3.1 Multi-temporal analysis
CEEMDAN was adopted for the multi-temporal decomposition of the annual runoff and sediment discharge series measured at the Tangnaihai station during 1960–2013. Finally, five layers were obtained. There are four were IMF components and one was a trend term (residual (RES) component). The decomposition results are shown in Figure 3.
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Figure 3 reveals that the annual runoff and sediment discharge series measured at Tangnaihai station in the source region of the Yellow River showed complex multi-period variations and fluctuations. Although they have different amplitude fluctuations, the runoff and sediment discharge components of the same frequency vary simultaneously. This indicates that the runoff and sediment discharge in the source region are reasonably correlated with each other on both the macroscopic and microscopic scales. The IMF1 component shows the greatest amplitude, the shortest period, and the highest frequency. The RES component reflects the macroscopic variations in the runoff and sediment discharge and it demonstrates that both variables decline gradually with time.
For all the decomposition series, their periods and amplitude variation were analyzed. The results are summarized in Table 1.
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According to Table 1, the quasi-periods of the IMF runoff components are the same as those of the corresponding IMF sediment discharge components. The IMF1 components for both the runoff and sediment discharge have high frequencies and short quasi-periods. The IMF2 components have medium frequencies and quasi-periods. Furthermore, IMF3 and IMF4 are low-frequency components and they have medium/long and long periods, respectively. Overall, the minimum, maximum, and average amplitudes of the IMF components decreased progressively. As the decomposition scale increased, the amplitude fluctuations of the components declined and the periods lengthened. Lastly, the annual runoff and sediment discharge declined gradually macroscopically.