*5.1. Annual, Seasonal and Monthly Evolution of Runoff and Climatic Factors on Main Scales Analyzed by MRA*

#### 5.1.1. Monthly Variation

The main aim of this section is to visualize the distribution of energy across scales (or resolution levels) of the hydrogeological time series. The MRA was performed on monthly data, and the results for the first 10 MRA levels are shown in Figure 3. Overall, the energy is distributed variably across levels in the hydrogeological time series and has significant periodic characteristics in different time scales, especially at a large scale. Runoff and rainfall show high energy oscillation at all levels, but they fluctuate with time, which indicates that the high-energy differences in monthly runoff and rainfall explain most of the differences. The energy vibrations at all time scales have a high consistency, and the vibration consistency is significant at a large scale, which demonstrates that runoff is significantly affected by rainfall. Evaporation shows high-energy vibrations at all time scales. Evaporation oscillation that gradually diminishes at 16-, 32- and 64-month time scales, however, is consistent with runoff and rainfall at 128- and 256-month time scales. Several obvious abrupt changes are detected from temperature in the vibration characteristics of 1 month to 4 months with the mutation years of 1990 (70-month) and 2000 (200-month) according to energy distribution. The oscillation characteristics of temperature are consistent with those of runoff and rainfall at time scales of 16, 64, 128 and 256 months. After 128-month time scales, the oscillation characteristics of runoff, rainfall, evaporation and temperature all appear to have the same vibration characteristics at 10–20-year time scales.

**Figure 3.** Multi-time-scale variations of monthly rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**).

#### 5.1.2. Seasonal Variation

As shown in Figures 4–7, there are some synchronization characteristics on different time scales for the evolution characteristics of surface runoff and climate factors on the annual scale and four seasonal scales after scale segmentation by MRA. Except for the small difference in runoff in autumn and winter, the evolution characteristics of runoff at other scales are basically synchronous, especially in summer. The amplitude of rainfall oscillation at each time scale is larger than that of runoff, but a minimal difference exists between them in spring, autumn and winter. Evaporation is asynchronous with temperature for the variation characteristics at 1-year scale in spring and winter and at less than 4-year scale in summer but relatively synchronous with insignificantly different amplitudes at other scales. Over 16-year time scales, the time series of each factor has shown the consistent evolution characteristics in four seasons and the amplitude of each factor increases with the increase in time scale.

**Figure 4.** Multi-time-scale variations of rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**) in spring.

**Figure 5.** Multi-time-scale variations of rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**) in summer.

**Figure 6.** Multi-time-scale variations of rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**) in autumn.

**Figure 7.** Multi-time-scale variations of rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**) in winter.

## 5.1.3. Annual Variation

It has been found that rainfall and runoff show the same oscillation characteristics in different annual scales and the oscillation is obvious at 1–2- and 16–32-year time scales (Figure 8). Temperature and evaporation oscillate at 4–32-year sales. Runoff, rainfall, temperature and evaporation have the same oscillation characteristics at 4-, 8- and 32-year time scales. Runoff is mainly affected by rainfall, whereas evaporation is mainly affected by temperature. As a whole, it has been found that there is a strong effect of rainfall over runoff but a lesser effect of temperature and evaporation over runoff.

**Figure 8.** Multi-time-scale variations of annual rainfall (**a**), temperature (**b**), evaporation (**c**) and runoff (**d**).

#### *5.2. Multi-Scale Evolution of Runoff and Climatic Factors Analyzed by CWT*

As shown in Figure 9, the higher the spectral value (that is, the stronger the oscillation energy) is, the more significant the periodic oscillation passes the 0.05 confidence level. Except for the breakpoints at 8–16-month time scales in 1990 in Figure 9—Month Q, a main cycle always exists at 12-month time scales, which reflects the overall and significant periodic variation characteristics of monthly runoff. Several subcycles appear at approximately 36-month time scales (1990–2000) and 18–24-month time scales (1993–1997 and 2007–2012), which are related to the significant increase in rainfall in this period. The cycle at 4–6-month time scales (1984–2015) fluctuates in the time domain.

**Figure 9.** The continuous wavelet power spectra of monthly runoff (Month Q), rainfall (Month P), evaporation (Month E) and temperature (Month T) in the Yinjiang River watershed. The thick black contour designates the 5% significance level against red noise and the cone of influence (COI) where edge effects might distort the picture is shown as a lighter shade.

There are three subperiods with different significant levels of monthly rainfall in the time domain (Figure 9—Month P). The subperiod at 64-month time scales (1993–2008) indicates that the runoff has an important characteristic at 5-year time scales and a basically stable periodic variation. The subperiod at 24-month time scales (2007–2013) and at 18-month time scales (1993–1997) denotes that rainfall exerts a significant impact on runoff. Rainfall has similar fluctuation characteristics to runoff at 4–6 month time scales (1985–2015) and shows large fluctuations in the time domain.

There are three subcycles at 32-month time scales (1988–1992), 24-month time scales (2007–2013) and 6-month time scales (1984–2015) with different significant levels of monthly rainfall in the time domain (Figure 9—Month E). The fluctuation characteristics of evaporation are similar to those of runoff and rainfall at 6-month time scales. Obvious differences are also observed in the energy distribution characteristics in different periods, which indicates that rainfall and evaporation have obvious local characteristics of subperiodic variation consistent with those of runoff, but their energy is relatively weakened.

The monthly temperature is close to the monthly evaporation periodic bandwidth without interruption (Figure 9—Month T), which reflects the global and significant periodic variation characteristics of the monthly temperature and evaporation and indicates that the monthly temperature may affect the runoff mainly by changing the monthly evaporation. The monthly temperature has significant high-energy characteristics in the time domain around 1990 and 2000. The energy is strong at high frequencies below the scale of 1–8 months and weak at low frequencies after 8 months, but the periodic bandwidth increases with the scale.

It has also been found that a main period for runoff and climatic factors appears at 12-month time scales, which indicates that the periodic changes in hydrometeorology are mainly reflected in the annual scale. The discontinuous period and periodic bandwidth of climatic factors are basically consistent with the monthly runoff. The monthly runoff is consistent with the monthly rainfall, and the monthly temperature is consistent with the monthly evaporation. In addition, it has been found that the monthly runoff, rainfall and evaporation have the significant global fluctuation characteristics at high-frequency scales of below 8 months, whereas temperature exhibits only local fluctuation characteristics in 1990 and 2001 but significant impacts over 12-month time scales from 1995 to 2005. It can be concluded that rainfall is the main factor that affects runoff change in high-frequency regions and temperature and evaporation are the main factors in low-frequency regions.

As can be shown in Figures 10 and 11, runoff in spring has a main cycle at 4–6 years (1995–2000) and a subcycle at 1–2-year time scales (1990–1997). Runoff in summer is an insignificant period on the 4-year time scales (1990–2000). There are global insignificant characteristics for the main period of runoff in autumn at 1–2-year time scales (2006–2010) and the subperiod at 7-year time scales (1993–2005).

**Figure 10.** The continuous wavelet power spectra of seasonal runoff in the Yinjiang River watershed. The thick black contour designates the 5% significance level against red noise and the cone of influence (COI) where edge effects might distort the picture is shown as a lighter shade.

**Figure 11.** The continuous wavelet power spectra of seasonal rainfall, evaporation and temperature in Yinjiang River watershed. The thick black contour designates the 5% significance level against red noise and the cone of influence (COI) where edge effects might distort the picture is shown as a lighter shade.

The evolution characteristics of rainfall, temperature, evaporation and runoff vary greatly in spring, autumn and winter, but they are relatively stable in summer. They have great variations in high-frequency scales in spring and in low- and high-frequency scales in autumn, as well as periodicity in middle- and high-frequency scales in winter. Moreover, no obvious periodicity is detected in summer, whereas the significant periodic characteristics exist in other seasons.

From the annual scale (Figure 12), annual runoff has a main period at 6-year time scales (1995–2007), and the main period of rainfall is insignificant on this scale in the same period. However, the high-power spectrum of rainfall at this scale shows that it has an important impact on runoff change. No significant main period of evaporation is observed in the entire valid spectrum period, but significant periodic variations in temperature occur at 1–6-year time scales in 1997–2003. The power spectrum value of annual temperature at 6–8-year time scales remains high but insignificant. Over the 8-year time scales, the periodicity is significant, but the period bandwidth is narrowed.

**Figure 12.** The continuous wavelet power spectra of annual rainfall, evaporation and temperature in Yinjiang River watershed. The thick black contour designates the 5% significance level against red noise and the cone of influence (COI) where edge effects might distort the picture is shown as a lighter shade.
