It can be seen from Table 5 that for the ECM-OTS model, in the forecasted 8 years of 2006-2013, only the relative error of runoff in 2009 exceeded 20%, and its forecasted qualified rate was 87.5%, reaching the level A. Meanwhile, for the whole predicted years, the relative error of runoff forecast that is less than 10% are 5 years, accounting for 62.5%. While for the ECM-CEEMDAN model, only in 2009, its forecasted relative error is 18.81% which is close to 20%. The whole forecasted qualified rate was 100%. Although the ECM-CEEMDAN model has the same as the ECM-OTS model, with the runoff forecast relative error of 10% in 5 years, its relative error value tend to smaller on the whole, which indicates that the overall forecast accuracy of the ECM-CEEMDAN model is better. Moreover, the average relative error of the ECM-CEEMDAN model is 8.59%, which is 2.7% lower than 11.29% of the ECM-OTS model. This shows that the ECM-CEEMDAN model has the higher forecast accuracy than the ECM-OTS model.
Furthermore, from the deterministic coefficient of runoff forecast, the DC value of the ECM-OTS model is 0.842, which is the level B, while the DC value of the ECM-CEEMDAN model is 0.901, reaching the level A. This shows that the ECM-CEEMDAN model has the high degree of agreement between the runoff forecasting process and the measured process.
  1. Conclusion
  1. The CEEMDAN method can reveal the periodic characteristics of rainfall, runoff and sediment on the multi-time scales in the source area of the Yellow River. These three variables have a good correlation in the short and the medium periods. In addition, runoff and sediment show a better synchronization in the trend item, which reveals the law of periodic fluctuations of rainfall, runoff and sediment.
  2. With the co-integration theory and ECM, the ECM-OTS model and the ECM-CEEMDAN model are established. They can reveal the long-term equilibrium and short-term fluctuations of the original sequence and component sequence of rainfall, runoff and sediment in the source area of the Yellow River, and also can effectively forecast the runoff in this source area.
  3. Both the ECM-OTS model and the ECM-CEEMDAN model can well describe the dynamic equilibrium relationship between rainfall, runoff and sediment in the source area of the Yellow River. However, the forecast period error of the ECM-CEEMDAN model is less than 20%, and its forecast qualified rate can attains to 100%, and the accuracy reaches the level A. Compared with the ECM-OTS model, it has the better forecasting accuracy, which provides a new and more accurate runoff forecasting method.