- 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.
- 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