4 Conclusions
This paper combined CEEMDAN, double cumulative curves, and the
cointegration theory to construct composite models that reflected the
overall and multi-temporal relationships between the runoff and sediment
discharge in the source region of the Yellow River. The models were then
adopted for runoff simulation to evaluate their accuracy. The main
conclusions were as follows:
(1) The raw series of both the runoff and sediment discharge of the
source region of the Yellow River could be decomposed into five layers,
including layers of four IMF components and one RES component.
Significant runoff-sediment discharge correlations were noted at
different time scales. The multi-temporal components of the same
frequency varied simultaneously. The IMF components of the same variable
had the same quasi-periods. Furthermore, the RES component revealed that
the runoff and sediment discharge declined simultaneously with time.
(2) The multi-temporal runoff-sediment discharge double cumulative
curves showed a high goodness of fit, and the multi-temporal components
were significantly positively correlated. More specifically, those of
the IMF1 and IMF2 components demonstrated higher goodness of fit,
whereas those of IMF3 and IMF4 showed distinct points of structural
breaks. Therefore, for relatively complex raw series, high-frequency
components could be employed to explore runoff-sediment discharge
relationships and the characteristics of their detailed evolution. Thus,
more attention could be paid to the relevant short- and/or medium-term
observations. Furthermore, when attempts were made to obtain information
on structural breaks, detailed evolution should be examined more
carefully. When the runoff-sediment discharge relationships changed and
the information (for example, years) on structural breaks had to be
determined, low-frequency components could be employed.
(3) As demonstrated by the raw series, the runoff was reasonably
correlated with the sediment discharge in the source region. However,
their relationships at different time scales varied slightly. The
relationship changes noted for the raw series were caused jointly by
those at different time scales. Hence, the weak runoff-sediment
discharge relationships on the medium/long and long-time scales would
affect the relationship between the raw runoff and sediment discharge
series.
(4) The runoff during the research period was simulated separately using
the original runoff-sediment discharge cointegration model (based on the
raw series), the composite model 1 (based on the multi-temporal
components), and the composite model 2 (based on the multi-temporal
components with the structural breaks). Their average relative errors
were 11.43%, 10.76%, and 7.82%, respectively. The composite model 2
considered both the local variation characteristics of the
multi-temporal components, as well as the structural breaks, and it
showed higher simulation accuracy and provided smaller relative errors.
It could more accurately reflect the long-term equilibrium and
short-term fluctuating relationships between the runoff and sediment
discharge in the source region of the Yellow River.