Trend and attribution analysis of water and sediment variations in sandy rivers

Human activities and climate change have led to significant changes in the flow and sediment of sandy rivers in northern China. The key work to reveal the changes of river water and sediment conditions is to quantitatively study the changes of precipitation, water and soil conservation in river basins, and the effect of reservoirs on sediment containment. Taking the Yongding River as a case study, we analyze the changing trend of the water and sediment into the Yongding River and find that their amount has greatly decreased. In particular, the sediment yield has decreased by more than 90% and its trend has changed, and the turning point occurred in the 1980s. Based on the statistical data analysis model, the influences of human activities on the sediment inflow of the Guanting Reservoir were quantitatively evaluated. The results show that sand retention of the upper cascade reservoirs is the main reason for the sharp reduction in sediment loads, but the sand retention effect of reservoirs has a certain time limit. Water and soil conservation played a vital role in the sediment loads reduction during the present stage. The present studies may provide insights into understanding the integrated reclamation of the river basin.

Because the rivers are the main channels for the transport of surface water and sediment, the changes in runoff and sediment load in river channels reflect the basic situation of water and soil loss in river basins. More importantly, the relevant research is helpful for the in-depth exploration of the mechanism of interactions between natural factors and human activities, thus providing a basis for decision-making in sustainable regional development strategies (John et al. ; Pu et al. ). In particular, the research on runoff and sediment load variations in river basins has become an important component of global change research, and the understanding of their changing process and driving mechanism is conducive to the management of the ecological environment of river basins (Pourshahbaz et al. ).
This study aims to analyze the water and soil loss situations and their multi-year trend, the cumulative effect of reservoir operation on sediment transport in river basins, and to reveal the relevant causes and patterns. Taking the Yongding River as a study case, we present the influences of soil and water conservation measures on variations in runoff and sediment load at the basin scale. Besides, this study also explores the dynamic relationship between reservoir operation and variations in basin sediment transport and reveals the influences of human activities (soil and water conservation measures and reservoir operation) and climate change on the variations in runoff and sediment load in the Yongding River basin.

STUDY AREA AND DATA COLLECTION
The Yongding River is one of the seven major river systems in northern China. This river is in the transition zone from the coastal plains of north China to the mid-temperate arid Inner Mongolia Plateau. The river water flows through the three provinces (Inner Mongolia, Shanxi, and Hebei) and two municipalities (Beijing and Tianjin), with a total length of 747 km, an average gradient of 2.85‰, and total basin area of 47,000 km 2 . The river basin covers a mountainous area of 45,063 km 2 (95.8% of the total basin area) and a plain area of 1,953 km 2 (4.2% of the total basin area). The regional climate is characterized by short summers and long winters, mean annual temperatures of 6-  Table 1.

Mann-Kendall test
The Mann-Kendall (M-K) test is a nonparametric test method recommended by the World Meteorological Organization for trend analysis of time series (Yue & Wang ).
In this study, the M-K test was used to detect abrupt changes and analyze the variation trend based on the data series of hydrological processes.

Trend analysis
It was assumed that for an independent and identically distributed time series X t (n) (n ¼ 1, 2 …, N), the statistical variable S is defined as follows: ( 2) where: N is the length of the time series data; X t (j) and X t (k) are the observed values at time j and k, respectively.

The statistical variance in S is
When N > 10, the statistical variable Z with a standard normal distribution is described as follows: If Z > 0, the time series exhibits an uptrend; otherwise, it exhibits a downtrend. When the absolute value of Z is greater than or equal to 1.28, 1.64, and 2.32, it indicates that there is an uptrend or downtrend of this data series at 90, 95, and 99% confidence levels respectively; if the absolute value of Z is less than 1.28, 1.64, and 2.32, it means that the significance test of the corresponding confidence has not been passed, which means that the corresponding upward and downward trends are not obvious.

Analysis of turning points
A new time series needs to be constructed when using the M-K algorithm to calculate the turning point of the time series.
, and the statistic is defined on this S k series.
where the mean value E(S k ) ¼ k(k À 1)=4, and the variance the time series has a significant changing trend at the 95% significance level. If |UF k | > U 0.01 , it indicates that the time series has a significant changing trend at the 99% significance level.
The above steps are repeated for the reverse time series of X t : X t (N), X t (N À 1) . . . :, X t (1) based on the numerical con- original time series is arranged in the reverse order, and then the UB k is calculated according to the above method. The principle of R/S analysis is described as follows: for a certain time series X t (i) (i ¼ 1, 2 …), the calculated mean value series and cumulative deviation are defined as follows: where: y(n) is the arithmetic mean of the daily observation sequence of n periods, and X t (i) is the observation value at where: f(i, n) is the cumulative deviation of n periods, and X t (j) is the observation value at the j-th time.
Thus, the range and standard deviation are calculated as follows: where: max Generally, the following relationship exists: where c is a constant, H is a Hurst index, and 0 < H < 1.
Taking the logarithm of this expression y ¼ ax þ b as follows: The equation can be rewritten as the following general linear equation: values can be obtained through a linear least-squares fitting.
when H > 0:5, this series has the characteristics of persistence, and the future changing trend of the series is the same as that in the past; when H < 0:5, the series has antipersistence, and the future trend of the series is opposite to its past trend; and when H ¼ 0:5, the time series is random and does not have any trend.

Estimation of sediment retention in water conservancy projects
The efficiency of sediment retention is commonly estimated using the Brune curve (Brune ). Based on the Brune curve, the sediment retention efficiency calculation method can be generalized as follows (Eizel-Din et al. ): where λ is the sediment retention efficiency of the reservoir (%), which represents the proportion of sediment deposited in the reservoir to the sediment that entered the reservoir; V represents the reservoir capacity (m 3 ), and W represents the runoff into the reservoir (m 3 ).

Estimation of sediment reduction by soil and water conservation measures
When the measures of soil and water conservation were Yongding River basin was calculated using the following formula: where ΔW w and ΔW s are the water retention capacity (m 3 ) and sediment reduction (

Trends of runoff and sediment loads
The M-K method was used to analyze the variation pat-   However, the trends of runoff and sediment inputs into the Guanting Reservoir from these two rivers are not completely consistent. Therefore, it is necessary to separately analyze the trends of runoff and sediment load in these       Table 4. During the statistical period, the average annual precipitation was 411 mm. It can be seen that there were precipitation changes in different   Table 5. According to Equation (16) Therefore, the cause for the drastic reduction in the current sediment input into the Guanting Reservoir is not closely related to the upstream reservoir operation.
The sediment load of the Yongding River has experienced a considerable reduction since the 1980s. In particular, the sediment concentration had also decreased drastically, which indicated that the erosion-caused sediment yield of the basin decreased. This result was related to the implementation of soil and water conservation measures in the basin.

CONCLUSIONS
(1) The annual runoff, sediment yield, and sediment concentration in the Yongding River basin declined in the 1960s and showed a significant decrease at the end of the 20th century. The runoff and sediment load after 2000 were 90% less than those in the 1960s, and the decrease in sediment load was greater than that in the runoff. The sediment concentration in the river considerably decreased. The water input, sediment input, and mean sediment concentration have remained stable since 2010.