Multiple time scale analysis of sediment and runoff changes in the Lower Yellow River

2.1 Study area description

The Yellow River originates from the northern Bayan Kala Mountain in the Qinghai Plateau and it through the Huanghuaihai Plain, finally into the Bohai Sea. The total length of the mainstream is 5464 km, the surface of the runoff drop is 4480 m, and the basin total area is 795 000 km². The downstream reaches in Taohuayu, Zhengzhou City, Henan Province is the Lower Yellow River (LYR), with length of 786 km and catchment area of it is about 23 000 km², accounting for 3 % of the total drainage area. The total drop of the downstream reaches is 93.6 m with average gradient of 0.12 ‰. The increase of the amount of water accounted for 3.5 % of the Yellow River water. At present, the estuary of the Yellow River is located at the junction of Bohai Bay and Laizhou Bay, it was a new channel shaped by Qingshuigou artificial diversion in 1976 (Yang et al., 2004).

LYR has a wide upper section and a narrow lower section. The reach upstream of Gaocun, with a typical braided channel pattern, is called the braided reach, with a length of 284 km. And the deposition of upside are seriously, the lower section is more stable. The reach lying approximately between Gaocun and Aishan with a channel pattern transitioning from braided to meandering is called the transitional reach, with a length of 184 km, and the reach roughly between Aishan and Lijin with a stable and well-restricted meandering channel pattern is called the meandering reach, with a length of 272 km. Floods in the LYR mainly come from three areas in the middle region. They are Helongjian, Longsanjian and Sanhuajian area. The middle reaches of the Yellow River formed Huayuankou floods. Floods from the upper reaches constitute the base flow of floods in the LYR. In the recent 40 years, the quantity of sediment which transported by flood to the estuary is averaged about 1 billion tons per year (Miao et al., 2010). Heavy sedimentation makes the surface of the Yellow River rise above 2–3 m on both side, even up to 10 m above sea level, which threaten the safety of the people on the coast (Xu et al., 2004). Heavy sedimentation also results in an obvious shrinkage of the main channel with a decrease of flood discharge capacity (Li et al., 2014). The transverse slope of water surface of parts of the Yellow river has already reached 1–2 ‰, which much larger than the vertical drop of 0.14 ‰ (Liu, 2011).

2.2 Data description

The hourly runoff and sediment data of Huayuankou (HYK), Jiahetan (JHT), Gaocun (GC), Sunkou (SK), Aishan (AS), Luokou (LK), and Lijin (LJ), which are the main hydrological stations along the LYR, are adopted in the study. The data is collected from 1980 to 2002. The annually sediment load and runoff are calculated by summing up the hourly data. The maximum value of the monthly, daily and hourly sediment load and runoff are also obtained by statistics of the hourly data.

3.1 Mann–Kendall trend test

The Mann–Kendall trend test is a rank correlation test between the ranks of observations and their time sequence (Yue et al., 2002). It has been used by many researchers to analyse the trends of precipitation, runoff, temperature, water quality and other elements in time series. The Mann–Kendall test does not require samples to follow a certain distribution (Zhang et al., 2007). It is suitable for non-normal distribution such as hydrology and meteorology. It is a frequently-used time series test method in hydrological and meteorological research (Guo et al., 2010). This method takes the sequence as a prerequisite. And it requires the sequences to be independent and random.

In the Mann–Kendall test, the hypothesis H₀ is time-series data (X₁…X_n), which are n independent samples with the same distribution of random variables. The alternative hypothesis H₁ is a bilateral test. For all k, j≤n, and k≠j, then the distribution of X_k and X_j are not the same. The test statistic S is calculated as follows:

Under the assumption that the data are independent and identically distributed, S is normal distribution. The mean is 0. The variance is $V_{\mathrm{or}}\left(S\right)=n(n-\mathrm{1})(\mathrm{2}n+\mathrm{5})/\mathrm{18}$. When n>10, the standard normal system variable is calculated by:

t is the range of any given node, and when n>10, Z_c converges to a normal distribution and is calculated by:

In the bilateral trend test, at a given alpha significance level, if $Z_{\mathrm{c}}\ge Z_{\mathrm{1}-\mathit{\alpha }/\mathrm{2}}$, rejecting the hypothesis H₀, that is, at the significance level of α, the time series data have obvious upward or downward trend. $\pm Z_{\mathrm{1}-\mathit{\alpha }/\mathrm{2}}$ is the standard normal distribution ($\mathrm{1}-\mathit{\alpha }/\mathrm{2}$) quantiles, and α is the test's significance level. The degree of the trend can be expressed as Kendall inclination β, which is calculated as follows:

In the formula, 1<j<i<n. When β>0, it means the rising trend, otherwise it means the falling trend.

3.2 Hurst coefficient

Hurst found that the data did not follow the Brownian motion and the normal distribution through the Nile hydrological data, if there was a large amount of water a year, the amount of water in the following year would also tend to be larger. The Hurst coefficient was proposed in 1951. The Hurst coefficient can be used to characterize the persistence or long-term correlation of time series quantitatively.

The Hurst coefficient h means: h<0.5, the sequence is anti-persistent, and the trend of the future is opposite to the trend of the present; h=0.5, it indicates the sequence is random. And the future trend will not be affected by the present; h>0.5, it indicates that the sequence has a positive continuity, the trend of the future change is the same as the current trend; h is closer to 1, it shows that the sequence is more persistent. When h is the closer to 0, the stronger the anti-persistence of sequences.

When 0.5<h<0.719, the degree of variation is low; when 0.719<h<0.839 the degree of variation is middle; when 0.839<h<0.924, the degree of variation is high; when 0.924<h<1.0, the degree of variation is acute (Xie et al., 2008). The time series with long-term correlation in nature are ubiquitous. The Hurst coefficient has been widely used in hydrology, geochemistry, climate, geology and earthquake and other fields.

4.1 Mann–Kendall test analysis

The Mann–Kendall test was used to analyse the changes of the runoff and sediment of the seven hydrological stations, and the Z_c of runoff at different time scale is shown in Table 1.

Table 1Z_c of runoff in different time scale.

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According to Table 1, Z_c are far greater than the significance level (α=0.01), which absolute value is 2.56. We can conclude that the runoff of the seven hydrological stations are shown obviously downward trend at different time scale. We can also observe that the Z_c is larger in smaller time scale from Table 1, which indicates that the runoff peak value reduced more obviously.

The Kendall inclination β of runoff at different time scale is shown in Fig. 1.

Figure 1β of runoff in different time scale (HYK: Huayuankou; JHT: Jiahetan; GC: Gaocun; SK: Sunkou; AS: Aishan; LK: Luokou; LJ: Lijin).

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It can be observed that the trend of the runoff changes at seven stations in the LYR are relatively consistent. Based on the calculated β value, the β of the runoff are all negative which shows that the trends of runoff are all decreasing. Since the middle of 1980s, runoff has decreased significantly, the largest decrease occurred in 2000. These results are consistent with the former research (Yao et al., 2015). In different time scales, at the same horological station, the smaller the scale is, the more obvious changes are, β tends to zero. Among them, the change of HYK Station is the most obvious one, β is −285 in hour scale, however, β turns out to be −106 in annually scale. At the same time scale, decline trends are gradually reduced from upstream to downstream.

Table 2Z_c of sediment in different time scale.

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The Z_c of sediment at different time scale is shown in Table 2.

According to the Z_c result (Table 2), $\left|Z_{\mathrm{c}}\right|\mathit{<}{Z}_{\mathrm{1}-\mathit{\alpha }/\mathrm{2}}$, Z_c are far smaller than the significance level (α=0.01), which absolute value is 2.56. We can accept the original hypothesis H₀ at α=0.01 significance level, there is no clear upward or downward trend in time series data.

The Kendall inclination β of sediment at different time scale is shown in Fig. 2.

It can be observed that although the trend has not reached a significant level, β is always greater than zero (Fig. 2) which means the amount of sediment in the LYR has slightly increased since the 1980s.

Figure 2β of sediment in different time scale (HYK: Huayuankou; JHT: Jiahetan; GC: Gaocun; SK: Sunkou; AS: Aishan; LK: Luokou; LJ: Lijin).

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The Z_c of upstream hydrological stations are close to the significance level, and the β of HYK and JHT are all greater than 0, which means their trends of sediment are slightly increased. However, the β value of downstream is more complicated, and it does not continue

the trend of upstream, and the β value decreases, even less than 0. This shows that in the flood season, a large amount of sediment are carried by the floodwater from upstream to downstream, resulting an upward trend of sediment in the upstream, However, due to the sedimentation effect, sediment has not been carried into the downstream by floods, which result in there is no trend of increase of sediment in the downstream.

According to the β of sediment in different time scales, we can find that most of the β values of sediment in the LYG over the past 20 years are greater than zero. Take HYK Station as an example, the value of β in each time scale is greater than zero. And the β value decreases in turn from the hour scale to the year scale. At the hour scale, the β of sediment in HYK station is 4.46, however, at the annually scale, the β becomes 1.16. Under different time scales, the scale becomes larger, the β gets smaller, closer to 0.

To sum up, it can be seen from the β value, whether it is in daily scale, monthly scale, or annually scale, the changes of sediment in the LYR in flood season all show the opposite trend of the change of runoff from 1980 to 2003. The trend of the runoff is decreased, the trend of sediment is slightly increased.The trends of different scales are similar. But the smaller the scale is, the more obvious the change will be. The changes of runoff and sediment are the response to the natural factors of climate change and human activities. Relevant studies show that in recent years, except the upstream regions where the trend of precipitation changed over time, in other regions, the annual precipitation series generally show a downward trend and the trend of downstream was more obvious (Xu and Zhang, 2006). In the past 20 years, the runoff into the LYR reduced, this trend is consistent with the trend of precipitation in the Yellow River Basin. But the sediment into the LYR has no obvious increased trend, there is no synchronized phenomenon between runoff sequence and sediment sequence change in the same station of the LYR.

The rapid change of runoff did not result to a response of the sediment. This is due to the factors that affect the change of sediment are multicomponent (Fan and Yang, 2010). The slope cropland in the Yellow River Basin is an important sediment source, rainfall erosion is the main driving force of sediment erosion, so heavy rains in the flood season can lead to the amount of sediment entering the Yellow River increased, while there is a large number of reservoirs built in the Yellow River Basin, which intercept a lot of sediment, has a great effect on reducing the amount of sediment (Xu and Zhang, 2006). Ultimately, the data show that, even the change of the flow rate is obvious increase, sediment deposition in the lower reaches did not show an obvious change.

4.2 Hurst coefficient analysis

Hurst Coefficient revealed the variation on dimension of time series, hence the H values demonstrated whether or not the data sets have changed over time. The Hurst value of runoff at different time scale is shown in Table 3.

Table 3Hurst value of runoff.

^a acute degree, ^b high degree
HYK: Huayuankou; JHT: Jiahetan; GC: Gaocun; SK: Sunkou; AS: Aishan; LK:Luokou; LJ: Lijin

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According to Hurst results of runoff, at the same hydrological station, the time scales get smaller, the Hurst value of the runoff get higher. Take LJ station as an example,at the hour, daily, monthly and annually scale, Hurst values are 0.96, 0.94, 0.92, and 0.82 respectively. At the same time scale, the Hurst value of downstream hydrological stations are higher than these of the upstream hydrological stations, which could prove that the persistence of upstream is higher than that of downstream.

The Hurst value of sediment at different time scale is shown in Table 4. According to the Hurst results of sediment (Table 4), it can be seen that Hurst results of 7 stations in different time scales are all very high ,all of them are greater than 0.8. The future trend of sediment in the LYR exists state persistence and has similar changing characteristics with past features.

Generally, both runoff and sediment series during the flood season correlated well in long term, and the trend of the future changes would be affected by the current regime. The future trend of runoff and sediment are positively related to the past situation, these results are consistent with the study of Yan et al. (2007) and Ma and Li (2008). Of all runoff variations, the moderate and strong alteration appeared in annually scale, monthly scale respectively. And all the sediment series altered sharply and existed significant jump variation.

Table 4Hurst value of sediment.

^a acute degree, ^b high degree
HYK: Huayuankou; JHT: Jiahetan; GC: Gaocun; SK: Sunkou; AS: Aishan; LK: Luokou; LJ: Lijin

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