1 Introduction
Water plays an essential role in the rock cycle, especially in sediment transport. Furthermore, runoff and sediment transport are the results of interactions of various natural and human factors and the superposition of their effects (Li et al., 2017; Gu et al., 2019; Zhao et al., 2014). The Yellow River is known for its huge sediment load. However, the large amount of sediment carried by the river is continuously deposited along its riverbed, which often causes devastating floods. This leads to significant hazards to the people and the country (Guo et al., 2020a; Bai et al., 2019). Although this issue usually affects the midstream and downstream regions, the sediment contents in the water in the upstream regions are closely related to those in the midstream and downstream regions. Understanding upstream sediment content variation is the basis for analyzing those midstream and downstream. Furthermore, the source region of the Yellow River is the most important headwater region in the Yellow River Basin in terms of the amount of water contributed. The runoff variation in the source region critically affects and governs the variation in the available water resources in the entire river basin (Lu et al., 2020). Runoff and sediment discharge are the main output variables of river basins. They must show certain correlations during their evolution (Guo et al., 2020b; Varvani et al., 2019; Han et al., 2019; Tanzil et al., 2019). Because the source region plays a critical role in the Yellow River Basin, the variation in the runoff and sediment discharge in the region because of environmental changes significantly affect both the socioeconomic development (Zhang et al., 2008) and ecosystem maintenance (Yu et al., 2012) in the basin. Hence, to realize reasonable control of the runoff and sediment discharge in the Yellow River Basin and to understand the causes and mechanisms of runoff and sediment discharge variation, it is necessary to investigate the runoff-sediment discharge relationship and its detailed evolution in the source region.
At present, existing time-series research on runoff-sediment discharge relationships and their evolution characteristics are mostly on annual, seasonal, monthly, or daily scales (Zhang et al., 2006; Gao et al., 2016; Cui and Li., 2011; Jiang et al., 2017). Runoff and sediment discharge often show certain seasonal or periodic variation and such periodicity is usually multi-temporal(Zhang et al., 2019a; Ren et al., 2015; Prasad et al., 2019). This means that the runoff and sediment discharge variation in a certain time series does not follow certain fixed and simple patterns (such as those with constant periods). However, the variation includes different periodic changes and local fluctuations. This is one of the important evolution characteristics of complex non-linear systems. Runoff and sediment discharge in rivers show complex relationships not only for raw long-term time series. Complex fluctuation characteristics and relationships are also noted for time series on different time scales. Therefore, studies on runoff and sediment discharge should not only focus on the macroscopic research on raw time series but also the detailed multi-temporal evolution characteristics of the series. Only in this manner, a comprehensive and in-depth understanding of the relationships between runoff and sediment discharge is possible. In recent years, multi-temporal analysis methods, such as wavelet analysis methods (Kuang et al., 2014; Nourani et al., 2019) and empirical mode decomposition (EMD) (Zhang et al., 2014), have been rapidly developed and combined with traditional hydrological methods to study the intrinsic relationships between hydrological variables and their evolution characteristics. These have become important approaches in hydrological research. However, pseudo-harmonics are found during decomposition using wavelet analysis methods, whereas EMD causes issues, such as mode mixing and end-point effects. Hence, the analysis results show certain deviations. Torres et al. (Torres et al., 2011; Colominas et al., 2014) proposed the Complete Ensemble Empirical Mode Decomposition with adaptive noise, which is an improved EMD algorithm. It can reasonably resolve the mode mixing problem of the original EMD and it is a relatively mature time-frequency analysis method.
Furthermore, runoff and sediment systems are highly complex, and they are influenced by various factors, such that the time series or multi-temporal component series of runoff and sediment discharge may be non-stationary (Chang et al., 2017). Nevertheless, previous studies on the time series of hydrological variables have usually assumed that the time series are stationary, and they have thereby constructed steady-state models. This may lead to pseudo-regression and certain errors in the analysis results. In economics, to avoid pseudo-regression during the construction of series models, cointegration theory has been proposed (Gu et al., 2017). Normally, the Engle–Granger two-step method (Engle and Granger., 1987) is adopted to determine whether long-term stable relationships exist. Runoff and sediment discharge do not only show long-term equilibrium relationships in their time series, but they also have short-term fluctuating relationships at different time scales. Unfortunately, most of the existing cointegration theory-based research on hydrological variables have investigated the entire time series (Zhang et al., 2013; Bello et al., 2018). Only a few studies have considered short-term fluctuating relationships with the help of multi-temporal analysis methods. Moreover, because of the effects of various factors, such as environmental and climate changes and human activities (Hu et al., 2019; Zhang et al., 2019b), structural breaks may be present for runoff and sediment discharge. This leads to variation in their relationships in raw time series or multi-temporal component series. Hence, it is necessary to combine the cointegration theory and multi-temporal analysis methods to analyze multi-temporal runoff-sediment discharge correlations and the structural breaks under the changing environment. The multi-temporal component model based on variable structure cointegration can be subsequently constructed to better reflect the runoff-sediment discharge relationship. This novel approach is herein adopted for the first time in the field.
This study first employed CEEMDAN to decompose the runoff and sediment discharge series of the source region of the Yellow River. Next, double cumulative curves were used to analyze the evolution characteristics and structural breaks of the multi-temporal runoff-sediment discharge correlations. Furthermore, the cointegration theory was used to analyze the runoff-sediment discharge relationships of different time series. For the time series with structural breaks, corresponding variable structure cointegration models were established. Their results were compared to examine their accuracy. Reasonable models were then selected to simulate and predict runoff.