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.