4.1. Change Process of Annual Streamflow
presents the annual runoff change processes of the four stations in the upper reaches of the Yellow River, namely Tangnaihai, Lanzhou, Xiaheyan and Shizuishan. It can be seen that the annual runoff change processes of Lanzhou, Shizuishan and Toudaoguai (Figure 3
) are consistent. The change process of Tangnaihai is different from those of the other three stations. The annual streamflow from Tangnaihai to Lanzhou increases, while the annual streamflow from Lanzhou to Xiaheyan, Shizuishan and Toudaoguai decreases.
presents the annual runoff variation trends of Toudaoguai, Longmen and Tongguan in the middle reaches of the Yellow River. It can be seen that the annual runoff change of Toudaoguai is consistent with that of Longmen. The annual runoff changes at Tongguan and Huayuankou (Figure 4
) are consistent. The annual flow from Toudaoguai to Longmen, Tongguan and Huayuankou increases along the way.
presents the annual runoff variation trends of Huayuankou, Gaocun and Lijin hydrological stations. In general, the annual runoff changes of the three stations are consistent. Especially before 1970 (except 1960), the runoff changes of the three stations were nearly identical. After 1970, annual streamflow from Huayuankou to Gaocun and Lijin decreased along the way.
4.2. Trend Change and Abrupt Change Points
The trend evaluation and level tests were carried out by using the linear regression method, the Mann Kendall rank method and the Spearman rank correlation method under a confidence level of 0.05. The runoff decrease trend of Tangnaihai was not significant. The significance of annual runoff decrease trend of Lanzhou station had mixed results. One result was a significant trend by the linear regression test (Figure 2
) and the Spearman’s rank test. Another result was not significant by the Mann-Kendall rank method. For the remaining 8 stations (Xiaheyan, Shizuishan, Toudaoguai, Longmen, Tongguan, Huayuankou, Gaocun and Lijin), the test results of three methods are a significantly decreasing trend. In identifying the abrupt change point, the T sliding method, the Lee-Heghinian method and the Orderly clustering method were used. The results of three methods are consistent for each station. The abrupt change point of Tangnaihai is in 1989, and for the remaining 9 stations, the abrupt change points are all in 1985 (Table 2
The average and the variation coefficient (CV) are the two most important parameters for hydrological design of water conservancy projects, which affect the scale and safety of water conservancy projects. Moreover, CV is also the main index reflecting the interannual change of river runoff. At the abrupt change point (excluding variation points), the whole time series are divided into two subsequences. Then the average and CV of the whole sequence, before variation and after variation sequences are calculated. The results are shown in Table 3
indicating that the mean annual runoff before the variation sequence in each station is largest. The average after the variation sequence in each station is smallest. From the upstream to the middle and the lower reaches, the change of the average is increasingly large. Compared with the average of the subsequence before variation, the streamflow of Tangnaihai, Toudaoguai and Lijin decreases to 86%, 66% and 38%, respectively. In general, the order of CV is the whole sequence, the sequence before variation and the subsequence after variation. From the upper to the middle and the lower reaches, the CV of the sequences (except Lanzhou) are larger and larger.
Period is an important component of runoff compositions. Wavelet transform was used to analyze the periods of flow along the Yellow River. The streamflows of Tangnanhai, Toudaoguai and Lijin were selected to carry out the analysis in detail.
(1) The real part of the wavelet coefficient
The real part of the wavelet coefficients can reflect runoff series periodic change at different time scales and the distribution in the time domain, and then can judge the future trend of flow series at different time scales. When the real part of the wavelet coefficient is positive, it shows that runoff is in a high flow period. If the real part of the wavelet coefficient is negative, it denotes that runoff is in a low flow period.
From the real part coefficients contour map of Tangnaihai (Figure 5
), it can be clearly seen that there are 3–6, 6–24 and 25–37 years periodical characters within a 40-year scale. The scales of 25–37 years were very stable in the whole time domain. There were 3 high water and 2 low water shocks. On 6–24 and 3–6-year scales, their oscillation frequencies are very high and complicated. The scale of 3–6 years occurred during 1975–1998.
For Toudaoguai station (Figure 6
), there are three time scale changes. Among them, the scales of 20–40 and 5–23 years are stable in the whole time domain. The former experienced 3 high water and 2 low water shocks, and the later underwent 4 high water and 5 low water shocks. The scale of 2–6 years is not stable and occurred during 1971–2002.
For Lijin station (Figure 7
), we can clearly see the multi-time scale characteristics of flow evolution. Among them, the scale of 25–40 years was very stable. There were 3 high water and 2 low water oscillation periods in the whole time domain. The scale of 12–24 years was not stable. Different high-low water oscillations occurred in different time domains. The scale of 3–10 years occurred during 1964–2004. There were more cycle oscillations.
(2) Modulus square of wavelet coefficients
The modulus square of the wavelet coefficients represents the energy spectrum. It can reflect the energy variability in time scale. The higher the energy is, the stronger the periodic oscillation is.
In the wavelet modulus square contour map of Tangnaihai (Figure 8
), the scale of 26–35 years has the strongest energy and shows the most significant period. The energy of the scale of 19–22 years is stronger, which occurred from 1970 to 2002. The energy of the scale of 9-21 years is weak, which is mainly concentrated in the two periods of 1956–1970 and 2004–2016. The energy of the scale of 2–7 years is weaker, which occurred mainly in the period 1968–2004.
For Toudaoguai (Figure 9
), the energy of the scale of 25–35 years is the strongest and the period is the most significant, which occurred in the whole time domain. However, the energy of the scales of 14–19 and 3–6 years is weak, and the periodic change is localized. The scale of 14–19 years is mainly focused from 1956 to 1976 and from 1995 to 2016. The scale of 3–6 years was mainly concentrated in the period from 1978 to 1995.
For Lijin (Figure 10
), the energy of the scale of 26–36 years was the strongest and the periods are the most significant, which occurred in the whole time domain. In the scale of 14–22 years, the energy is stronger and the period is significant, which occurred for the whole period. On the scale 6–10 years, the energy is weak and the period is not significant, which is mainly concentrated in the periods from 1956 to 1973 and 2002 to 2016.
(3) Wavelet variance
The wavelet square can reflect the distribution of fluctuation energy with scale in flow time series. It can be used to determine the main period of flow evolution.
As Figure 11
, Figure 12
and Figure 13
show, the corresponding period of the maximum values of each station is 30 year, which indicates the oscillation in this period are very strong, and are the first main period of annual flow evolution in the Yellow River basin. The second main periods of Lanzhou, Xiaheyan, Toudaoguai, Longmen and Tongguan are 15.33 years. The second main periods of Tangnaihai, Huayuankou, Gaocun and Lijin are 20.67 years. The second main period of Shizuishan is 6 years. The third main periods of Tangnaihai, Shizuishan and Lijin are 15.33 years, and the third main periods of Xiaheyan, Toudaoguai and Longmen are 6 years. The third main periods of Huayuakou and Gaocun are 16 years. The third main period of Lanzhou is 20.67 years. The third main period of Tongguan is 8 years. The fourth main periods of Huayuankou, Gaocun and Lijn are 8 years. The fourth main periods of Xiaheyan, Toudaoguai and Tongguan are 20.67 years. The fourth main period of Tangnaihai is 5.33 years. The fourth main period of Lanzhou is 6.0 years. The fourth main period of Shizuishan is 10 years. The fourth main period of Longmen is 3.33 years.