1 Introduction

Extreme weather events, such as frequent droughts and floods, have profound impacts on both economic and human welfare (Xia et al. 2015). Extreme precipitation events are among the most deadly and destructive natural disasters worldwide (Plummer et al. 1999; Potop et al. 2014) and the corresponding losses of life and property have demonstrated the importance of relevant research (Easterling et al. 2000). Although most such events have negative influences, extreme precipitation may be beneficial in some situations (Meehl et al. 2000). Many numerical experiments have shown that the number of extreme weather events may be more dependent on changes in climate variability than mean trends (Katz and Brown 1992). Thus, any subtle changes in the number or intensity of excessive events may have meaningful impacts on human society.

Changes in extreme rainfall patterns are vital indicators of climate change. Su et al. (2006) investigated extreme summer rainfall trends over the Yangtze River, China, and found that an increase in the number of rainstorm days, rather than intensity, was the main contributor to an observed upward precipitation trend in the Yangtze River Delta. Becker et al. (2006) concluded that monthly rainfall trends in the Yangtze River catchment were positively correlated with an increase in severe events in the area, leading to flood disasters in summer. Similarly, Wang et al. (2017) used gridded observation data with Coupled Model Intercomparison Project Phase 5 simulations based on the representative concentration pathway (RCP) 4.5 and 8.5 scenarios to analyze changes in average and excessive climate events in the arid region of northwestern China. Liu et al. (2008) indicated that annual precipitation in the Yellow River Basin (YRB) mainly showed a downward trend, and abrupt changes in the upstream and midstream regions occurred later than those in the downstream regions. Hu et al. (2012) noted a four-season pattern in the excessive rainfall trend, but only analyzed the YRB source region although the YRB flows from the Tibetan Plateau to eastern China and mountainous areas represent 67% of the basin’s extent (Feng et al. 2007; Wang et al. 2010). In general, precipitation patterns are significantly affected by terrain (Shu et al. 2005; Liu et al. 2015; Henn et al. 2017; Stauffer et al. 2017) and the changing climate is sensitive to complex orographic effects in many parts of the world (Beniston 2003; Seidel and Free 2003). Thus, a detailed analysis of the trends in extreme climate events in China is important for reducing climate-induced flood and debris flow risks (Huang et al. 2013).

Previous studies mainly considered annual precipitation, ignoring the impact of seasonality (She et al. 2013; Jin et al. 2016). These studies indicated apparent trends in annual rainfall over the YRB (Liang et al. 2015; Cui et al. 2017), but failed to account for the connection between changes in average values and changes in extremes. Moreover, precipitation in the autumn and winter has a profound impact on the following spring’s drought conditions. Thus, in this study, we analyzed both annual and seasonal precipitation for the entire YRB and three sub-regions and considered the connections between the changes in average and extreme rainfall values. Such detailed analysis and understanding of precipitation trend events in the YRB are important for predicting and mitigating floods and droughts.

2 Data and methods

2.1 Data

We employed the historic basic meteorology dataset, version 3.0, provided by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA); this consisted of 2474 gauge stations with daily precipitation records from 1961 to 2016. Although this dataset had previously undergone strict quality control measures including an extreme value check and internal consistency check by data providers, a further NMIC assessment found 35 gauge stations with inhomogeneity among the total 2474 stations (Shen and Xiong 2016). Most stations in the northwestern area of China were homogeneous (Yang and Li 2014).

The YRB contained 749 rainfall gauge stations, though we applied strict criteria to avoid missing values that could skew accurate results and removed stations with inconsistencies. For example, if a year’s data contained < 3% missing days, it was considered sufficiently complete. Moreover, only stations containing all 56 years of complete data from 1961 to 2016 were retained (Gao and Wang 2017). A total of 423 stations met these standards and were therefore selected to represent the spatiotemporal variations of precipitation over the YRB.

The number of days from January to December during which precipitation exceeded 50 mm (rainstorm) and 100 mm (downpour) and the number of days of non-storm precipitation (i.e., light rain that exceeded 0.1 mm, moderate rain that exceeded 10 mm, and heavy rain that exceeded 25 mm) were calculated for statistical purposes (Zhao et al. 2016). For seasonal analysis, we defined four seasons as spring (March–May, MAM), summer (June–August, JJA), autumn (September–November, SON), and winter (December–February, DJF) (Ali et al. 2015). In order to further analyze the spatial variability of precipitation, the area was divided into three parts (areas A, B, and C), based on the region’s topographic “staircase” pattern of three distinct elevation regions (Fig. 1). There were 50 gauge stations in area A (the upper YRB, with altitudes greater than 2000 m), 181 gauge stations in area B (the middle YRB, with altitudes from 1000 to 2000 m), and 192 gauge stations in area C (the lower YRB, with altitudes less than 1000 m).

Fig. 1
figure 1

Locations of 423 weather stations (black dots) along the Yellow River (blue line in the red box) used in the study area (red box, 33.5° N–41.5° N, 96° E–119° E). Terrain elevation is shown by color scale; purple dashed lines mark the rough boundaries of the three topographic regions forming the “staircase” pattern. Area A represents the upstream portion of the YRB, area B represents the midstream portion, and area C represents the downstream portion

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2.2 Methods

2.2.1 Precipitation index

We used annual (PreANU), seasonal (PreSEA), and monthly (PreMON) rainfall as mean precipitation indices (Table 1). The annual mean single-station precipitation was 16.8 mm over the entire YRB. The maximum annual single-station precipitation was 24.9 mm in 1964 and the minimum was 12.4 mm in 1997. In areas A, B, and C, the annual mean single-station precipitation was 12.6 mm, 13.7 mm, and 20.8 mm, respectively. The maximum annual single-station precipitation was 17.1 mm, 19.5 mm, and 32.4 mm, respectively, while the minimum was 9.7 mm, 9.5 mm, and 14.8 mm. After considering the extreme climate indices proposed by previous research (e.g., Karl et al. 1999; Trenberth and Owen 1999; Zhang et al. 2005), we selected five indices for extreme precipitation analysis (Table 1): the number of days that daily precipitation was greater than 0.1 mm (PN01), 10 mm (PN10), 25 mm (PN25), 50 mm (PN50), and 100 mm (PN100), and we calculated these for the YRB overall and for each of the three subareas (Norrant and Douguédroit 2006; Pethybridge et al. 2009).

Table 1 Definitions of mean and extreme rainfall indices
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2.2.2 Trend test

The Mann-Kendall (M-K) test (Mann 1945; Kendall 1975; Gilbert 1987) is used to determine whether a variable follows a positive or negative trend over time. A monotonic positive (negative) trend shows that the variable consistently increases (decreases) over time, but the linear trend is not always clear. The M-K test is used for parametric linear regression analysis and examines whether a non-zero trend is present in the gradient of the estimated linear regression line. Most regression analysis assumes that fitted regression line residuals are normally distributed, but the M-K test is a distribution-free test that does not require such an assumption.

The M-K test is depended on the relative ranking of the data values. The M-K statistic S, used to estimate the significance, is calculated as (Wang and Swail 2001; Jung et al. 2015):

$$ S={\sum}_{i=1}^{n-1}{\sum}_{\mathrm{k}=\mathrm{i}+1}^n\operatorname{sgn}\left({x}_k-{x}_i\right)\kern0.5em \operatorname{sgn}(x)=\left\{\begin{array}{c}1\left({x}_k-{x}_i\right)>0\\ {}0\left({x}_k={x}_i\right)\kern0.86em \\ {}-1\left({x}_k-{x}_i\right)\;\end{array}\right., $$
(1)

where xk and xi are continuous information values, and n is the size of the dataset. If S is above zero, observed values will increase over time while variable values will decrease over time. The variance of S is given by:

$$ {V}_S^2=\frac{n\left(n-1\right)\left(2n+5\right)-{\sum}_{i=1}^m{e}_i\left({e}_{i-1}\right)\left(2{e}_i+5\right)}{18}, $$
(2)

where m is the number of tied groups and ei is the number of observations in the m group. The ZMK (M-K test statistic) is calculated as:

$$ {Z}_{\mathrm{MK}}=\left\{\begin{array}{c}\frac{S-1}{V_S},S>0\\ {}0,S=0\\ {}\frac{S+1}{V_S},S<0\end{array}\right.. $$
(3)

An above-zero (below-zero) value of ZMK illustrates that the data have a positive (negative) trend over time. In the null hypothesis H0, S is expected to have a normal distribution and should display no trend over time, while ZMK is accepted if \( \mid {Z}_{\mathrm{MK}}\mid \ge \mid {Z}_{1-\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\mid \), where \( \mp {Z}_{1-\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.} \) indicate the standard normal deviates and α is the significance level for the test (Im et al. 2011).

3 Results and analysis

3.1 Average rainfall trends

Figure 2 shows the PreANU variations in the entire YRB region and areas A, B, and C from 1961 to 2016. The overall mean annual precipitation had a downward trend with a 95% confidence level, as did areas B and C; only area A had an upward trend.

Fig. 2
figure 2

Variations from 1961 to 2016 of inter-annual station mean precipitation (different colored lines and points) and trends (solid lines) in a the entire YRB, b area A, c area B, and d area C

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As for seasonal trends (Fig. 3, Table 2), all four seasons showed downward trends in the YRB overall, with summer and winter having 90 and 95% confidence levels, respectively. Area B was similar, though the summer trend was less pronounced. Area C showed negative trends in spring, summer, and winter, with the a summer trend at a 90% confidence level. In contrast, area A showed positive trends in spring, summer, and winter, the latter with a 95% confidence level.

Fig. 3
figure 3

Trends in seasonal precipitation from 1961 to 2016 determined using the Mann-Kendall test with 423 observation stations. Triangles indicate an upward or downward trend with at least 90% confidence. Blue line marks the course of the Yellow River. Terrain elevation is shown by color scale; purple dashed lines mark the rough boundaries of the three topographic regions forming the “staircase” pattern

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Table 2 The Mann-Kendall test statistics for seasonal mean rainfall within the YRB and areas A–C for 1961–2016
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Fifteen stations had negative springtime trends in area B at a 90% confidence level (Fig. 3a). Area C had negative summertime trends, with 44 stations trending at 90% confidence; area B also had 14 stations with the same negative trend at the same confidence level (Fig. 3b). Positive trends dominated areas B and C in the autumn, with 29 stations in the regions meeting the 90% confidence interval. These positive trends tended to be distributed near the transitional areas between different “staircase” zones (Fig. 3c). Areas A and B had 20 and 24 positively trending stations in the winter at the 90% confidence level, respectively (Fig. 3d).

3.2 Extreme rainfall trends

Analysis of the number of annual extreme rainfall (> 50 mm) days at stations located in the research area from 1961 to 2002 indicated negative trends. Every area had a downward trend from 1961 to 2002, all but area A at 90% confidence (Fig. 4). Additionally, the number of annual extreme precipitation days over the entire YRB, area A, and area C had slightly downward trends in recent years (2003–2016), while B showed inconsistent fluctuations.

Fig. 4
figure 4

Inter-annual variations (black lines and points) and trends (solid red lines) in the number of extreme precipitation days (> 50 mm) at stations located in a the YRB, b area A, c area B, and d area C from 1961 to 2016. The vertical axes represent the total rainstorm days at all stations in the different areas

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Next, the five selected indices were employed for extreme precipitation analysis. PN01 in all three areas showed a downward trend from west to east (Fig. 5) but all other indices showed the opposite trend. Annually, area A did not achieve a precipitation mean of 50 mm, while area C was the only area to reach 100 mm. Seasonally, PN100 only occurred in area C in the spring (0.01 times) and summer (0.29 times). PN50 only occurred in areas B and C, especially in the summer and in the autumn; in the latter, PN50 occurred 1.7 times at the average gauge station in the summer and 0.21 times in the autumn.

Fig. 5
figure 5

Number of precipitation days of different levels (PN01, PN10, PN25, PN50, and PN100) at gauge stations within the three areas annually and seasonally from 1961 to 2016. Red arrow indicates the trend in rainfall values across the three areas. Values for 0.1 mm have been reduced by a factor of 10 to improve the figure’s legibility

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Next, seasonal trends in extreme precipitation were evaluated. We found that 51 (58%) gauge stations had positive trends in area B, and 96 (53%) gauge stations had positive trends in area C in the spring. There were a comparable number of positively (15, 83) and negatively (18, 88) trending gauge stations in area A and area B from summer to autumn. Area C had primarily negative summertime trends at 140 (73%) gauge stations; this trend continued into the autumn with 134 (70%) stations. Figure 6 shows that, in the analysis of extreme precipitation, 27 gauge stations had negative trends in area C during the summer, with at least 90% confidence. Area B and area C had 18 and 15 stations, respectively, with negative trends in the autumn, with at least a 90% confidence level.

Fig. 6
figure 6

Trends in the number of seasonal extreme precipitation (> 50 mm) days determined using the M-K test from 1961 to 2016. Triangles indicate an upward or downward trend with at least 90% confidence. Blue line marks the course of the Yellow River. Terrain elevation is shown by color scale; purple dashed lines mark the rough boundaries of the three topographic regions forming the “staircase” pattern

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3.3 The connection between mean and extreme rainfall indices

After analyzing the spatial and temporal characteristics of average and extreme rainfall levels in the YRB, we attempted to correlate the two. Most correlations met at least the 95% confidence limit (Table 3). In the spring and autumn, the degree of correlation was nearly equal for different areas and precipitation levels. Correlations of PN[ABC]01 were more significant in the spring and autumn than annually or in other seasons. In the summer and annually, the correlation of PNC25 was more significant, while in spring, autumn, and winter, PN[ABC]10 was relatively significant. The highest correlation between mean and extreme precipitation clearly occurred in summer over the YRB. The highest correlations were mainly concentrated in areas B and C.

Table 3 Correlation coefficients between average precipitation and extreme rainfall days
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4 Discussion and conclusions

The YRB was divided into three parts according to its three constituent “staircase” topographic features in order to facilitate regional climate change research. From both inter-annual and seasonal points of view, the spatiotemporal changes in mean and extreme precipitation over the YRB and its three sub-regions were analyzed from 1961 to 2016 using the M-K trend test on the basis of 423 rainfall gauge stations. The results showed that mean and extreme precipitation had different trends and distinct seasonal shifts over the whole basin and its sub-regions, leading to the following conclusions:

  1. (1)

    The annual mean precipitation had a negative trend over the whole basin except the upper YRB. The seasonality trend of mean precipitation was evident over the YRB and it three sub-regions.

  2. (2)

    Five indices were employed for precipitation extremes. Annual extreme precipitation days over the whole basin and three sub-regions had a consistent downward trend from 1961 to 2002. From 2003 to 2016, rainstorm days over the whole basin and sub-regions had a slightly downward trend except in the middle YRB. Spatially, rainstorms days increased from west to east over the YRB in every, and rainstorms days were mainly concentrated in the middle-lower reaches of the YRB, especially in the summer and autumn. The trends of extreme precipitation days also showed obvious seasonality over the whole basin and three sub-regions.

  3. (3)

    Relationships between mean precipitation and rainstorm days were investigated in different regions and seasons. Every extreme precipitation index had a significant positive correlation with mean precipitation in the corresponding region and season; the highest positive correlation occurred over the middle-lower YRB in the summer.

Other research has detected variations in mean precipitation and extremes over the YRB (e.g., Yang and Chunhui 2004; Li et al. 2011; Ma et al. 2013). Xu and Zhang (2006) identified a downward trend of annual mean precipitation over the YRB in the past 50 years from 77 stations. Liu et al. (2008) found that an upward trend of annual mean precipitation was significant in the upper reaches of the YRB, while downstream areas showed the opposite trend based on 81 stations. Zhang et al. (2014) confirmed these annual mean precipitation patterns over the whole YRB and sub-regions from 64 rainfall stations and found a downward trend over the whole YRB in the spring and autumn. Although our results matched such previous research, we investigated and discussed the seasonality of mean precipitation in every sub-region of the YRB in more detail on the basis of 423 observation stations, a higher level of detail than previously reported.

Furthermore, Dong et al. (2011) used a generalized linear model to report a significant downward trend in annual extreme precipitation over the central-east YRB with 215 stations from 1951 to 2004. Gao and Wang (2017) reported an enhanced rainfall extreme intensity but a declining extreme precipitation days in the middle-lower YRB. Hu et al. (2012) proposed a varying seasonality of extreme precipitation across the YRB based on only 17 widely distributed stations and highlighted a negative extreme precipitation trend in the summer. At an inter-annual scale, our results clearly showed annual extreme precipitation trends over the whole basin and three sub-regions, but also detected spatial patterns from west to east over the YRB. At a seasonal scale, we reported varying seasonal trends of extreme precipitation with a negative trend over the middle-lower YRB in the summer and autumn, new information not reported by the previous research.

Finally, though previous research compared mean precipitation and extreme precipitation days over the YRB and sub-regions using only 62 meteorological stations (Liang et al. 2015), the relationship between the two remained unclear. Our results highlighted their significant positive relationship over the YRB and sub-regions at seasonal and inter-annual scales.

Our results could play a crucial role in water resource management, agriculture, human activities, and further studies of regional climate change in arid and semi-arid regions of China. The annual mean precipitation results indicate a drought tendency in the central-east YRB, while the western parts of the YRB may experience alleviated water resource shortages. Further research on mean precipitation in different regions and seasons would assist the sustainable development of the YRB and provide efficient fresh water utilization in the north of China. In addition, the association of extreme and mean precipitation implies that, once summer rainfall begins to occur over the middle-lower YRB, it may tend to develop into heavier rainstorms despite the overall downward rainfall trend in these regions. This phenomenon would complicate attempts at forecasting extreme weather.

Additionally, some past research has attributed precipitation across the YRB to large-scale external forcing. Gao and Wang (2017) claimed that extreme precipitation variations over the YRB were associated with elevation and the East Asian summer monsoon. Li et al. (2016) showed that precipitation patterns in the YRB were mainly affected by topographic factors and atmospheric water sources. Liang et al. (2015) explored the relationship between monthly extreme precipitation indices and subtropical highs in the Northern Hemisphere. However, as the possible causes of the seasonal and annual characteristics of mean and extreme precipitation across the YRB reported here are unclear, further research into this question is warranted.