1. Establishing ECM
According to the ECM method, The ECM-OTS for x0 ,z0 and y0 and the ECM-CEEMDAN model for xi , zi and yi (i =1, 2, 3, 4, 5) is as follows:
(17)
(0.061223) (0.004417) (0.149456) (3.221133)
(18)
(0.045599) (0.003267) (0.164667) (2.288407)
(19)
(0.075293) (0.004075) (0.143114) (1.268256)
(20)
(0.073105) (0.010246) (0.040804) (0.482288)
(21)
(0.013844) (0.001382) (0.025256) (0.061591)
(22)
(0.061745) (0.005481) (0.023369) (0.051960)
In the formula, ecmt (-1) represents the error correction term, and the coefficient beforeecmt (-1) is the short-period adjustment coefficient, and the coefficient before the difference terms of each variable represent the short-period dynamic change of the model.
It can be seen that the rainfall, runoff and sediment in the source area of the Yellow River show a long-term equilibrium relationship. The component time series also has a long-term equilibrium relationship at different time scales, and the error correction term coefficients of all equations are all negative, which is consistent with the reverse correction mechanism. It can be seen from equation (17) that runoff is not only affected by rainfall and sediment, but also by the deviation of runoff from equilibrium level in the previous year. The coefficients of Δx 0 and Δy 0 are 0.23665 and 0.03767 respectively, which indicates that the short-term influence of rainfall and sediment on runoff in the source area of the Yellow River is different, and the influence of rainfall is stronger than that of sediment. The coefficient before ecmt (-1) is -0.70057, which indicates that the deviation of runoff from equilibrium in this year will be adjusted by 70.06% in the next year.
  1. Annual Runoff Forecast
The ECM-OTS and the ECM-CEEMDAN models are established by using the measured data series of rainfall, runoff, and sediment from 1966 to 2005, and the forecast test is conducted with the measured data series from 2006 to 2013. Fig. 6 shows the fitting between the measured value and the fitted value of the two models. Fig. 7 shows the relative error between the fitting value and the measured value of the two models. Table 5 shows the forecasted values and relative errors of the two models during the forecast period.
Fig. 6 Fitting between the fitted value and measured value of two models
It can be seen from Fig. 6 that both models can well describe the dynamic equilibrium relationship between rainfall, runoff and sediment in the source area of the Yellow River. Moreover, the accuracy of runoff fitting value of the ECM-CEEMDAN model is better than that of ECM-OTS.
Fig. 7 Relative error between the fitted value and the measured value of the two models
It can be seen from Fig. 7 that in the year that the relative error is greater than 20% from 1967 to 2005, the ECM-CEEMDAN model has only one 28.11% in 2002, but ECM-OTS model has two years, 20.83% in 1997 and 32.17% in 2002. The average relative error of the ECM-CEEMDAN model is 6.21%, which is 1.42% lower than the 7.63% of the ECM-OTS model. It can be seen that the ECM-CEEMDAN model has better fitting accuracy.
According to the Standard for Hydrological Information and Hydrological Forecasting (GB / T 22482-2008) of China, 20% of the measured value is taken as the allowable error for runoff forecasting. When the error is less than the allowable error, it is available. The percent of qualified forecast times and total forecast times is the qualified rate of forcast. Meanwhile, the degree of agreement between the runoff forecasting process and the measured process can be evaluated by the deterministic coefficient, which is calculated as follows:
(23)
In the formula, is the deterministic coefficient, is the measured value, is the forecasted value, is the mean of the measured values, and is the length of the sequence.
The accuracy of runoff forecast is divided into three grades according to the qualification rate or the deterministic coefficient, as shown in Table 4.
Table 4 Runoff forecast accuracy class table