly transit water vapor and does not converge in the HRB (Fig. 17c2). These indicate sufficient water vapor from the oceans, especially from the Indian Ocean, and its convergence in the HRB is a key factor in the formation of extreme precipitation in the HRB.

Fig. 17
figure 17

The anomalous field of the whole-layer average water vapor flux and the water vapor flux divergence of PRE (a1, a2), EP (b1, b2), and IBEP (c1, c2) in high-value and low-value years

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4.4 The impact of climate factors on extreme precipitation

From 1970 to 1985, there was a negative correlation between AMO and PRE for about 10 years. From 1989 to 1993, AO and PRE had a negative correlation of about 2.5 years. From 1984 to 1991, there was a positive correlation between NPI and PRE for about 6 years. The specific results are shown in Fig. 18, which will not be repeated here. The phase changes between EP and IBEP and climate variables were similar. There was a positive correlation between AO and EP and IBEP for about 8 years from 1975 to 1993. The specific results are shown in Fig. 19 and Fig. 20, which will not be repeated here.

Fig. 18
figure 18

The BWC of PRE and eight climate variables (arrows indicate the phase angle of the wavelet spectrum, the thin solid line divides the cone of influence, and the thick solid line represents the 95% confidence level, same below)

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Fig. 19
figure 19

The BWC of EP and eight climate variables

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Fig. 20
figure 20

The BWC of IBEP and eight climate variables

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AC and PASC are used to determine the influence intensity of climate variables on precipitation. The larger the value of AC and PASC, the stronger the influence. Generally, the size of the PASC value is given priority, and in the case of the same PASC value, the size of the AC value is compared. AMO has the greatest impact on PRE, followed by PDO and third by NPI (Fig. 21a). AO has the greatest impact on EP, followed by AMO, and the third is NPI (Fig. 21b). AO has the greatest impact on IBEP, followed by NPI and third by AMO (Fig. 21c). The top three factors that had the greatest effect on EP and IBEP were the same, but there were differences in the strength of the effect.

Fig. 21
figure 21

AC and PASC of BWC between PRE (a), EP (b), and IBEP (c) and eight climate variables

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From 1975 to 2002, there was a significant correlation between PRE and AMO-NPI-PDO for about 9 years (Fig. 22). The relationship between EP and AMO-AO-NPI and IBEP and AMO-AO-NPI was similar, with a significant correlation of about 8 years from 1976 to 1990, and a significant correlation of about 16 years from 1978 to 2000. Both AC and PASC of PRE and AMO-AO-NPI were significantly improved (Fig. 23). AC was improved for EP and AMO-AO-NPI, and IBEP and AMO-AO-NPI, but PASC decreased. This indicates that PRE was significantly affected by multiple climate variables, while EP and IBEP are more significantly affected by single climate variable.

Fig. 22
figure 22

MWC between PRE (a), EP (b), and IBEP (c) and the combination of climate variables

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Fig. 23
figure 23

AC and PASC of MWC between PRE, EP, and IBEP and the combination of climate variables

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5 Discussion

In recent years, global extreme weather events have occurred frequently, especially extreme precipitation events (Dar et al. 2021; Wang et al. 2020; Zhang et al. 2014). Both the magnitude and intensity of precipitation exceed previous records (Ergin et al., 2021; X. Liu et al. 2021a, b). For example, the extreme precipitation events in Germany and Henan Province of China in July 2021 have caused huge losses to the lives and property of the local people (Mandal et al. 2022). Analysis of the causes of extreme precipitation events has become a global hot issue, and it is urgent to establish a rapid monitoring and early warning system for extreme precipitation events (Y. Li et al. 2021a, b, c; Ren et al. 2021; Wang et al. 2019; P. Wang et al. 2021a, b). However, precipitation is extremely random, which brings great challenges to the accuracy of precipitation forecasts (MacDonald et al. 2018; Vázquez et al. 2020; Wang et al. 2020). Affected by climate change, the magnitude of extreme precipitation has also been increasing in recent years (Douluri and Chakraborty, 2021; X. Li et al. 2021a, b, c; S. Liu et al. 2021a, b). Some areas with less precipitation, such as northern China, are also facing the challenge of extreme precipitation disasters (Lei et al. 2021; L. Xu et al. 2021a, b; Zhang et al. 2014). The occurrence of extreme precipitation is inextricably linked with anomalies of atmospheric circulation and temperature (X. Li et al. 2021a, b, c; Ren et al. 2021; Zhang et al. 2020). In this regard, it is necessary to analyze the impact of various meteorological indicators on the occurrence of extreme weather events (Gao et al. 2021; Mou et al. 2020; L. Xu et al. 2021a, b; Zhang and Zhou 2020).

In this study, precipitation events were extracted from 1960 to 2018 in the HRB by using the recorded precipitation sequences. Then extreme precipitation events of PRE, EP, and IBEP were extracted from the precipitation events. We further analyzed the anomalies of meteorological factors in the years in which extreme PRE, EP, and IBEP events occurred and found that many indicators can reflect the occurrence of extreme PRE, EP, and IBEP. The abnormal climate conditions such as temperature, wind field, subtropical high, and water vapor transport all create favorable conditions for the occurrence of extreme precipitation events in the HRB (Nguyen et al. 2020; Schauwecker et al. 2021; Xu et al. 2019). However, the time scale selected in this study was years, which is relatively large and not accurate enough compared to extreme precipitation that only occurs within a certain period of time (Mo et al. 2021; Mondal et al. 2021; Yin et al. 2020). The various meteorological elements are interconnected, and the change of extreme precipitation events is the result of the comprehensive influence of each element (Cao et al. 2021; X. Li et al. 2021a, b, c; Wei et al. 2021). Therefore, the influence of other meteorological factors, such as humidity and cloud cover, on the occurrence of extreme precipitation events needs to be further studied, and the time scales can be reduced to days or hours (Dar et al. 2021; Douluri and Chakraborty 2021; Schauwecker et al. 2021). Moreover, through the analysis of climate factors, increasing the forecast period of extreme precipitation is more conducive to the prevention and control of extreme precipitation disasters, which is also the focus of future research.

6 Conclusions

In recent years, affected by global climate change, extreme precipitation events have occurred frequently in the world. In this study, we selected PRE, EP, and IBEP three indicators to extract extreme precipitation events and analyzed the causes of extreme precipitation events in the HRB. This study provides an important reference for the prevention and monitoring of extreme precipitation disasters. The main conclusions drawn from this study are as follows:

  1. 1)

    Although the PRE, EP, and IBEP in the HRB have no significant trend change, they had an increasing trend after 2000. The large cycle period was decreasing, while the small cycle period was increasing, which increases the uncertainty of the occurrence of extreme precipitation events.

  2. 2)

    The air temperature of the North Pacific, the Indian Ocean, and the Qinghai–Tibet Plateau had an important influence on the occurrence of extreme precipitation in the HRB. The decrease in air temperature in the Pacific and Indian Oceans will cause extreme precipitation in the southwest and northeast of the HRB.

  3. 3)

    The temperature drop on the Qinghai–Tibet Plateau, the occurrence of El Niño, and the abnormal atmospheric circulation all contribute to the occurrence of extreme precipitation in the HRB. The subtropical high was stronger in the years of extreme precipitation that occurred in the HRB, and most of the water vapor that causes extreme precipitation comes from the Indian Ocean.

  4. 4)

    By BWC analysis, AMO, PDO, and NPI had the greatest impact on PRE; AO, AMO, and NPI had the greatest impact on EP; AO, NPI, and AMO had the greatest impact on IBEP. The MWC analysis found that PRE was greatly affected by multiple climate variables, while EP and IBEP were greatly affected by a single climate variable.

Various meteorological factors jointly determine the generation of extreme precipitation. This study only analyzed the generation of extreme precipitation from the perspective of each factor. Moreover, this study only analyzed the causes of extreme precipitation from the annual anomaly. In future research, it is necessary to increase the time scale to more accurately predict when extreme precipitation will occur during the year.