1 Introduction

Flooding is one of the most common and devastating natural hazards due to its impacts on the socio-economy and on human health. Each year ~20–300 million people are affected by floods worldwide (Han and Coulibaly 2017; Ogie et al. 2018), especially people in developing countries because of the dense population, urbanization, and poor drainage infrastructure (Liu et al. 2017). Because of the projected increase in extreme weather events in the future (Wang et al. 2013), investigating changes in floods and the underlying drivers is helpful for flood risk management under changing environments (climate change and or enhanced human activities).

To minimize floods damage, various structural and non-structural flood control measures have been taken. Reservoirs, dykes and dams are built along large rivers for flood control and management (Li et al. 2015). Flood forecasting and estimation have been implemented increasingly for mitigation and adaptations (Han and Coulibaly 2017; Ogie et al. 2018). The assumption of stationarity is the basis for flood frequency analysis and flood forecasting (Petrow and Merz 2009; Li et al. 2015). However, this assumption is under challenge of changing environments, which would bias hydrological analysis and water resources management (Ishak et al. 2013; Mediero et al. 2014).

Petrow and Merz (2009) documented a significant upward trend in floods that were driven by increasing precipitation and atmospheric circulation in the west, south and center of Germany. Ishak et al. (2013) identified significant downward trends in the annual maximum flooding in south-east and south-west Australia, which were associated with the El Niño Southern Oscillation (ENSO). With significant trends and change points detected in the annual maximum flood peak series, Salvadori and Neila (2013) confirmed the non-stationarity in the flood series in the Northeastern United States, which was owing to precipitation variation and large-scale climate patterns. Based on the annual maximum and peaks-over-threshold series, Mediero et al. (2014) discovered a decreasing trend in the magnitude and frequency of floods in Spain, which could be explained by the increasing evapotranspiration. In China, the annual maximum flood series in the Wangkuai watershed exhibited significant decreasing trends, with a detected change point in 1979 due to the construction of hydraulic structures (Li et al. 2015).

Generally, these studies well advanced our knowledge of nonstationary flood behavior in terms of trends and or change points in flood series, which highlighted the response of floods to changing environments varied greatly at regional scale. However, limited studies have investigated floods in semi-humid and semi-arid regions, especially regarding their nonstationarity. Furthermore, most of previous studies used conventional methods, such as the Mann-Kendell test and the Pettitt test, to detect abrupt change points in the mean of the flood series (Salvadori and Neila 2013; Li et al. 2015; Bai et al. 2016). Note that the mean change points in the flood series focus on the magnitude (Liu et al. 2018) of flood events, which would have an influence on the storage capacity during the reservoir operation and thus affect the benefit of irrigation. Nevertheless, little attention was paid to the change point in the variance of the flood series. Since variance reflects the flood stability (Liu et al. 2018), a change point in the variance of the flood series is critical for flood control and water resources management (Zhang et al. 2017). With a variance change point found in the flood series, the uncertainty of flood forecasting would increase significantly. Furthermore, it would directly affect the storage capacity of a multi-year regulation reservoir, which would adversely influence the allocation of regional water resources (Tu and Chen 2010; Zhang et al. 2017).

Therefore, the main objectives of this study are: (1) to examine the nonstationarity of flood series; (2) to identify the possible drivers for nonstationary floods; and (3) to explore the implications of the nonstationary flood series. The primary novelty of this study lies in: (1) comprehensively identifying nonstationary flood series in terms of trends, the mean and the variance change point; and (2) developing a complete framework of flood analysis concerning the changing patterns, causes and implications, which can be extended to any region without any limitation.

2 Methods

2.1 Flood Indices

Eight flood indices were defined to study the magnitude and timing of floods (Table 1). The annual maximum flood peak (AFP) and the maximum daily mean streamflow (AMF) were used to characterize the magnitude of annual floods, whereas the AMFs in summer (AMFS) and in autumn (AMFA) were for seasonal floods. Trends and possible change points of these indices were identified to investigate the nonstationary behavior of floods. Moreover, the occurrence day of AFP, AMF, AMFS and AMFA, i.e. AFPD, AMFD, AMFSD and AMFAD, was defined to study changes in the timing of floods.

Table 1 Definitions of flood indices used in the study
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2.2 The Modified Mann-Kendall Trend Test

The modified Mann-Kendall (MMK) trend test was used to detect trends in flood indices. It is distribution-free, robust and widely used. Different from the Mann-Kendall trend test, the MMK considers the lag-i autocorrelation (Mann 1945; Kendall 1955; Hamed and Rao 1998), which can effectively eliminate the effects of serial autocorrelation in a hydro-meteorological time series. More information about this method can refer to Huang et al. (2014, 2015). In this study, the trend was evaluated at a 95% confidence level.

2.3 The Heuristic Segmentation Method

The heuristic segmentation method was employed to identify possible mean change points in the flood series. When dealing with a nonlinear and nonstationary time series, this method outperforms conventional methods such as the sliding T/F test, the MK test, and the rank sum test (Bernaola-Galván et al. 2001; Huang et al. 2017; Liu et al. 2017).

For a time series X = x1, x2, ⋯xn − 1, xn, use a sliding pointer to separate X into two subseries. When the pointer reaches the position i (1 ≤ i < n), calculate the averages (μL and μR) and the standard deviations (sL and sR) of these subseries. The difference between μL and μR is estimated by the Student’s t test statistic at the 95% confidence level:

$$ T(i)=\mid \frac{\mu_L(i)-{\mu}_R(i)}{s(i)}\mid $$
(1)

where

$$ s(i)=\sqrt{\frac{\left({n}_{\mathrm{L}}-1\right)\cdot {s}_{\mathrm{L}}+\left({n}_{\mathrm{R}}-1\right)\cdot {s}_{\mathrm{R}}}{n-2}\times \left(\frac{1}{n_{\mathrm{L}}}+\frac{1}{n_{\mathrm{R}}}\right)} $$
(2)

is the pooled variance; and nL and nR are the length of the left and right subseries, respectively.

When moving the pointer along the X, the statistical significance P(tmax) corresponding to the largest T is calculated as follows:

$$ P\left({t}_{\mathrm{max}}\right)\approx {\left\{1-{I}_{\left[v/\left(v+{t}_{\mathrm{max}}^2\right)\right]}\left(\delta v,\delta \right)\right\}}^{\eta } $$
(3)

where δ = 0.40, v = n-2 and η = 4.19 ln(n) − 11.54 are simulated by the Monte Carlo; and Ix (a, b) is the incomplete beta function. If P(tmax) is smaller than the threshold P0 ∈ [0.90 − 0.95], there is no change point. Instead, there is a change point; and the iteration continues until P(tmax) < P0 or the length of the acquired subseries is less than the preset minimum segment length l0 (l0 = 25).

2.4 The Schwarz Information Criterion-Based Test

The SIC-based test is used to identify potential change points in the variance of the flood series. The merit of the SIC is that it reduces the heavy computations that are usually incurred with the change point analysis (Chen and Gupta 1997), without resorting to either the distribution or the significance level (Nosek 2010; Tu and Chen 2010).

Given a time series X = x1, x2, ⋯xn − 1, xn that follows the normal distribution, use a sliding pointer to divide X into two subseries and moves sequentially from x1 to xn − 1. When the pointer reaches position r (5 ≤ r < n − 5), the mean and standard deviations of these two subseries are μ1, μ2 and δ21δ22, respectively. The null hypothesis is that:

$$ {H}_0:{\mu}_1={\mu}_2,{\delta^2}_1={\delta^2}_2 $$
(4)
$$ versus\ the\ alternative:{H}_1:{\mu}_1={\mu}_2,{\delta^2}_1\ne {\delta^2}_2 $$
(5)

The SIC is defined as \( -2\log L\left(\hat{\theta}\right)+p\log n \), where \( L\left(\hat{\theta}\right) \) is the maximum likelihood function for the model, p is the number of free parameters in the model, and n is the sample size. Hence, for X, the calculation formulas for the SIC-based test are as follows (Chen and Gupta 1997; Tu and Chen 2010):

$$ \Big\{{\displaystyle \begin{array}{l} SIC(n)=n\log 2\pi +n\log {\sigma}^2+n+\log n\\ {} SIC(r)=n\log 2\pi +r\log {\sigma_1}^2+\left(n-r\right)\log {\sigma_2}^2+n+2\log n\\ {}{S}_{\mathrm{max}}= SIC(n)-\underset{1<r<n}{\mathit{\operatorname{Min}}} SIC(r)\end{array}} $$
(6)

where SIC(n) is the original SIC of the X; σ2 denotes the population variance of X; SIC(r) is the SIC at the r position; and Smax represents the maximum SIC difference.

The statistically significant difference at α level is C(α). if Smax ≥ C(α), there is a variance change point, otherwise there is no change point. The iteration continues until the acquired Smax < C(α) or the length of the acquired subseries is shorter than the minimum segment length l0.

2.5 The Cross Wavelet Analysis

The cross wavelet analysis is useful for identifying the relationship between two signals, both in time and frequency domains, with the combination of the wavelet transform and the cross-spectrum analysis (Hudgins 1993; Torrence and Compo 1998). It provides the distribution laws of the energy resonance and covariance of two time series in both time and frequency fields, thus being able to capture the nonlinear characteristics in their relationships (Torrence and Compo 1998; Huang et al. 2017). Being different from the wavelet coherence method, the cross-wavelet analysis is calculated by non-normalized wavelet power spectrums and has a high common power (Nourani et al. 2018), which makes it simpler and more popular. In this study, this technique is used to investigate the causes for nonstationary flood series. Details of this method can be found in Torrence and Compo (1998).

3 Study Area and Data

The Wei River Basin (WRB; Fig. 1), a typical semi-humid and semi-arid region, is the case study. It is the biggest tributary of the Yellow River Basin (YRB) with an area of 135,000 km2. Topographically, the basin is high in the northwest and low in the southeast with the maximum elevation difference exceeding 3000 m. The mean annual precipitation in the catchment is nearly 600 mm. More than 60% of the total runoff occurs in the flooding season; i.e., June to September, with flood hazards concentrating in the midstream and downstream. Serious soil loss, shrinking river channels, rising Tongguan elevation and changes in the extreme precipitation events in the basin have increased the flood risk (Guo et al. 2018), which seriously restricted the sustainable development there.

Fig. 1
figure 1

Location of the WRB and hydro-meteorological stations across the WRB

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There are three hydrological stations in the WRB, i.e. Xianyang, Zhangjiashan and Huaxian station. Hence, besides the whole WRB, the WRB was divided into two sub-basins (Fig. 1): the basin above Xianyang (BAX) and the basin above Zhangjiashan (BAZ). The annual flood peak and daily runoff data (1960–2010) were collected from the YRB hydrology bureau. Daily precipitation data were provided by China Meteorological Administration. Furthermore, the monthly Multivariate ENSO Index and the Pacific Decadal Oscillation (PDO) Index were obtained to investigate the teleconnection between floods and large-scale ocean-atmospheric circulation patterns. Additionally, the Normalized Difference Vegetation Index (NDVI) dataset (1982–2010) were collected to study the impact of vegetation coverage on floods.

4 Results and Discussion

4.1 Trends in the Timing and the Magnitude of Floods Events

Figure 2 shows the trends in the occurrence time and the magnitude of floods. Generally, non-significant trends in timing are identified. The MMK statistics of AFPD, AMFD, AMFSD and AMFAD in the BAX were 0.40, −0.75, 0.50 and 0.28, respectively and they were 0.74, 1.18, 0.88 and 0.80, respectively in the BAZ. For the whole WRB, the MMK statistics of these indices were 0.52, −0.11, 1.63 and 0.50, respectively. Therefore, the occurrence time of AFP and seasonal floods tend to be delayed across the basin, whilst it is expected to occur earlier with the decreasing trend identified for the AMF in the BAX and the whole WRB.

Fig. 2
figure 2

The MMK trend test results of flood indices of the two sub-basins and the whole WRB. The red dash line refers to the 95% significance level (i.e. ±1.96)

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Magnitude of floods in the basin exhibits remarkable fluctuations, with the AMF varying from 139 m3/s to 12,380 m3/s in the BAX, from 213 m3/s to 3730 m3/s in the BAZ and from 776 m3/s to 5130 m3/s in the whole WRB. The MMK statistics of AFP, AMF, AMFS and AMFA in the BAX were − 3.27, −2.83, −1.87 and − 2.72, respectively. For the BAZ, the MMK statistics of these indices were − 1.16, −1.50, −1.51 and − 2.62, respectively. For the whole basin, the MMK statistics of them were − 3.66, −3.69, −2.44 and − 2.71, respectively. Generally, there were widespread, significantly decreasing trends in the magnitude of the annual floods in the BAX and in the WRB, which is broadly consistent with the study of Bai et al. (2016).

4.2 Change Point in the Mean of the Flood Series

The heuristic segmentation method was adopted to identify potential mean change point of the flood series. The P0 and l0 were set to 0.95 and 25, respectively.

Figure 3a and b illustrates the detection of change points in the AMF time series in the BAX and in the BAZ. The blue line in Fig. 3a is the first iteration and segmentation process. The maximum T of the first iteration occurred in 1981, with corresponding P(tmax) = 0.9699 > P0 = 0.95, which suggests that the year 1981 is a change point in the mean of the AMF time series. Since the length of the segments was larger than 25, the segmentation process continued. The green line in Fig. 3a is the second iteration and segmentation process. The second maximum T appeared in 1994. However, it is not another change point because the corresponding P(tmax) = 0.7397 < P0 = 0.95. Finally, the segmentation process ended, because the length of the obtained subseries was shorter than l0. Figure 3b shows the iteration and segmentation process in the BAZ. There is no change point, because the corresponding P(tmax) = 0.7714 < P0 = 0.95.

Fig. 3
figure 3

The mean and the variance change points in the flood series: a and b are the change points in the mean of AMF time series in the BAX and the BAZ examined by the heuristic segmentation method, respectively; c is the change point in the variance of AMF time series in the BAZ based on the SIC test

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Table 2 shows the mean change points in the flood series of these basins. For the BAX, there were change points in the AFP (1984), AMF (1981) and AMFS (1981). For the BAZ, the change point only existed in the AMFA series (1977). For the whole basin, the change points existed in all flood indices: AFP (1993), AMF (1986), AMFS (1994) and AMFA (1985).

Table 2 Change points in the mean of flood series of the two sub-basins and the whole WRB based on the heuristic segmentation method
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4.3 Change Point in the Variance of the Flood Series

Since the heuristic segmentation method is only capable of detecting potential mean change point of the flood series, the SIC test was employed to explore the possible variance change point of the flood series. The r and l0 were set to 10 and 20, respectively. The C(α) of this length at 95% confidence level is 9.256.

Figure 3c shows the detected variance change point in the AMF series in the BAZ. The Smax was identified in 1981, and the acquiredSmax = 33.820 > C(α) = 9.256. Hence, the year 1981 is a significant variance change point in the AMF series. The segmentation process stopped, because the obtained subseries could not meet the requirements of r and l0. Table 3 shows the variance change points of the flood series of these basins. The variance change points were found in AMF (1981) and in AMFA (1981) in the BAX. For the BAZ, the change points of variance exist in AFP (1977), AMF and AMFS (1996), and AMFA (1981). For the whole WRB, the change points were detected in AMFS (1993) and in AMFA (1985).

Table 3 Change points in the variance of flood series of the two sub-basins and the whole WRB based on the SIC test
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Comparing Tables 2 and 3, the change points in the flood series across the basin were likely to occur in a clustered pattern. Spatially, the mean change points of the flood series were primarily identified in the BAX and in the whole WRB, while the variance change points of the floods series were observed mostly in the BAZ. Temporally, these change points occurred mainly in the 1980s and 1990s. Further, AMF and AMFA in the BAX exhibited both mean and variance change points in 1981.

4.4 Implications of the Nonstationary Flood Series

To explore the implications of the non-stationary flood series on hydrological frequency analysis, the AFP series in the BAX and BAZ were taken as examples. The AFP series in the BAX was identified with a mean change point while no variance change point was found, which was contrary to the AFP series in the BAZ. The Pearson type III distribution was adopted as the theoretical distribution to estimate the design floods of different frequencies by using the nonstationary AFP series and the pre-change point and post-change point AFP series. Results are shown in Fig. 4.

Fig. 4
figure 4

The flood frequency curve based on the nonstationary AFP series and series before and after change point of AFP series and their corresponding design floods of different frequency. The red dash line on the left is the theoretical curve of nonstationary AFP series. The green and blue dash lines refer to the theoretical curves of series before and after change point of AFP series, respectively. The red bar on the right is the design floods of different frequency estimated by nonstationary AFP series. The green and blue bar are the design floods of different frequency estimated by series before and after change point of AFP series, respectively. On the top are AFP series in the BAX with change point detected in the mean of series. On the bottom are AFP series in the BAZ with change point detected in the variance of series

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Generally, notable changes were found in the shape of the curves and in the magnitude of the design flood (Fig. 4). For the AFP series with a mean change point, if the frequency < 1%, the design floods of the pre-change point AFP series were larger than those estimated by the nonstationary AFP series or the post-change point AFP series. However, if the frequency > 1%, they became smaller (Fig. 4b). In the first case, it would lead to the overinvestment of water projects, whilst the second case would result in an increased risk of hydraulic works. The situation is opposite when the design floods are based on the post-change point AFP series.

Figure 4d shows the design floods based on these three kinds of AFP series in the BAZ. The design floods that were estimated by the pre-change point AFP series tended to be the largest, and those of the post-change point series were the smallest. If the flood frequency < 2%, the difference between the design floods of the pre-change point (or the post-change point) series and those based on the nonstationary AFP series would be more than 50%. Taking Fig. 4b and d as a whole, it is evident that the bias that arises from the variance change point is much more significant than that of the mean change point in estimating floods. Therefore, the variance change point of the hydrologic series should not be ignored when dealing with the problem of nonstationarity, which is necessary for water resources management and the safety of water control projects.

4.5 Discussion

To find out the drivers for nonstationary floods, the impacts of antecedent precipitation (AP), ENSO/PDO events and vegetation coverage on floods were investigated. Since the AMF series was extracted from the yearly maximum daily mean runoff, this section does not account for AMFS and AMFA.

4.5.1 The Impact of AP on Floods

AP refers to the accumulated amount of precipitation from X-days prior to the flood peak, which usually ranges from 2 to 7 days (Salvadori and Neila 2013). Here, X was set to 3 days, since the predominant precipitation events in the WRB usually have a duration of 1–3 days (Liu et al. 2017). During 1960–2010, the MMK statistics of the AP of AFP and AMF in the BAX, the BAZ and the whole WRB were 0.58, −4.13, 0.51, −1.93, −2.62 and − 1.93, respectively.

Figure 5 displays the cross wavelet transforms between AFP (AMF) and their corresponding AP in these basins. For the BAX, the AFP series was positively correlated with its corresponding AP in 2001–2005 with a 1–2 year signal (Fig. 6a). Also, AMF was positively correlated with its corresponding AP in 1978–1985 with a signal of 1–4 year (Fig. 6b). For the BAZ, there were statistically significantly positive correlations between AFP and its corresponding AP in 1965–1975 with a 1–2 year signal and a 4 year signal in 1975–1980 and a 6–10 year signal in 1996–2008 (Fig. 6c). Meanwhile, AMF in the BAZ was positively correlated with its corresponding AP in 1970–1978 with a signal of 3–4 year (Fig. 5d). For the whole WRB, significantly positive correlations were found between AFP and its corresponding AP in 1968–1972 with a 1–2 year signal and a 3 year signal in 1978–1984 (Fig. 5e). In addition, there were statistically positive correlations between the AMF series and its corresponding AP in 1970–1972 with a 1–2 year signal and a 2–4 year signal in 1980–1984 (Fig. 5f). These findings are consistent with the study of Guo et al. (2018), who stated that AP are closely related to floods in the WRB.

Fig. 5
figure 5

The cross wavelet transforms between AP and floods series in the BAX (a and b), the BAZ (c and d) and the whole WRB (e and f). On the top is those of the AFP series, while on the bottom is those of the AMF series. The 95% significance confidence level against red noise is exhibited as a thick contour, and the relative phase relationship is denoted as arrows (with anti-phase pointing left, in-phase pointing right). The color bar on the right denotes wavelet energy

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Fig. 6
figure 6

The cross wavelet transforms between ENSO/PDO and APF series in the BAX (a and b), the BAZ (c and d) and the whole WRB (e and f). On the top is the cross wavelet transforms between ENSO and AFP series, while on the bottom is the cross wavelet transforms between PDO and AFP series

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4.5.2 The Impact of ENSO (PDO) on Floods

The relationship between ENSO (PDO) events and floods was also investigated since they have strong influences on precipitation in the WRB.

Figure 6 is the cross wavelet transforms between ENSO (PDO) and the AFP series. For the BAX, ENSO was positively correlated with AFP in 1980–1982 with a 1–3 year signal (Fig. 6a). Besides, PDO was positively correlated with the AFP series in 1978–1982 with a 1–3 year signal (Fig. 6b). For the BAZ, there was a significant positive correlation between ENSO and AFP with a 3–4 year signal in 1970–1978 (Fig. 6c). Also, PDO displayed statistically positive correlations with AFP in 1972–1976 with a 4 year signal and a 7–9 year signal in 1996–2006 (Fig. 6d). For the whole basin, ENSO showed significant positive correlations with AFP in 1982–1984 with a 2 year signal, and negative correlations in 1980–1984 with a 3–4 year (Fig. 6e). This paradox of the relationship between them might be attributed to the effect of ENSO on the Walker Circulation, which in turn influence local precipitation and floods. In addition, there was a statistically significant positive correlation between AFP and PDO in 1982–1984 with a 2–3 year signal (Fig. 6f). Similar relations between ENSO (PDO) and the AMF series in these basins were also been found (for brevity, results are not shown). These results agree with previous studies that report large-scale ocean-atmospheric circulation patterns are remote drivers for changing floods (e.g., Petrow and Merz 2009; Ishak et al. 2013).

4.5.3 The Impact of Vegetation Coverage on Floods

During 1982–2010, there were significant increasing trends of vegetation coverage across the basin, and the MMK statistics of the NDVI series in the BAX, the BAZ and the whole WRB were 2.95, 3.25 and 3.45, respectively.

Figure 7 shows the cross-wavelet transforms between the NDVI and the floods series in the three basins. For the BAX, there were significant negative correlations between the NDVI and AFP (AMF) series, with a 1-3 year signal from 2001 to 2003 (Fig. 7a and b). For the BAZ, the NDVI was positively correlated with the AFP series with a 7–9 year signal in 1992–2002 (Fig. 7c). Although vegetation coverage usually plays a role in flood peak reduction, it also influences the regional hydrological cycle by regulating the surface energy balance and the evapotranspiration. In addition, it would increase the base flow and soil moisture. Therefore, it might amplify the flooding (Chen et al. 2014), to some extent. Figure 7d shows no relationship between the AMF and NDVI. For the whole basin, vegetation coverage has significant negative correlations the AFP (AMF) series in 1988–1991 with a 5 year signal (Fig. 7e and f). Overall, vegetation coverage is closely linked with floods in the WRB.

Fig. 7
figure 7

The cross wavelet transforms between NDVI and floods series in the BAX (a and b), the BAZ (c and d) and the whole WRB (e and f). On the top is those of the AFP series, while on the bottom is those of the AMF series

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4.5.4 The Possible Causes for the Non-stationarity of Flood Series

The AP, PDO/ENSO events and vegetation coverage all exerted strong impacts on the floods in the WRB. According to the trend test, significantly decreasing AMF in the BAX and AFP in the whole WRB could be due to their significantly decreasing corresponding AP (see section 4.5.1). Meanwhile, the significantly increasing trends of vegetation coverage were also responsible for the floods reduction in the basin (Bai et al. 2016).

Taking Figs. 5 and 6 and Tables 2 and 3 as a whole, it is notable that change point in the AMF series in 1981 in the BAX corresponds to the time when AP and ENSO were significantly correlated. Moreover, change point in the variance of the AFP series in 1977 in the BAZ corresponds to the time when the AP and ENSO (PDO) events showed significant correlations with AFP. Additionally, the AP shows a significant relationship with the AMF of the BAZ in 1996, when a variance abrupt change was found in the AMF series. Therefore, the AP and ENSO (PDO) events played a certain role in the nonstationary behavior of floods in the WRB, especially before the year 2000, which means that, aside from climate change, human activities should not be ignored.

In addition to the Natural Forest Conservation and the Grain for Green projects that aim to improve vegetation coverage, a series of soil conservation practices also had been implemented since the 1970s. Figure 8 shows the area (number) of different soil conservation practices in the WRB during 1960–2006. The huge growth of different soil conservation practices effectively reduced runoff in the WRB (Bai et al. 2016; Zhang et al. 2017). Hence, both climate change and human activities were responsible for the nonstationary floods in the WRB.

Fig. 8
figure 8

The area (number) of different soil conservation practices in the WRB during 1960 to 2006

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On the other hand, the comparison of Figs. 5, 6, and 7 shows that the impacts of AP, ENSO/PDO events and vegetation coverage on floods in the BAX and in the whole WRB generally were consistent with each other, yet they were different from those in the BAZ. This might account for the clustering effects of the change points in the mean and variance of floods series across the basin (see section 4.3).

5 Conclusions

Examining the assumption of stationarity in the flood series and the underlying causes is important for flood mitigation and water resources management. In this study, we focused on floods in the WRB of China.

Magnitude of floods across the basin showed high fluctuations. With detected significantly decreasing trends and change points, floods in the WRB exhibited nonstationary behaviors, which would lead to considerable changes in the design floods. Bias arising from the variance change point is much more significant than that of the mean change point in estimating floods.

Invalidity of stationarity in the flood series can be attributed to climate change and human activities. ENSO and PDO events are remote drivers for changing floods in the WRB, which could be used as input factors for flood prediction models. This study emphasizes the importance of identifying the potential variance change point in the flood series, which has great implications for flood control and water resources management.