1 Introduction

Well-evidenced global warming might result in increase and intensification of extreme events (World Meteorological Organization 2003). Extreme events such as floods, drought, and heat waves or cold spells have been drawing sharply increasing concerns in recent decades (Terray and Cassou 2000; Beniston and Stephenson 2004; Lehner et al. 2006; Sheffield et al. 2012), because of their more tremendous and profound impacts on both human society and the natural environment (Wigley 1985; Easterling et al. 2000; Patz et al. 2005; Parry et al. 2007) than their mean values (Aguilar et al. 2009; Katz and Brown 1992). Too much precipitation could lead to floods, while too little precipitation is likely to lead to drought. Therefore, it is of scientific and practical merit to investigate changing characteristics of precipitation extremes.

Precipitation extremes events have been widely investigated worldwide on different spatial scales. On the global scale, Frich et al. (2002) chose ten indicators of extreme climatic events, in which five indicators were based on precipitation, to clarify whether frequency and/or severity of climatic extremes changed during the second half of the twentieth century. Alexander et al. (2006) provided the most comprehensive analysis of observed global temperature and precipitation extremes. The two representative researches on global precipitation extremes were also discussed in the Fourth Assessment Report of IPCC (IPCC 2007). On the regional scales, representative studies include those in the Asia-Pacific region (Choi et al. 2009), Central and South Asia (Klein Tank et al. 2006), Central America and Northern South America (Aguilar et al. 2005), North American (Peterson et al. 2008), the Caribbean region (Peterson et al. 2002), Western Central Africa (Aguilar et al. 2009), Southern and West Africa (New et al. 2006), Europe (Klein Tank et al. 2002; Klein Tank and Können 2003; Moberg et al. 2006), and Central and Western Europe (Moberg and Jones 2005). On the national scales, representative studies include those in Canada (Zhang et al. 2000, 2001; Vincent and Mekis 2006), UK (Osborn et al. 2002), New Zealand (Salinger and Griffiths 2001), Spain (Brunet et al. 2007), and Iran (Rahimzadeh et al. 2008). The precipitation extremes in these regions have remarkable difference, and there is little spatial coherence in precipitation extremes in almost these studies.

Both the Fourth Intergovernmental Panel on Climate Change (IPCC) Assessment Report (Jones et al. 2007) and China’s National Assessment Report on Climate Change (Ding et al. 2006) indicate that the frequency of heavy precipitation events will very likely increase in China. Numerous studies have been carried out for extreme precipitation changes in China in recent years. For China as a whole, Zhai et al. (2005) assessed trends in extreme daily precipitation (defined as those large than 95th percentile for the year) for the period 1951–2000. You et al. (2011) investigated changes in precipitation extremes indices during 1961–2003 and analyzed their connection to the large-scale atmospheric circulation. Xu et al. (2011) investigated variations of extreme precipitation amount and extreme precipitation days at 532 meteorological stations in two periods of 1960–1989 and 1990–2007. On the regional and catchment scales in China, representative studies include those in the arid area of Northwest China (Wang et al. 2012), the eastern and central Tibetan Plateau (You et al. 2008), Loess Plateau (Li et al. 2010), the Yangtze River basin (Zhang et al. 2008a), and the Pearl River basin (Yang et al. 2010; Gemmer et al. 2011). Because of the regional differences in climate and geomorphology, the characteristics of precipitation extremes in these regions have remarkable difference.

According to the regional differences in climate and geomorphology, it is well acknowledged that China could be divided into three natural zones, namely the eastern monsoon region, northwest arid and semi-arid region, and the high-cold region of Tibet plateau (Huang 1958; Luo 1954, see Fig. 1). The Yellow River, as the second largest river in China, is across the three natural zones in China (Fig. 1), which makes it the ideal region for studying the extreme precipitation changes on the regional scales. In addition, the Yellow River basin is the area of shortage of water resources in China (Fu et al. 2004; Liu and Xia 2004; Liu and Zheng 2002, 2004), and the changes of spatial and temporal distribution of precipitation will then exert significant impacts on availability of water resources in the Yellow River basin (Zhang et al. 2008b). Therefore, it is very important to investigate the spatial and temporal variability of the extreme precipitation changes in the whole Yellow River basin.

Fig. 1
figure 1

Sketch map of study area

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As for the extreme precipitation changes in the Yellow River basin, Li et al. (2010) chose four precipitation extreme indicators (i.e., greatest 5-day total rainfall, simple daily rainfall intensity, longest dry days, and heavy rainfall days) to investigate the spatial distribution and temporal trends during 1961–2007, but the study area was limited in the loess plateau, rather than the whole Yellow River basin. These existing studies on the extreme precipitation changes in the Yellow River basin did not investigate more detailed indexes to comprehensively investigate the more characteristics of precipitation extremes but also never considered the correlation between precipitation extremes and the large-scale atmospheric circulation. In the face of anticipated climate warming, more detailed information on the regional and temporal distribution of the extreme precipitation changes in the whole Yellow River basin is needed. The objectives of this study are, therefore, (1) to characterize the regional distribution (based on the three natural zones) and temporal changes in mean precipitation and extremes in the Yellow River basin from 1961 to 2012, and (2) to investigate the correlation between precipitation extremes and the large-scale atmospheric circulation.

2 Materials and method

2.1 Study area

The Yellow River (95°53′E-119°5′E; 32°10′N–41°50′N), also known as Huanghe in Chinese, as the second largest river in China and fifth largest river in the world, has a length of 5,464 km with a basin area of 752,443 km2 (Fu et al. 2004; Liu and Zheng 2002). The annual average precipitation (multiannual average from 1961 to 2012) in the basin is about 435.1 m, and precipitation from May to October accounts for 88.5 %. According to the regional differences in climate and geomorphology, the Yellow River basin could be also divided into three sub-regions (i.e., the eastern monsoon sub-region, the arid and semi-arid sub-region, and the high-elevation sub-region), which is accordance with the three natural zones in China (Fig. 1). The annual average precipitation in the eastern monsoon sub-region, the arid and semi-arid sub-region, and the high-elevation sub-region of Tibet plateau are 483.6, 261.8, and 443.3 mm, respectively.

2.2 Data

The time series of daily precipitation records at 87 meteorological stations on the whole Yellow River basin were provided by the Climate Data Center (CDC) of the National Meteorological Center of the China Meteorological Administration, and has gone through the quality control procedures of the CDC, including departure accumulating method (Buishand 1982), standard normal homogeneity test (Alexandersson 1986), and the moving t test (Peterson et al. 1998). Stations that were installed after 1961 and those with data gaps were excluded. In addition, the RClimDex software package (available at the ETCCDI website, http://etccdi.pacificclimate.org/software.shtml) was used for further data quality control and homogeneity assessment. As a result, 62 weather stations with daily precipitation records for 52 years (1 Jan 1961 to 31 Dec 2012) were eventually employed for this study (Table 1). The distributions of the 62 meteorological stations are as follows: 37 stations in eastern monsoon sub-region, 11 stations in the arid and semi-arid sub-region, and 14 stations in the high-elevation sub-region.

Table 1 List of selected stations in the Yellow River basin with World Meteorological Organization (WMO) number, station name, latitude, longitude, elevation, and ranges of the data
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Large-scale atmospheric circulation indices were provided by the Climate Diagnostics and Prediction Division of the National Climate Center of the China Meteorological Administration. The original data set includes 74 indexes with monthly data, and time range is from 1951 to 2012 years. In the 74 indexes, Northern Hemisphere Subtropical High (NHSH) (5°E–360°) and Northern Hemisphere Polar Vortex (NHPV) (0–360°) were the two dominating large-scale atmospheric circulation in the Northern Hemisphere whose variation would remarkably impact on the change in precipitation extremes in the Yellow River basin. In addition, on the basis of longitude, Northern Hemisphere Subtropical High (NHSH) (5°E–360°) could be divided into three parts: North Africa–Atlantic–North America Subtropical High (NAANASH) (110°W–60°E), India Subtropical High (ISH) (65°E–95°E), and Pacific Subtropical High (PSH) (110°E–115°W). Similarly, Northern Hemisphere Polar Vortex (NHPV) (0–360°) could be divided into four parts: Asia Polar Vortex (APV) (60°E–150°E), Pacific Polar Vortex (PPV) (150°E–120°W), North America Polar Vortex (NAPV) (120°W–30°W), and Atlantic European Polar Vortex (AEPV) (30°W–60°E).

2.3 Extreme precipitation indices

There were a variety of definitions for climate extremes (Li et al. 2010; Rahimzadeh et al. 2008). The indices recommended by the Expert Team on Climate Change Detection and Indices (ETCCDI) were most widely used in extreme events study. ETCCDI gave the exact definitions of the 27 core indices (http://etccdi.pacificclimate.org) (Karl et al. 1999; Peterson et al. 2001; Peterson and Manton 2008). Since not all the indices were meaningful in the Yellow River basin, ten precipitation indices were chosen from the indicators for this study which were shown in Table 2. Calculation of precipitation indices is facilitated using the RclimDex software package (see http://etccdi.pacificclimate.org/software.shtml). In the ten indices, there are eight indices calculated on annual basis, while four indices (PRCPTOT, SDII, Rx1day, and Rx5day) calculated on monthly basis. So PRCPTOT, SDII, Rx1day, and Rx5day could be used for monthly analysis.

Table 2 Definition of ten precipitation indices in the Yellow River basin
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3 Methods

The trends in indices of precipitation extremes from the 1961 to 2012 were determined by linear regression. The nonparametric Mann–Kendall test (Kendall 1975; Mann 1945) was conducted to determine whether the trend of the regression line was significant, which was widely used for trend detection due to its robustness for non-normally distributed data (Belle and Hughes 1984; Partal and Kahya 2006; Abarghouei et al. 2011; Liu et al. 2011). For a given data series composed of X 1 , X 2 …X n , their ranks are R 1 , R 2 …R n , and the Mann-–Kendall rank statistic (S) is calculated as:

$$ S={\displaystyle \sum_{i=1}^{n-1}\left[{\displaystyle \sum_{j=i+1}^n sign\left({R}_j-{R}_i\right)}\right]} $$
(1)

where

$$ \left\{\begin{array}{l} sign(X)=1\ \mathrm{for}\ X>0\\ {} sign(X)=0\ \mathrm{for}\ X=0\\ {} sign(X)=-1\ \mathrm{for}\ X<0\end{array}\right. $$
(2)

A positive S indicates an increasing trend in the time series and a negative S indicates the opposite. If the null hypothesis H 0 (there is no trend in the data) is true, then S can be assumed to be approximately normally distributed with:

$$ \left\{\begin{array}{l}\mu =0\\ {}\sigma =n\left(n-1\right)\left(2n+5\right)/18\end{array}\right. $$
(3)

The Z score of S is calculated as:

$$ Z=S/{\sigma}^{0.5} $$
(4)

The corresponding p value of a Z score can be obtained from the normal probability table. In this study, by assuming a normal distribution at the significant level of P = 0.05 (0.01), a positive Mann–Kendal statistics Z larger than 1.96 (2.58) indicates a significant increasing trend, while a negative Z lower than −1.96 (−2.58) indicates a significant decreasing trend.

Pearson correlation coefficient (Lee Rodgers and Nicewander 1988) was used to estimate the relationship between indices of precipitation extremes and indices of large-scale atmospheric circulation. The Student’s t test (two-tailed) (Student 1908a, b) was employed to detect whether the Pearson correlation was significant or not.

4 Results

4.1 Annual and monthly precipitation trends

Figure 2 shows annual precipitation in the Yellow River basin and the three sub-regions. The annual average precipitation (multiannual average from 1961 to 2012) in the basin is about 451.7 mm, showing a decrease trend, with a trend of –8.8 mm/decade. The annual average precipitation in the eastern monsoon sub-region, the arid and semi-arid sub-region, and the high-elevation sub-region are 483.8, 267.5, and 470.1 mm, respectively. Trends of annual precipitation in the three sub-regions are –14.4, −2.7, and 1.3 mm/decade, respectively. According to the Mann–Kendall statistics Z, only the annual precipitation in the eastern monsoon sub-region shows significant decreasing trends (at the significant level of P = 0.05), and the change point approximately appears in 1980 years. The annual average precipitation in the period of 1961–1979 and 1980–2012 are 526.7 and 483.8 mm, respectively.

Fig. 2
figure 2

Annual precipitation in the Yellow River basin and the three sub-regions, in which m1 and m2 are average precipitation during the first period and the second period

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The annual average precipitation in the Yellow River basin gradually reduced from southeast to northwest, from more than 1,000 mm to less than 200 mm (Fig. 3). For the annual precipitation of the 62 stations in the Yellow River basin, there are 44 stations (71.0 %) having negative trends, in which nine stations (14.5 %) are significant, while 18 stations (29.0 %) show positive trends. For the nine stations with significant decreasing trends, eight stations are in the eastern monsoon sub-region, while one in the high-elevation sub-region. The trends of annual precipitation in the Yellow River basin range from –42 to 16 mm/decade (Fig. 3).

Fig. 3
figure 3

Annual precipitation trends (symbols, left legend) and annual average precipitation (area, right legend) in the Yellow River basin, 1961–2012. Positive/negative trends (left legend) are shown as up/down triangles, and the filled symbols represent statistically significant trends (significant at the 0.05 level). The size of the triangles is proportional to the magnitude of the trends

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The monthly precipitation (multiannual average from 1961 to 2012) in the Yellow River basin shows a different seasonality. Eighty-seven percent of the annual precipitation appears from May to October, and July (December) is the month with the highest (lowest) precipitation, with an average of 97.8 (2.9 mm) (Fig. 4). For the three sub-regions, July (December) is also the month with the highest (lowest) in the eastern monsoon sub-region and the high-elevation sub-region, with an average of 108.8 (3.8 mm) and 94.3 (1.7 mm), respectively. While the highest (lowest) monthly precipitation in the arid and semi-arid sub-region is in August (December), with an average of 71.6 (1.2 mm). For the monthly precipitation time series of the 62 stations, the Mann–Kendall test shows that there are five months (January, February, May, June, and December) having the main positive trends, while the remaining seven months (March, April, July, August, September, October, and November) have the main negative trends, and trends are from –17.7 to 13.2 mm/decade (Table 3). The number and proportion of stations with positive and negative trends shows in Table 3. According to Table 3, December and June are the first and second largest positive trends, while November and October are the first and second largest negative trends. Taking November and December as example, the trends at 62 stations are shown in Fig. 5. The monthly precipitation in November (multiannual average from 1961 to 2012) gradually reduced from southeast to northwest, from 27.8 to 0.6 mm, and the trends in the whole basin are from –3.7 to 1.1 mm/decade. The Mann–Kendall test shows that 55 stations (88.7 %) have negative trends, in which nine stations (14.5 %) are significant (at the significant level of P = 0.05). For the monthly precipitation in December, the range is from 10 to 0.2 mm; there are 51 stations (82.3 %) are positive, in which eight stations (12.9 %) are significant, and the trends are from –0.3 to 1.0 mm/decade. The trends of monthly precipitation in other months also gradually reduced from southeast to northwest; number and proportion of stations are shown in Table 3.

Fig. 4
figure 4

Monthly precipitation in the Yellow River basin and the three sub-regions, 1961–2012

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Table 3 Number and proportion of stations with positive (significant at the 0.05 level), and negative (significant at the 0.05 level) trends for the monthly precipitation during 1961–2012
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Fig. 5
figure 5

Same as Fig. 3, but for monthly precipitation in November and December

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4.2 Trends in annual extremes

Figure 6 shows changes of the ten annual precipitation extremes indices from 1961 to 2012 in the Yellow River basin. There are three indices have slight positive trends, namely consecutive dry days (CDD), number of very heavy precipitation days (R20), and extremely wet days (R99p). While seven indices have slight negative trends, namely consecutive wet days (CWD), annual total wet-day precipitation (PRCPTOT), simple daily intensity index (SDII), number of heavy precipitation days (R10), very wet days (R95p), max 1-day precipitation amount (Rx1day), and max 5-day precipitation amount (Rx5day). The Mann–Kendall test was applied to the annual extremes, the results (expressed as Z in Fig. 6) shows trends of all the ten annual extremes are not significant (at the significant level of P = 0.05). The variation trends of the ten annual extremes indices indicate that the Yellow River basin has been becoming drier, intuitively shown by increase of CDD and decrease of CWD, PRCPTOT, and SDII, so extreme drought is most likely to be more prone to appear.

Fig. 6
figure 6

Same as Fig. 2, but for the ten annual precipitation extremes indices in the Yellow River basin, 1961–2012

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Table 4 shows minimum and maximum annual precipitation extremes and their occurrence year in the whole Yellow River basin and the three sub-regions. For the same index, different sub-regions have distinct minimum and maximum annual extremes, and so do the corresponding occurrence years. In addition, for the nine wet index (CWD, PRCPTOT, SDII, R10, R20, R95p, R99p, Rx1day, and Rx5day), the general rule is that minimum and maximum in the eastern monsoon sub-region is the largest, followed by the high-elevation sub-region, and the arid and semi-arid sub-region is the lowest. But for some indices in some year, such as maximum of SDII (7.2 mm/day in 1995), R99p (101.3 mm in 2012), and Rx1day (48.0 mm in 1985) are the largest in the arid and semi-arid sub-region. For dry index (namely CDD), the general rule is that the variation range (from 17 to 168 days) in the arid and semi-arid sub-region is the largest. As for the occurrence years of minimum and maximum, the 1960s (i.e., 1965, 1966, 1964, and 1962) and 2012 are more frequent than other years.

Table 4 Minimum and maximum annual precipitation extremes and their occurrence years in the different regions during 1961–2012
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Table 5 shows trends and Mann–Kendall statistics Z of annual precipitation extremes indices in the whole basin and the three sub-regions. In the whole basin, the trends of CWD, PRCPTOT, SDII, R10, R95p, R99p, Rx1d, and Rx5day are 1.50 days/decade, −8.70 mm/decade, –0.02 (mm/day)/decade, –0.19 days/decade, –2.65 mm/decade, –0.16 mm/decade, –0.14 mm/decade, and –0.29 mm/decade, respectively. While the trends of CDD and R20 are 1.50 and 0.02 days/decade, respectively. On the whole, the degree of precipitation extremes in the whole Yellow River basin decreased. Comparison of trends in the three sub-regions shows that different sub-regions have different direction and magnitude of trends. For direction of trends, CDD, R10, R20, R95p, and Rx5day in the three sub-regions have same direction, while other five indices have distinct direction (Table 5, Fig. 7). Taking CDD and PRCPTOT as example (Fig. 7), trends of CDD in the high-elevation sub-region and the eastern monsoon sub-region are negative, while slightly positive in the arid and semi-arid sub-region. PRCPTOT in the eastern monsoon sub-region has a significant negative trends, and slightly negative in the arid and semi-arid sub-region, but slightly positive in the high-elevation sub-region. As for the magnitude of trends, for the seven wet index (CWD, PRCPTOT, R10, R95p, R99p, Rx1day, and Rx5day), magnitude in the eastern monsoon sub-region is the largest. For dry index (namely CDD), the trends in the high-elevation sub-region are largest, while trends of SDII and R20 are largest in the arid and semi-arid sub-region. In general, the degree of most precipitation extremes decreased in the three sub-regions.

Table 5 Trends and Mann–Kendall statistics Z of annual precipitation extremes in the different regions
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Fig. 7
figure 7

Same as Fig. 2, but for CDD and PRCPTOT in the three sub-regions, 1961–2012

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Spatial trends of annual precipitation extremes indices are shown in Figs. 8 and 9. Stations at different sub-regions may have similar or distinct magnitude and direction of trends. Number of stations with non-trend, positive, and negative for annual precipitation extreme indices in the different regions are shown in Table 6. In the whole basin, except for SDII, for the other nine indices (i.e., CDD, CWD, PRCPTOT, R10, R20, R95p, Rx1day, and Rx5day), the main trends of stations are negative (which means that more than 50 % stations have negative trends). In the eastern monsoon sub-region, for all the ten indices, more stations mainly have negative trends. In the arid and semi-arid sub-region, except for CDD, for the other nine indices, stations mainly have positive trends. In the high-elevation sub-region, seven indices (i.e., PRCPTOT, SDII, R10, R95p, R99p, Rx1day, and Rx5day) mainly have more stations with positive trends. For the same indices in the three sub-regions, different sub-regions have a different main trend. For the ten indices in the three sub-regions, combination of main trends could be divided into three kinds (Table 6, Figs. 8 and 9): (1) main negative trends in the three sub-regions, only CDD belongs to this kind; (2) main negative trends in the eastern monsoon sub-region and the high-elevation sub-region, but main positive trends in the arid and semi-arid sub-region, only CWD and R20 belong to this kind; (3) main negative trends in the eastern monsoon sub-region, but main positive trends in the arid and semi-arid sub-region and the high-elevation sub-region, seven indices (i.e., PRCPTOT, SDII, R10, R95p, R99p, Rx1day, and Rx5day) belong to this kind. For the first kind of main trends, taking consecutive dry days (CDD) as example, 38 stations (61.3 %) in the whole basin have negative trends, in which five stations (8.1 %) are significant, and the trends are from –22.1 to 6.7 days/decade. Trends of CDD in the three sub-regions are mainly negative. For the second kind of main trends, taking consecutive wet days (CWD) as example, 12 stations (19.4 %) have positive trends, and 50 stations (80.6 %) have negative trends, in which nine stations (14.5 %) are significant. The trends of CWD are from –0.55 to 0.20 days/decade. CWD in the eastern monsoon sub-region and the high-elevation sub-regions mainly have negative trends, while positive trends in the arid and semi-arid sub-region. For the third kind of main trends, take PRCPTOT, SDII, and Rx1day as examples. As for annual total wet-day precipitation (PRCPTOT), 41 stations (66.1 %) are positive, in which seven stations (11.3 %) are significant, and the six significant stations lie in the eastern monsoon sub-region. The trends of PRCPTOT are from –41.6 to 15.4 mm/decade, and only PRCPTOT in the eastern monsoon sub-region mainly have negative trends. Trends of simple daily intensity index (SDII) are from –0.25 to 0.38 (mm/day)/decade. Only SDII in the eastern monsoon sub-region mostly have negative trends. Trends of Max 1-day precipitation amount (Rx1day) are from –4.3 to 4.0 mm/decade.

Fig. 8
figure 8

Trends of CDD, CWD, PRCPTOT, and SDII in the Yellow River basin, 1961–2012. Positive/negative trends and non-trends are shown as up/down triangles and hollow circle, and the filled symbols represent statistically significant trends (significant at the 0.05 level). The size of the triangles is proportional to the magnitude of the trends

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Fig. 9
figure 9

Same as Fig. 8, but for R10, R20, R95p, R99p, Rx1day, and Rx5day

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Table 6 Number of stations with non-trend, positive (significant at the 0.05 level), and negative (significant at the 0.05 level) for annual precipitation extreme indices in the different regions during 1961–2012
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In conclusion, the change degree of most annual precipitation extremes in the whole Yellow River basin decreased but significantly different in the three sub-regions. Specifically, trends of all the ten annual precipitation extremes indices in the eastern monsoon sub-region were mainly negative, while most indices had mainly positive in the arid and semi-arid regions and high-elevation sub-region.

4.3 Trends in monthly extremes

There are four monthly extremes indices, namely monthly total wet-day precipitation (PRCPTOT), monthly simple daily intensity index (SDII), monthly max 1-day precipitation amount (Rx1day), and monthly max 5-day precipitation amount (Rx5day). The Mann–Kendall trend test is also applied to the four monthly indices. Table 7 shows number and proportion of stations with positive and negative trends for the four monthly precipitation extreme indices during 1961–2012. For the four indices, either positive or negative trends appear in certain months. Specifically, all the four indices have main positive trends in February, May, June, and December, while negative trends in April, August, September, October, and November. As for the remaining 3 months (i.e., January, March, and July), PRCPTOT, Rx1day, and Rx5day have positive trends in January, while SDII has negative trends. SDII and Rx5day have positive trends in March, while PRCPTOT and Rx1day have negative trends in March. SDII has positive trends in July, while PRCPTOT, Rx1day, and Rx5day have negative trends. According to Table 7, the months having the most dominant positive trends are distinctly different, while months with the most dominant negative trends are the same. Specifically, for PRCPTOT, the first 3 months having the most dominant positive trends are orderly February, June, and May, and number (proportion) of stations in the 3 months are 49 stations (79.0 %), 49 stations (79.0 %), and 44 stations (71.0 %), respectively. For SDII, February, June, and December are successively the first 3 months with the most dominant positive trends, and number (proportion) of stations in the 3 months are 49 stations (79.0 %), 48 stations (77.4 %), and 41 stations (66.1 %), respectively. For Rx1day, number (proportion) of stations in December, February, and May are 49 stations (79.0 %), 48 stations (77.4 %), and 47 stations (75.8 %), respectively. For Rx5day, number (proportion) of stations in June, February, and December are 46 stations (74.2 %), 41 stations (66.1 %), and 41 stations (66.1 %), respectively. As for the four indices, the first 3 months with the most dominant negative trends are successively November, October, and April. In November, number (proportion) of stations for PRCPTOT, SDII, Rx1day, and Rx5day are 53 stations (85.5 %), 48 stations (77.4 %), 53 stations (85.5 %), and 55 stations (88.7 %), respectively. In October, number (proportion) of stations for PRCPTOT, SDII, Rx1day, and Rx5day are 53 stations (85.5 %), 48 stations (77.4 %), 47 stations (75.8 %), and 51 stations (82.3 %), respectively.

Table 7 Number and proportion of stations with positive and negative trends for the monthly precipitation extreme indices during 1961–2012
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Taking the months with most dominant positive and negative trends as the representative, spatial trends of the four indices are shown in Figs. 10 and 11, and number of stations with positive and negative for the four indices in typical months in the different regions are shown in Table 8. Trends of PRCPTOT and SDII in February are from –0.5 to 1.4 mm/decade, from –0.3 to 0.6 (mm/day)/decade, respectively. For PRCPTOT, numbers (regional relative proportion) of stations with positive trends in the three sub-regions are 31 stations (83.8 %), 6 stations (54.5 %), and 12 stations (85.7 %), respectively, and stations with significant trends lie in the eastern monsoon sub-region and high-elevation sub-region. Trends of PRCPTOT and SDII in November are from –3.6 to 1.2 mm/decade and from –0.9 to 0.4 (mm/day)/decade, respectively. For PRCPTOT, numbers (regional relative proportion) of stations with negative trends in the three sub-regions in November are 37 stations (100 %), 6 stations (54.5 %), and 10 stations (71.4 %), respectively, and for SDII, there are 36 stations (97.3 %), 5 stations (45.5 %), and 7 stations (50 %), respectively. And stations with significant negative trends mostly lie in the eastern monsoon sub-region. For Rx1day, in December, trends are from –0.4 to 1.8 mm/decade, and numbers of stations with positive trends in the three sub-regions are 26 stations (70.3 %), 11 stations (100 %), and 12 stations (85.7 %), respectively. Trends of Rx5day in June range from –3.8 to 4.3 mm/decade, and numbers with positive trends in the three sub-regions are 26 stations (70.3 %), 10 stations (90.9 %), and 11 stations (71.4 %), respectively. Trends of Rx1day and Rx5day in November range from –1.8 to 2.1 mm/decade, from –3.3 to 3.3 mm/decade, respectively. And stations with the significant negative trends mainly lie in the eastern monsoon sub-region.

Fig. 10
figure 10

Same as Fig. 8, but for monthly precipitation extremes, namely PRCPTOT and SDII in February and November

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Fig. 11
figure 11

Same as Fig. 8, but for monthly precipitation extremes, namely Rx1day in December and November, and Rx5day in June and November

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Table 8 Number of stations with positive and negative monthly precipitation extreme indices in typical months in the different regions during 1961–2012
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5 Discussion

Relationship between annual precipitation extremes trends and elevation in the different regions are analyzed (Table 9). In the whole basin, eight indices (PRCPTOT, SDII, R10, R20, R95p, R99p, Rx1day, and Rx5day) have positive relations with elevation, while two indices (CDD and CWD) have negative relationship with elevation. Especially, PRCPTOT, R10, R95p, and Rx5day have significant positive relationship with elevation. But in the three sub-regions, relations between the ten indices and elevation are not significant.

Table 9 Correlation coefficient between annual precipitation extremes trends and elevation in the different regions
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Relationship between the ten extreme precipitation indices and the 74 large-scale atmospheric circulation indices were analyzed, and the results showed that Northern Hemisphere Subtropical High (NHSH) and Northern Hemisphere Polar Vortex (NHPV) were the two dominating large-scale atmospheric circulation in the Northern Hemisphere whose variation would remarkably impact on the change in precipitation extremes in the Yellow River basin. From 1961 to 2012, the area of NHSH index and the strength of NHSH index (Fig. 12) significantly increased (P < 0.01), and the area of NHPV index and the strength of NHPV index significantly decreased (P < 0.01).

Fig. 12
figure 12

Variation of in large-scale atmospheric circulation index in the Northern Hemisphere during the period 1961 to 2012

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Relationship between the ten annual precipitation extreme indices and the NHSH index, NHPV index were shown in Table 10. All the ten annual indices have little relationship with NHSH and NHPV.

Table 10 Correlation coefficient between annual precipitation extremes and NHSH, NHPV
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Relationship between the four monthly precipitation extreme indices and the NHSH index, NHPV index were shown in Tables 11 and 12. As for the four monthly indices (i.e., Rx1day, Rx5day, PRCPTOT, and SDII), there were significant positive relationships (P = 0.01) with NHSH, while there were significant negative relationships with NHPV. It could be deduced that when the NHSH was strong or the NHPV was weak, the extreme precipitation increased, and vice verse. In addition, Northern Hemisphere Subtropical High (NHSH) could be divided into three parts: NAANASH (North Africa–Atlantic–North America Subtropical High), ISH (India Subtropical High), and PSH (Pacific Subtropical High), and relationship between the four indices and NAANASH are the strongest. Similarly, Northern Hemisphere Polar Vortex (NHPV) could be divided into four parts: APV (Asia Polar Vortex), PPV (Pacific Polar Vortex), NAPV (North America Polar Vortex), and AEPV (Atlantic European Polar Vortex), and APV has the most significant impacts on the four monthly indices.

Table 11 Monthly correlation coefficients between monthly indices and Northern Hemisphere Subtropical High
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Table 12 Monthly correlation coefficients between monthly indices and Northern Hemisphere Polar vortex
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Comparison of the sensitivity to atmospheric circulation in the three sub-regions shows that indices in the high-elevation sub-region are the most vulnerable to the effects of atmospheric circulation, followed by the eastern monsoon sub-region, and last one is the arid and semi-arid sub-region.

6 Conclusion

In this study, we studied the temporal and spatial trends of mean precipitation and extremes in the Yellow River basin during 1961–2012. Ten indices of precipitation extremes were selected, recommended by the ETCCDI. The following conclusions could be drawn:

  1. 1.

    Annual average precipitation (multiannual average from 1961 to 2012) in the whole Yellow River basin is about 451.7 mm, and gradually reduced from more than 1,000 mm in southeast to less than 200 mm in northwest. Annual average precipitation in the whole basin shows a slight decrease, with a trend of –8.8 mm/decade. Annual average precipitation in the three sub-regions has different trends, with trends of −14.4 mm/decade in the eastern monsoon sub-region, –2.7 mm/decade in the arid and semi-arid sub-region, and 1.3 mm/decade in the high-elevation sub-region, respectively. Only the annual precipitation in the eastern monsoon sub-region shows significant decreasing trends, and the change point approximately appears in 1980 years.

  2. 2.

    Monthly precipitation (multiannual average from 1961 to 2012) in the Yellow River basin shows a different seasonality. Eighty-seven percent of the annual precipitation appears from May to October, and July (December) is the month with the highest (lowest) precipitation, with an average of 97.8 (2.9 mm). There are five months (January, February, May, June, and December) having the main positive trends, while the remaining seven months (March, April, July, August, September, October, and November) have the main negative trends, and trends are from –17.7 to 13.2 mm/decade. December and June are the first and second largest positive trends, while November and October are the first and second largest negative trends. Spatial distribution of monthly precipitation is similar to annual precipitation, namely gradually reduced from southeast to northwest.

  3. 3.

    As for the ten annual precipitation extremes indices in the Yellow River basin: There are seven indices (CWD, PRCPTOT, SDII, R10, R95p, Rx1day, and Rx5day) have negative trends, while three indices (CDD, R20, and R99p) have slight positive trends. And trends of all the ten annual extremes are not significant trends of CWD, PRCPTOT, SDII, R10, R95p, R99p, Rx1day, Rx5day, CDD, and R20 are 1.50 days/decade, −8.70 mm/decade, –0.02 (mm/day)/decade, –0.19 days/decade, –2.65 mm/decade, –0.16 mm/decade, –0.14 mm/decade, –0.29 mm/decade, and 1.50 and 0.02 days/decade, respectively. The change degree of annual precipitation extremes in the whole Yellow River basin decreased but significantly different in the three sub-regions. Specifically, trends of all the ten annual precipitation extremes indices in the eastern monsoon sub-region were dominant negative, while mainly positive in the arid and semi-arid region and the high-elevation sub-region.

  4. 4.

    For the four monthly extremes indices (PRCPTOT, SDII, Rx1day, and Rx5day), all the four indices have main positive trends in February, May, June, and December, while negative trends in April, August, September, October, and November. As for the remaining 3 months (i.e., January, March, and July), different indices have different directions of trends. The months having the most dominant positive trends are distinctly different (in February, June, or December), while months with the most dominant negative trends are the same (in November).

  5. 5.

    In the whole basin, eight indices (PRCPTOT, SDII, R10, R20, R95p, R99p, Rx1day, and Rx5day) have positive relations with elevation, while two indices (CDD and CWD) have negative relationship with elevation. Especially, PRCPTOT, R10, R95p, and Rx5day have significant positive relationship with elevation. But in the three sub-regions, relations between the ten indices and elevation are not significant.

  6. 6

    All the ten annual indices have little relationship with NHSH and NHPV. But for the four monthly precipitation indices (i.e., Rx1day, Rx5day, PRCPTOT, and SDII), there were significant positive relationships with NHSH, while there were significant negative relationships with NHPV. Comparison of the sensitivity to atmospheric circulation in the three sub-regions shows that indices in the high-elevation sub-region are the most vulnerable to the effects of atmospheric circulation, followed by the eastern monsoon sub-region, and last one is the arid and semi-arid sub-region.