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.