1 Introduction

According to the fifth assessment report of the Intergovernmental Panel on Climate Change (IPCC), the global mean surface temperature has increased since the late nineteenth century, with a total increase of about 0.85 °C during 1880–2012 (IPCC, 2013). The global warming can probably strengthen the atmospheric moisture levels, thunderstorm activity, and/or large-scale storm activity, which may result in an increase in the magnitude and frequency of extreme precipitation events (Trenberth, 1998; Sen Roy and Balling, 2004). Studies about extreme precipitation have been carried out in various regions around the world (Alexander et al., 2006), such as southern Brazil (Sansigolo and Kayano, 2010), Japan (Duan et al., 2015), Australia (Fiddes et al., 2014), Thailand (Limsakul and Singhruck, 2016), and Korea (Min et al., 2015). These studies have concluded that the changes in extreme precipitation exhibit large regional variability. For example, significant decreasing trends in extreme precipitation events were observed in some areas of western central Africa (Aguilar et al., 2009), whereas extreme precipitation events were found to become more intense in Thailand (Limsakul and Singhruck, 2016). In China, changes in extreme precipitation also attracted many interests (Zhai et al., 2005; You et al., 2011; Xia et al., 2012). Previous studies indicated large variability of the changes in extreme precipitation in space and time in this country (You et al., 2011; Song et al., 2015; Sun et al., 2016). Decreasing trends can be observed in southwestern China, whereas increasing trends were observed in Xinjiang, eastern Tibetan Plateau, northeastern China, and southeastern China (Zhai et al., 2005; You et al., 2011). Moreover, the changes in frequency and intensity of extreme precipitation can usually lead to extreme hydrological events, which can exert significant negative impacts on the social and natural environment (Alexander et al., 2006; Choi et al., 2009; dos Santos et al., 2011). For example, the extreme flooding disaster occurred in the Nenjiang River and the Songhua River in northeastern China and the Yangtze River in southern China in 1998 was induced by extreme precipitation events and resulted in more than 3000 casualties and 3.6 billion dollar economic losses (Zong and Chen, 2000). Hence, the research on changes in extreme precipitation is of great significance to provide a scientific basis to reduce the risk of extreme events.

Statistical models are widely regarded as efficient and useful tools to better understand the changes in extreme events. Various statistical distributions were used to model extreme hydrometeorological series, such as extreme value distributions (Xia et al., 2012; Najafi and Moazami, 2016), extended Burr XII distribution (Shao et al., 2004), and Pearson III distribution (Griffis and Stedinger, 2007). The efficiency of these distributions in modeling the precipitation extremes in China has also been assessed by many previous studies (Su et al., 2009; Yang et al., 2010; Fischer et al., 2012). For example, Fischer et al. (2012) compared the efficiency of the three-parameter gamma (gamma 3), generalized extreme value (GEV), generalized Pareto (GP), and Wakeby distributions in modeling the precipitation extremes in the Zhujiang River Basin and revealed that GEV was the most reliable and robust distribution in their study area. Xia et al. (2012) and Du et al. (2014) used GEV and GP distribution, respectively, to describe the extreme precipitation events in the Huaihe River Basin. The probability distributions can comprehensively describe the statistical characteristic of precipitation extremes and detect the changes of precipitation extremes by their changes (Alexander et al., 2006; Fischer et al., 2012). Furthermore, a deep understanding of the statistical characteristic of precipitation extremes can reflect the changes of risks of extreme events and is useful for the planning of adaption (Fischer et al., 2012).

The present study selected the middle reaches of the Yellow River Basin (MRYRB), which is located in the north of China, as the study area to investigate the spatiotemporal variation and statistical characteristic of extreme precipitation. The daily precipitation observation data at 44 meteorological stations during 1960–2013 was used. To the best of our knowledge, previous studies about in this area were mainly focused on trends of extreme precipitation (Liang et al., 2015; Sun et al., 2016). Given that extreme precipitation can usually result in serious socioeconomic losses and casualties, a comprehensive and further analysis of changes in the extreme precipitation covering spatiotemporal variation and statistical characteristic is quite needed. Furthermore, the relationships between precipitation extremes and large-scale atmospheric circulation in the MRYRB were also explored.

The major objectives of this study are as follows: (1) to identify the extreme precipitation events using various indices at all stations and analyze the changes of these indices in space and time; (2) to investigate the statistical characteristic of extreme precipitation in the MRYRB using several probability distributions; (3) to assess the potential changes of risk of extreme precipitation in various time period and analyze whether the precipitation is getting more extreme in the considered area; and (4) to explore whether there are significant relationships between precipitation extremes and large-scale atmospheric circulation patterns.

The structure of this study is as follows: Sect. 2 presents the used data and methods including the definition of extreme precipitation indices; Sect. 3 shows the results and discussions, followed by the conclusion in Sect. 4.

2 Data and method

2.1 Study area

The MRYRB is located in northern China (103° 58′–113° 40′ E, 33° 39′–40° 34′ N) (Fig. 1), covering an area of about 345,600 km2. This region belongs to the arid and semi-arid climate zone in China. The long-term mean annual precipitation exhibits large spatial variability, ranging from less than 350 mm in the northwest to more than 800 mm in the southeast of the MRYRB. Precipitation during the flooding season (June to September) accounts for about 70% of the total annual precipitation. The mainstream of the MRYRB flows through the Loess Plateau, which is famous for serious soil erosion problem. The average annual erosion rate is about 2480 t km−2 for the whole Yellow River Basin, which is the highest over the world for any large rivers (Shi and Shao, 2000). The native vegetation has mostly been cleared for crop production, causing severe soil erosion, land degradation, and soil fertility loss (Jia et al., 2017).

Fig. 1
figure 1

Spatial distribution of meteorological stations and mean annual precipitation in the MRYRB

Full size image

2.2 Data

In this study, the daily precipitation data at 44 meteorological stations during 1960–2013 were used to analyze the spatiotemporal variability and statistical characteristic of extreme precipitation in the MRYRB. These data were provided by China Meteorological Administration (CMA) with high quality. Daily precipitation datasets may have different degrees of heterogeneity due to changes in relocations, measuring techniques, and environment, which often leads to significant bias in the extreme precipitation trend detection. Therefore, the homogeneity of the datasets should be carefully examined before the use of datasets. In this study, the RH test-dlyprcp software, which was developed by Wang and Feng (2013) (available at http://etccdi.pacificclimate.org/software.shtml) specifically for daily precipitation data time series homogeneity test, was employed to check the homogeneity of daily precipitation series in all stations. The results showed that all the daily precipitation series at 44 meteorological stations passed the homogeneity test at the significance level of 0.05, which confirmed their reliability in the extreme precipitation analysis. The regional averages were calculated as arithmetic means of the values at all selected stations in the study area.

To examine the relationships between the precipitation extremes and the large-scale atmospheric circulation patterns, the correlations between the extreme precipitation indices and El Niño–Southern Oscillation (ENSO)/Pacific Decadal Oscillation (PDO) indices were investigated. In this study, the Nino 3.4 index, which is defined as the monthly sea surface temperature averaged over the east central tropical Pacific (5° N–5° S, 170°–120° W), was used to represent the state of ENSO. The monthly PDO index is defined as the leading principal component of North Pacific monthly sea surface temperature variability, which has been proved to be closely related to the variability of extreme precipitation (Limsakul and Singhruck, 2016; Liu et al., 2017). These data were downloaded from the National Oceanic and Atmospheric Administration (NOAA) Earth System Research Laboratory (available online at http://www.esrl.noaa.gov/psd/data/climateindices/list/).

2.3 Method

2.3.1 The definition of extreme precipitation indices

Generally, extreme precipitation events often refer to these precipitation events that occur infrequently but with severe impacts. The Expert Team on Climate Change Detection and Indices (ETCCDI) has defined 27 types of extreme indices, including 11 types of indices about extreme precipitation and 16 types of indices about temperature. The standard indices established by ETCCDI have been widely used to assess climate changes of extreme precipitation in different regions of the world (Alexander et al., 2006; You et al., 2011; Sun et al., 2016). We selected nine of extreme precipitation indices from the ETCCDI to reflect the changes in extreme precipitation intensity, frequency, and duration in the MRYRB. As the study area is frequently attacked by serious drought hazards, which are mostly related to light precipitation (Wu and Qian, 2016), the number of precipitation days (R0.1 mm), which relates to precipitation amount no less than 0.1 mm, was considered. On the other hand, as the erosive rainfall has an evident impact on runoff and soil erosion in the study area, the erosive rainfall should be specifically considered when analyzing the precipitation extremes in the MRYRB. Here, the threshold of 12 mm/day, which was suggested by Xie et al. (2000) as the standard for describing erosive rainfall on the Loess Plateau, was used. Moreover, the number of heavy precipitation days, which refers to a day with precipitation amount exceeding 25 mm/day defined by the National Climate Center of China, was also considered. To sum up, the foregoing mentioned 12 indices of precipitation extremes can be generally divided into two groups: (1) the indices that describe the precipitation intensity, including SDII, PRCPTOT, R95, R99, RX1day, and RX5day and (2) the indices that reflect the number of precipitation days, including CDD, CWD, R0.1mm, R10mm, R12mm, and R25mm. Detailed descriptions about these indices were provided in Table 1.

Table 1 Definitions of the 12 precipitation extreme indices used in this study
Full size table

2.3.2 Mann-Kendall test

Non-parametric Mann-Kendall (MK) test is a simple and robust trend detection method (Mann, 1945; Kendall, 1975). It is recommended by the World Meteorological Organization (WMO) as a standard procedure for examining trends in independent hydrometeorological series and has been widely used (Gocic and Trajkovic, 2013; She et al., 2016; Yang et al., 2017). In this study, we used the MK test to examine the temporal trends in extreme precipitation indices in the MRYRB.

The MK statistical test is given as follow:

$$ Z=\left\{\begin{array}{cc}\frac{S-1}{\sqrt{Var(S)}}& S>0\\ {}0& S=0\\ {}\frac{S+1}{\sqrt{Var(S)}}& S<0\end{array}\right. $$
(1)

where statistic S can be calculated as:

$$ S=\sum \limits_{i=1}^{n-1}\sum \limits_{j=i+1}^n\operatorname{sgn}\left({x}_{\mathrm{j}}-{x}_{\mathrm{i}}\right) $$
(2)

where xi and xj are the observations at the ith and jth moments, respectively; n is the length of the series. When xi − xj is more than, equal to or less than 0, sgn(xi − xj) equals to 1, 0, or − 1, respectively.

The statistic Z can be used as a measure of a trend. Z > 0 and Z < 0 indicate an increasing and decreasing trend, respectively. A larger |Z| value refers to a more significant trend. In this study, the significance level of 0.05 is considered, which means that Z > 1.96 and Z < − 1.96 will indicate a significant increasing and decreasing trend, respectively.

However, many previous studies have stated that the possible existence of autocorrelation in the time series can lead to inaccurate estimation of the trends (Yue and Wang, 2002). Therefore, we should remove the autocorrelation, if it exists, before the application of MK test. In this study, the method given in Yue and Wang (2002) was performed to remove the possible autocorrelation in the extreme precipitation series in the MRYRB.

Moreover, the Sen’s slope (Sen, 1968) was also used to determine the magnitude of the trend, as it can eliminate the impact of missing data or anomalies on the trend test. The slope is estimated by

$$ \beta = Median\left[\frac{\left({x}_{\mathrm{j}}-{x}_{\mathrm{i}}\right)}{\left(j-i\right)}\right],\forall j>i $$
(3)

where β is the estimate of the slope of the trend; xi and xj are the observations at the ith and jth moments, respectively.

2.3.3 Statistical distribution models

In this study, the statistical characteristic of extreme precipitation was analyzed using the extreme value distributions. Many extreme distributions have been used to simulate the changes in extreme hydrometeorological time series (She et al., 2015; She et al., 2016). Here, the GEV distribution and GP distribution were considered due to their good performance in modeling the extremes (Xia et al., 2012; Fischer et al., 2012; Bhunya et al., 2013). Additionally, given that the gamma distribution has been proved to be the appropriate model for the simulation of precipitation time series in China (Liang et al., 2012; Jiang et al., 2014), this distribution was also used. Therefore, we selected three models to fit the extreme precipitation time series and further analyze the statistical characteristic in the precipitation extremes in our study area. Here, we only gave the description of the three distributions in brevity, which can be seen in Table 2, and the details can be referred to Xia et al. (2012). The parameters of these distributions were estimated using the L-moments method (Hosking, 1990; Hosking and Wallis, 1997). The most prominent feature of L-moments is that it is not so sensitive to the maximum and minimum values compared to ordinary moments, which makes the estimates of parameters by L-moments method are more robust (Cai & Jiang 2007). Besides, the Kolmogorov-Smirnov (KS) test was employed to choose the optimal models. The readers can find the details of the L-moment method in Hosking and Wallis (1997) and the KS test in Young (1977).

Table 2 The cumulative distribution function and L-moments estimates of parameters
Full size table

2.3.4 Cross wavelet analysis

Wavelet transforms have become a useful tool for investigating local variation in time series and have been widely used in hydrological and climatic time series analysis (She et al., 2016; Yang et al., 2017; Liu et al., 2017). The cross wavelet analysis, introduced by Torrence and Compo (1998), was adopted to understand how the changes of ENSO and PDO can affect the extreme precipitation changes in the MRYRB. The details of cross wavelet analysis are given below.

For two time series xn and yn, the cross wavelet spectrum is defined as

$$ {W}^{\mathrm{X}\mathrm{Y}}={W}^{\mathrm{X}}{W}^{\mathrm{Y}\ast } $$
(4)

where WX and WY represent the wavelet transforms and * denotes the complex conjugation. The cross wavelet power is further defined as |WXY|. The complex argument arg(Wxy) can be interpreted as the local relative phase between xn and yn in time frequency space.

The theoretical distribution of the cross wavelet power of two time series with background power spectra \( {P}_{\mathrm{k}}^{\mathrm{X}} \) and \( {P}_{\mathrm{k}}^{\mathrm{Y}} \) is given in Torrence and Compo (1998) as

$$ D\left(\frac{\left|{W}_{\mathrm{n}}^{\mathrm{X}}(s){W}_{\mathrm{n}}^{\mathrm{Y}\ast }(s)\right|}{\sigma_{\mathrm{X}}{\sigma}_{\mathrm{Y}}}<p\right)=\frac{Z_{\mathrm{v}}(p)}{v}\sqrt{P_{\mathrm{k}}^{\mathrm{X}}{P}_{\mathrm{k}}^{\mathrm{Y}}} $$
(5)

where Zv(p) is the confidence level associated with the probability p for a probability density function defined by the square root of the product of two χ2 distributions. In this study, the 5% significance level is calculated using Z2(95%) = 3.999. The more details of the cross wavelet transforms can be found in Grinsted et al. (2004), and the relevant codes can be downloaded from http://www.pol.ac.uk/home/research/waveletcoherence/ .

3 Results and discussions

3.1 Temporal trends of extreme precipitation

3.1.1 Indices of precipitation intensity

We first analyzed the spatial variation and temporal changes of the indices representing the extreme precipitation intensity (Fig. 2). The Kriging method was employed to interpolate the values into the whole study area by means of the software of ArcGIS. The temporal trends were detected by the MK test with a significance level of 0.05. Besides, we also gave the variation of the regional time series of these six extreme precipitation indices in Fig. 3.

Fig. 2
figure 2

Spatial patterns of values and trends in indices of precipitation intensity in the MRYRB during 1960–2013. The significance level of 0.05 is considered

Full size image
Fig. 3
figure 3

Regional average series for indices of precipitation intensity in the MRYRB during 1960–2013. The red line represents the slope of the datasets during 1960–2013

Full size image

As shown in Fig. 2a, the PRCPTOT values ranged from 334.1 to 809.4 mm across the whole study area. The highest value of annual PRCPTOT was distributed in the southeast region while the lowest value appeared in the northwest region, which was consistent with the spatial distribution of annual precipitation in this area (Zhang et al., 2014). Additionally, the spatial patterns of SDII, RX1day, RX5day, R95, and R99 also showed similarities with that of PRCPTOT, that the values increased from the northwest to the southeast of the MRYRB (Fig. 2b–f). The linear correlation coefficients between the regional average time series of each index were calculated to illustrate the relationship between these indices. The PRCPTOT was well correlated (at the 0.01 significance level) with the other five extreme precipitation indices (Table 3). This can partially illustrate the consistency between the spatial variation of the other five indices and PRCPTOT. From the definition of the aforementioned six indices, the higher the index value, the wetter of the climate condition may occur. Therefore, we can infer that the southeast of the MRYRB was the wettest region as all of these six indices were largest in this area, whereas the northwest region was a relatively dry region. On the other hand, considering that the higher the index value (except CDD), the higher risk of occurrence of extreme precipitation, the occurrence probability of extreme precipitation events in the southeast was also higher than that in the northwest region.

Table 3 Correlation coefficient of extreme precipitation indices in the MRYRB during 1960 – 2013
Full size table

Decreasing trends in PRCPTOT can be seen in the majority of stations (38 of 44 stations, 84%) (Fig. 2a), with only three of them was significant. There were only five stations presenting insignificant increasing trends, which were mainly distributed in the north of the MRYRB. This can also be seen in the regional average PRCPTOT time series that an insignificant decline trend at a rate of − 7.65 mm/decade can be detected (Fig. 3a). There were 27 and 17 stations that showed increasing and decreasing trends of SDII, respectively (Fig. 2b). Except two stations with significant increasing trends, all of the trends in the other stations were insignificant. Over the whole study area, we found that SDII insignificantly increased at a rate of 0.04 mm/day/decade (Fig. 3b). The combination of the decline in PRCPTOT and increase in SDII at most stations may link to a decrease in the number of wet days, and this will be further discussed in the following section. There were more stations for RX1day showing increasing trends, while much more stations displayed with decreasing trends for RX5day (Fig. 2c and d). Moreover, there were only three stations showing significant increasing trends, two for RX1day and one for RX5day, respectively. Moreover, the regional RX1day and RX5day presented insignificant increasing and decreasing trends during 1960–2013, respectively (Fig. 3c and d). The trends in R95 and R99 also did not show any evident spatial patterns; however, the number of stations giving decreasing trends was larger than that giving increasing trends for R95 (Fig. 2e), whereas more stations showed increasing trends for R99 (Fig. 2f). From the perspective of regional average series, the R95 and R99 also exhibited no significant trend (Fig. 3e and f).

3.1.2 Indices for the number of precipitation days

We analyzed the spatial variation and temporal changes of the indices for the number of precipitation days (Fig. 4) and also gave the temporal variation of the regional time series of these six extreme precipitation indices in Fig. 5.

Fig. 4
figure 4

Spatial patterns of values and trends in indices for the number of precipitation days in the MRYRB during 1960–2013. The significance level of 0.05 is considered

Full size image
Fig. 5
figure 5

Regional average series for indices for the number of precipitation days in the MRYRB during 1960–2013. The red line represents the slope of the datasets during 1960–2013

Full size image

As shown in Fig. 4a, the CDD values increased from the southeast to the northwest of the MRYRB. The CWD values ranged from 4.0 to 6.4 days/year across the whole study area (Fig. 4b). The highest value of CWD was distributed in the southwest region, while the lowest value appeared in the northwest region. The distribution of R0.1mm was quite similar with that of CWD (Fig. 4c), while the highest values of R10mm, R12mm, and R25mm were located in the southeast region (Fig. 4d–f). The similarities and differences in spatial distributions among these indices can be illustrated from the correlation coefficients in Table 3. The correlation coefficients between indices for the number of precipitation days were relatively small (Table 3). For example, the correlation coefficients between CDD and other extreme precipitation indices, except R0.1mm (at the 0.05 significance level), did not pass the 0.05 significance level. From the definition of CWD, R0.1mm, R10mm, R12mm, and R25mm, higher values indicated wetter conditions, whereas lower values suggested drier conditions. Therefore, the spatial distributions of these indices revealed that the southeast of the MRYRB was the relatively wet region as R10mm, R12mm, and R25mm were largest and CDD was smallest in this area, whereas the northwest region was the relatively dry region. On the other hand, the occurrence probability of extreme precipitation events in the southeast was also higher than that in the northwest region. These results were consistent with the results given in Sect. 3.1.1.

The proportion of stations with decreasing trends (43%) was less than that with increasing trends (57%) for CDD (Fig. 4a). Only 1 and 2 stations showed significant increasing and decreasing trends, respectively. Moreover, the regional average CDD time series presented an insignificant decline trend at a rate of − 0.31 days/decade (Fig. 5a). The temporal trends showed that 40 of 44 stations (91%) gave decreasing trends for CWD (Fig. 4b), with only five of them were significant. This can also be seen in the insignificant decline trend of regional average CWD time series (− 0.15 days/decade, Fig. 5b). All stations exhibited negative trends of R0.1mm, of which 35 stations (80%) were significant (Fig. 4c). Over the whole study area, we observed that the R0.1mm significantly decreased at a rate of − 3.04 days/decade (Fig. 5c). For R10mm, more stations exhibited decreasing trends, with only five of them being significant (Fig. 4d). Moreover, the regional R10mm time series significantly decreased (− 0.32 days/decade) (Fig. 5d). The number of stations showing decreasing trends (75%) was also more than that with increasing trends (25%) for R12mm (Fig. 4e). However, the regional R12mm time series gave an insignificant decline trend at a rate of − 0.24 days/decade (Fig. 5e). As for R25mm, the number of stations giving decreasing trends was the same as that giving increasing trends (Fig. 4f). This can also be seen in the regional average R25mm time series that an insignificant decline trend at a rate of − 0.02 days/decade can be detected in Fig. 5f.

The values of most indices (except CDD) increased from the northwest to the southeast of the MRYRB, which was consistent with the spatial variation of annual precipitation in this area, revealing that the southeast region was the wettest region, whereas the northwest region was relatively dry in the MRYRB. These results were consistent with the previous studies in the similar regions, such as Liu et al. (2008) and Sun et al. (2016). In the MRYRB, we have not found any evidence of disproportionately large increase in the precipitation extremes, which have been revealed in the global (Alexander et al., 2006) and many other regions (Wang et al., 2013; Limsakul and Singhruck, 2016). The trend of regional average PRCPTOT was insignificant negative at the 95% confidence level. Except the significant decreasing trends exhibited in R0.1mm and R10mm, no significant changes were observed in the annual regional average series of other extreme precipitation indices. The trends in the extreme precipitation indices indicated that the MRYRB was becoming drying with less frequent precipitation events, which was consistent with the results given by Liu et al. (2008) and Zhang et al. (2014). Moreover, You et al. (2011) revealed that the magnitude of negative changes at the stations in the Yellow River Basin is larger than the other regions in China. Zhang et al. (2014) revealed that there is an evident decline in the precipitation in the Yellow River Basin, particularly in the MRYRB; such decline is mainly caused by the decrease in precipitation amount and rainy days. Changes in extreme precipitation events play an important role in the generation of floods. Significant increasing trends in extreme precipitation can be observed in many large river basins in China, such as the Yangtze River Basin (Chen et al., 2013) and Songhua River Basin (Song et al., 2015), which may result in more severe flood disasters in these areas. However, in our study area, no significant change can be observed in these considered indices, which may suggest that the risk of flood disaster in this area may also have few changes. Besides, the significant decreasing trend of regional R0.1mm series may accompany with aggravation of droughts in the whole region, which can partly explain why the Yellow River always suffered from severe drought and occurrence of flow-break during recent decades (Cong et al. 2009). Moreover, the insignificant decline of regional R12mm suggested probable mitigation of soil erosion. Simultaneously, many previous studies have proved that the reduction of soil erosion and sediment transported in the Yellow River is due to climate change (decrease of precipitation) and human activities (such as landscape engineering, terracing, and the construction of check dams) (Xu, 2004; Wang et al., 2007; Wang et al., 2015).

3.2 The statistical characteristic of extreme precipitation series

3.2.1 Selection of best fit distribution

In this study, the GEV, GP, and gamma distributions were used to fit the extreme precipitation time series of all indices in the MRYRB during 1960–2013. The optimal model was determined using the KS test at the confidence level of 0.95. The results were summarized in Tables 4 and 5. On the station scale, the GEV distribution can be accepted as the optimal choice for most occasions. This was also proved by the results at the regional scale. GEV distribution can best simulate the regional time series of all indices except R12mm, of which Gamma was proved to be the optimal distribution. However, the KS statistics of the GEV and gamma distribution were quite close, and both of them have passed the KS test at the confidence level of 0.95. These results indicated the efficiency of GEV in modeling of extreme precipitation time series in our study area. In fact, GEV distribution has been reported to be the best fit model in many regions by the comparison with other extreme value distributions, e.g., Fischer et al. (2012). It is worth noting that, although the GP distribution was widely used in many studies (Bhunya et al., 2013; She et al., 2015) to simulate the extreme precipitation time series, it was found to be the worst choice in our study. At station scale, the KS statistic showed that many GP distributions cannot pass the KS test, especially for fitting CWD, R0.1mm, and R25mm. Furthermore, none of the indices showed that the GP distribution was the optimal distribution at the regional scale. To sum up, considering the wide acceptance of the GEV distribution at regional and station scale, we employed this distribution to analyze the statistical characteristic of extreme precipitation in the study area.

Table 4 The Kolmogorov-Smirnov test values of extreme precipitation indices series
Full size table
Table 5 The numbers of optimal distributions and unqualified distributions
Full size table

3.2.2 The return levels of various indices

According to the best fit distribution results given in Sect. 3.2.1, extreme precipitation indices in each individual station under return period of 50 years were calculated (Fig. 6). As shown in Fig. 6, the spatial distributions of extreme precipitation indices under the return period of 50 years were similar to the spatial patterns of corresponding extreme precipitation indices during 1960–2013, which indicated the rationality to use the GEV distribution to simulate extreme precipitation indices in the MRYRB. The majority of the highest values of these indices (except CDD, of which high value means dry) were distributed in the southeastern region, while most of the lowest values of indices were located in the northwest region. These results confirmed the results in Sects. 3.1.1 and 3.1.2 that the southeastern region was relatively wet, whereas the northwestern region was relatively dry in the MRYRB. The spatial variation of the return level revealed that the risk of extreme precipitation was highest in the southeast of the MRYRB. Therefore, more engineering and non-engineering measures are needed to reduce the losses of extreme precipitation in this region.

Fig. 6
figure 6

The quantiles of the indices under the 50-year return period using the GEV distribution

Full size image

3.2.3 Changes in the extreme precipitation in different subperiods

To further examine the temporal changes in the precipitation extremes, we divided the whole time series into two subseries with the same length, i.e., the time period from 1960 to 1986 and from 1987 to 2013. Then, the GEV distribution, which was determined as the optimal distribution in the previous section, was chosen to fit the two subseries, and the changes in the probability distribution functions (PDFs) were given in Fig. 7. The black and red lines represent the annual PDFs in 1960–1986 and 1987–2013, respectively. The shaded area denotes the 5 and 95% cumulative percentages’ values.

Fig. 7
figure 7

Annual PDFs of regional average extreme precipitation indices in 1960–1986 (black line) and 1987–2013 (red line). The part for exceeding the 95th percentile and the part for falling under the fifth percentile are considered

Full size image

The PDFs of R25mm, R95, R99, and RX1day changed a little in the two subperiods, which indicated that changes in these indices were quite small during the past several decades. The PDFs of CDD, CWD, PRCPTOT, R10mm, R12mm, RX5day, and SDII moved to the left during the recent several decades. For example, as for the CDD, the 95th percentile during 1960–1986 corresponded to 77.6 days/year, while the 95th percentile during 1987–2013 corresponded to 63.3 days/year (Fig. 7a). The 95th percentile in CWD during 1960–1986 corresponded to 9.0 days/year, while the 95th percentile in CWD during 1987–2013 corresponded to 6.47 days/year (Fig. 7b). The PDF of R0.1mm after 1987 roughly moved to the left; however, the part exceeding the 95th percentile moved to the right. The fifth percentile in R0.1mm during 1960–1986 corresponded to 80.8 days/year, while the fifth percentile during 1987–2013 corresponded to 74.6 days/year; the 95th percentile during 1960–1986 corresponded to 110.0 days/year, while the 95th percentile during 1987–2013 corresponded to 126.0 days/year (Fig. 7d). All in all, general distribution changes in extreme precipitation indices showed a tendency toward drier conditions, which was in accordance with the result of trends analysis in the previous sections.

3.3 Relationship between extreme precipitation indices and large-scale atmospheric circulation

Large-scale atmospheric circulation is an important factor influencing global climate and shows strong correlations with extreme precipitation events in many regions of the word (Sun et al., 2015; Zhang et al., 2016; Jiang et al., 2017). Therefore, analyzing the relationship between extreme precipitation indices and large-scale atmospheric circulation in the MRYRB is significant. Both PDO and ENSO events have shown strong relations with extreme precipitation events, as observed worldwide (Krichak et al., 2014; Limsakul and Singhruck, 2016; Liu et al., 2017). Here, the cross wavelet analysis was applied to study the connections between ENSO and PDO and extreme precipitation indices (Figs. 8 and 9). For the sake of convenience, we only selected RX1day, R25mm, and CWD which represented the intensity, frequency, and duration of precipitation extremes, respectively, to describe. More details of the cross wavelet transforms between ENSO/PDO and other indices can be found in Figs. 8 and 9.

Fig. 8
figure 8

The cross wavelet transforms between the ENSO and extreme precipitation indices in the MRYRB. The thick black contour denotes the relations which are significant at the 95% confidence level against the red noise. The cone of influence (COI) where edge effects might distort the picture is shown as lighter shades. The relative phase relationship is indicated by the arrow direction (with anti-phase pointing left, in-phase pointing right). The color bar on the right denotes the wavelet energy

Full size image
Fig. 9
figure 9

Same as Fig. 8, but for PDO events

Full size image

Figure 8 exhibited the cross wavelet transforms between ENSO and precipitation extremes in the MRYRB. Figure 8j illustrated that the ENSO events showed a statistically significant negative correlation with the RX1day variation with a 2–4-year signal at the 95% confidence level from 1964 to 1970. In addition, ENSO events had a statistically significant positive correlation with the RX1day with a 13–14-year signal at the 95% confidence level from 1983 to 1994. The results indicated that ENSO events played an important role in triggering intensive precipitation in the MRYRB. Figure 8g indicated that the ENSO had a statistically significant negative correlation with R25mm variation in the MRYRB at the 95% confidence level, with a 2–4-year signal from 1964 to 1973 and a 3–6-year signal from 1983 to 1993. Moreover, ENSO had a statistically significant positive correlation with the R25mm with an 8–9-year signal at the 95% confidence level from 1999 to 2002. This implied that the ENSO was closely related to the frequency of extreme precipitation events in this area. Figure 8b demonstrated that the ENSO had a statistically significant negative correlation with CWD variation at the 95% confidence level, with a 2–5-year signal from 1980 to 1990, suggesting that the ENSO was closely associated with long-lasting rainy days in the MRYRB.

The cross wavelet transforms between PDO and precipitation extremes in the MRYRB were displayed in Fig. 9. Obviously, the PDO exhibited a statistically negative correlation with RX1day in the MRYRB with a 1–2-year signal from 1998 to 2000 and a positive correlation with a 7–10-year signal from 1996 to 2002 and a 2–4-year signal in 2007–2009 at the 95% confidence level (Fig. 9j). Similarly, Fig. 9g showed that the PDO exhibited a statistically significant negative correlation with R25mm variation in the MRYRB with a 5–6-year signal at the 95% confidence level from 1987 to 1991 and a positive correlation with a 6–10-year signal from 1991 to 2003. Figure 9b illustrated that the PDO showed a statistically significant negative correlation with the CWD variation in the MRYRB with a 2–3-year signal at the 95% confidence level from 1981 to 1984 and a 10-year signal from 1981 to 1992 at the 95% confidence level. In addition, PDO had a statistically significant positive correlation with the CWD with a 2-year signal at the 95% confidence level from 1999 to 2000. These findings indicated that the PDO also had a strong association with changes in the intensity, frequency, and duration extreme precipitation events in the MRYRB.

Figures 8 and 9 showed that both ENSO and PDO had statistically evident correlations with precipitation extremes in the MRYRB, indicating that both ENSO and PDO had a strong influence on precipitation extremes. This result is in accordance with Liu et al. (2017). The study of Ouyang et al. (2014) has revealed that precipitation in the major of China decreases during El Niño/PDO warm phase periods and increase during La Niña/PDO cool phase periods. Moreover, the relationships between the extreme precipitation indices and the ENSO and PDO implied that for the El Niño (La Niña) years and the PDO warm (cool) regimes, the variability in the frequency and magnitude of heavy and more intense precipitation events tended to be reduced (enhanced) (Kenyon and Hegerl, 2010; Limsakul and Singhruck, 2016). Our study further revealed that the relationship between ENSO events and precipitation extremes was more significant, indicating that ENSO can have a larger influence on the precipitation extremes in the MRYRB compared to PDO. This might be due to the limitations of the relatively short record length and uncertainty from the potential interaction between PDO and ENSO (Kiem and Verdon-Kidd, 2009). PDO can indirectly affect precipitation variability via modulation of ENSO impacts (Verdon et al., 2004; Kiem and Verdon-Kidd, 2009). There is much evidence (Chan and Zhou, 2005; Andreoli and Kayano, 2005) that PDO coupled with ENSO affects precipitation constructively (strong and well defined anomalies), when they are in phase, and destructively (weak and noisy anomalies), when they are out of phase. Moreover, some researchers also used other large-scale atmospheric circulation indices to explore the relationship between extreme precipitation and large-scale atmospheric circulation in this study area (Liang et al., 2015; Zhang et al., 2014; Sun et al., 2016). For example, Liang et al. (2015) indicated that the monthly Rx1day, Rx5day, PRCPTOT, and SDII have significant positive relationships with Northern Hemisphere Subtropical High (NHSH) but significant negative relationships with Northern Hemisphere Polar Vortex (NHPV) in the Yellow River Basin. Sun et al. (2016) found that the Western Pacific Subtropical High Intensity Index (WPSHII) is associated with the drying trend through an increase in the CDD in the Loess Plateau. These studies have verified that the large-scale atmospheric circulation index has the potential to improve the prediction of extreme precipitation in the study region.

4 Conclusion

In this study, based on the daily precipitation data of 44 meteorological stations in the MRYRB during 1960–2013, 12 extreme precipitation indices, which can reflect the magnitude, intensity, and duration of precipitation extremes, were selected to analyze the spatiotemporal variation and statistical characteristic of extreme precipitation in the MRYRB. The main conclusions are given as follows:

  1. (1)

    Spatially, the values of most indices (except CDD) increased from the northwest to the southeast of the MRYRB, suggesting that it was wetter in the southeast region than the northwest region of the MRYRB. The regional average R0.1mm and R10mm showed significant decreasing trends with rates of − 3.04 and − 0.32 days/decade, respectively. For other indices, insignificant decreasing or increasing trends can be observed. These changes in extreme precipitation indices indicated that the MRYRB presented a drying trend with less frequent precipitation.

  2. (2)

    The GEV distribution was found to be the optimal statistical distribution for the extreme precipitation indices of the MRYRB. The spatial distributions of extreme precipitation indices under the return period of 50 years were similar to the spatial patterns of corresponding precipitation extreme indices during 1960–2013. Moreover, changes in PDFs of indices for the period of 1960–1986 and 1987–2013 indicated a drying trend in the recent decades.

  3. (3)

    Both ENSO and PDO had statistically correlations with RX1day, R25mm, and CWD, which demonstrated that the intensity, frequency, and duration of precipitation extremes in the MRYRB. That is to say, both ENSO and PDO had a strong influence on precipitation extremes in the MRYRB. This suggested that the large-scale atmospheric circulation index had the potential to improve the prediction of extreme precipitation in the study region.