**3.2 Non-stationarity of extreme rainfall with different thresholds**

Extreme rainfall events increased with intensified urbanization in the MLRYRB. Previous studies have shown that non-stationary characteristics were found in various


**Table 1.**

*Silhouette coefficient (SC) information for the K-means clustering analysis.*

**Figure 2.**

*Five sub-regions with similar dry and wet characteristics in the MLRYRB.*

extreme rainfall indices in the MLRYRB, indicating that the assumption of the stability of extreme rainfall would be no longer applicable [10, 40]. Some studies have shown that the extreme rainfall models under different thresholds will generate different non-stationary characteristics [14, 41]. The non-stationarity of rainfall will also affect the analysis of the runoff series [42]. So, the non-stationary detection of extreme rainfall events under different thresholds becomes particularly important.

**Figure 3** shows the distributions of the breakpoints of the extreme rainfall events under different thresholds for the five sub-regions, respectively. For Sub-region I, the breakpoints were mainly distributed in 1978, 1980, and 1994. When the threshold changed from 40 to 55 mm, the breakpoints were in 1983, 1986, and 1989. When the threshold was greater than 52 mm, the breakpoint began to appear in 2014, and disappeared when the threshold reached 74 mm. When the threshold was greater than 75 mm, the non-stationarity of extreme rainfall in Sub-region I disappeared. Compared with the whole MLRYRB, changing years in Sub-region I were significantly different. The breakpoints in Sub-region I were sensitive within the threshold of 40–60 mm, while the extreme rainfall events exceeding 75 mm were stable. The situation of Sub-region II was almost consistent with that of the whole MLRYRB, and the difference was that the breakpoints were not continuous with the change of the threshold in 1968. At the same time, when the threshold was less than 50 mm, the breakpoints between 1980 and 2000 were messy. When the threshold was greater than 75 mm, the breakpoints from 1960 to 1980 were still chaotic, which illustrated that the extreme rainfall events fluctuated between 1960 and 1980 in Sub-region II. The breakpoints in Sub-region III changed steadily along with the threshold, and the breakpoints were concentrated around 2000, 1993, and 1970, which was consistent with the overall changing trend. The breakpoints in Sub-region IV varied chaotically along with the threshold, and the breakpoints were relatively stable around 1968, 1970, and 2013; however, they were chaotic between 1970 and 2000, showing that the extreme rainfall events in Sub-region IV fluctuated greatly. The breakpoints of the extreme rainfall sequence in Sub-region V fluctuated relatively steadily along with the threshold, which were concentrated around 2012, 1992, and 1968.

**Figure 3.** *Year distribution of breakpoints under different thresholds in the five sub-regions of the MLRYRB.*

*Threshold Recognition Based on Non-Stationarity of Extreme Rainfall in the Middle… DOI: http://dx.doi.org/10.5772/intechopen.109866*

When the threshold was greater than 70 mm, the breakpoint in 1992 disappeared, and when the threshold was greater than 85 mm, the breakpoint in 1968 disappeared. These results showed that the extreme rainfall events with the rainfall over 85 mm were stable. Overall, breakpoints varied widely between subregions. The selection of extreme rainfall thresholds in the five sub-regions of the MLRYRB would have certain impacts on the nonstationarity of extreme rainfall series, and the non-stationarity of extreme rainfall events corresponding to different thresholds would be quite different. This will affect the judgment of environmental factors of hydrological sequence and extreme rainfall.

#### **3.3 Fitting results with different thresholds**

In **Figure 4**, it reveals the fitted GPD of the extreme rainfall sequences selected by different thresholds in the five sub-regions of the MLRYRB. Since the p-values of the KS-test fitted by the GEV were all less than 0.05, they are not shown in this figure. For Sub-region I, when the threshold was greater than 40 mm, the p-value increased significantly, and then decreased significantly when the threshold was greater than 50-60 mm. When the threshold was greater than 60 mm, the p-value gradually increased. For Subregion II, the fitting results were relatively good when the threshold was between 30 and 40 mm, the fitting results were better after the threshold was greater than 60 mm, and the fitting results fluctuated greatly when the threshold was between 40 and 60 mm. For Subregion III, when the threshold was within 40–50 mm and greater than 70 mm, the fitting results were better. However, when the threshold was between 50 and 70 mm, the fitting results had larger deviations. For Sub-region IV, when the threshold was between 40 and 65 mm, the fitting results were good but fluctuated greatly. After the threshold was greater than 60 mm, the fitting results were not satisfactory. For Sub-region V, when the threshold was within 60–70 mm, the fitting results were the best; however, the fitting results had a large fluctuation in the whole interval of 0–100 mm.

It is shown that variation ranges of different design return periods in the five subregions of the MLRYRB in **Figure 5**. For different design return periods, the trends in these five sub-regions were consistent. When the return period increased from 5 to 100 years, the corresponding extreme rainfall values showed increasing trends. When

**Figure 4.** *P-value of KS-test of the GPD fitting with different thresholds in the five sub-regions of the MLRYRB.*

#### **Figure 5.**

*Variation ranges of different design return periods in the five sub-regions of the MLRYRB.*

the threshold was less than 20 mm, different levels of extreme rainfall could not be well differentiated. The rainfall of the 5-year return period in different sub-regions had similar rainfall. The median rainfall of the 10- and 20-year return periods in Subregions I, II, III, and IV all had similar performances between 40 and 60 mm, while the threshold in Sub-region V was between 50 and 60 mm. The threshold in Subregion V was slightly higher than those in the other four sub-regions, which might be related to the geographical location of Sub-region V being closer to the coast. For the median rainfall of the 50-year and 100-year return period, Sub-regions I, II, and IV performed similarly with the threshold between 60 and 80 mm. The threshold was lower than 60 mm in Sub-region III and greater than 80 mm in Sub-region V. In terms of uncertainty for different design return periods, Sub-regions II and III behaved similarly, while Sub-region V had the highest uncertainty and Sub-region IV had the lowest uncertainty.

#### **3.4 Correlations between large-scale climatic patterns and extreme rainfall**

Large-scale climatic patterns can potentially affect the non-stationarity of extreme hydrological and meteorological events [43], so correlation analysis of large-scale climatic patterns and extreme rainfall events can help to analyze the causes of extreme rainfall non-stationarity. This study used the CWT to analyze the correlation of the maximum daily rainfall of the year (RX1day) with ENSO and WPSH in the MLRYRB and its five sub-regions (**Figures 6** and **7**), as well as their resonance frequency and phase shift in the time-frequency domain.

**Figure 6** illustrates the cross wavelet spectrum of RX1day and ENSO for each subregion. In Sub-region I, there was a periodic signal of 3–5 years during 1968–1976, a periodic signal of 2–4 years during 1994–1996, and a periodic signal of 5–8 years as well as a periodic signal of 9–10 years during 1994–2001. In Sub-region II, RX1day and ENSO showed a significant negative correlation. There was a periodical signal of 2–3 years during 1964—1971, a periodical signal of about 4 years during 1996–2000, and a signal of about 12 years during 2000–2006. In Sub-region III, there was only a

*Threshold Recognition Based on Non-Stationarity of Extreme Rainfall in the Middle… DOI: http://dx.doi.org/10.5772/intechopen.109866*

#### **Figure 6.**

*Cross wavelet power spectra of RX1day and ENSO in the five sub-regions of the MLRYRB. Note: the noise is shown with a thick outline for the 95% significance confidence level, and the relative phase relationship is shown with the arrows. The area enclosed by the black cone outline is considered significant. The phase angle represents the relationship between the two variables. When the phase angle points to right, it indicates a positive correlation between the two variables. When the phase angle points to left, it represents two variables have a negative correlation.*

#### **Figure 7.**

*Cross wavelet power spectra of RX1day and WPSH in the five sub-regions of the MLRYRB.*

periodic signal of 2–7 years during 1982–1996. In Sub-region IV, there were periodic signals of 3–5 years, 2–3 years, and 4–6 years distributed during 1980–1990, 1996– 1998, and 1997–2000, respectively. Except for some short-period signals of less than 5 years in Sub-region V, the long-period signals of 13–15 years from 1968 to 1990 was noticeable. In general, RX1day in the MLRYRB had a significant positive correlation with ENSO. RX1day in different sub-regions had relatively similar responses to the

changes in ENSO. However, in Sub-region II, there was a significant negative correlation between RX1day and ENSO, which was inconsistent with those in other subregions. This indicates that the impacts of ENSO on the extreme rainfall of the MLRYRB needs further study.

The cross wavelet spectrums of RX1day and WPSH for each sub-region are displayed in **Figure 7**. In Sub-region I, there were periodic signals of 3–4 years, 2–4 years, and 6–8 years during 1970–1984, 1994–2004, and 1994–2016, respectively. In Sub-region II, there was a negatively correlated periodic signal of 7–8 years from 1976 to 1981 and a positively correlated periodic signal of 2–4 years during 1990–2006. In Sub-region III, there was only one periodic signal during 1978–2003 with 1–5 years. In Sub-region IV, there were two positively correlated periodic signals of 1–5 years during 1978-1988 and 1994-2004, and there was also a negatively correlated periodic signal of 6–10 years during 1976–1990. In Sub-region V, there were periodic signals of 2–4 years, 3–5 years, and 1–2 years during 1979–1989, 1996–2004, and 2002–2008, respectively. Most of the signals showed an obvious positive correlation, but there were also some negative correlation signals. Most of these negative correlation signals appeared before 1990. Moreover, during the same time period, different signal cycles showed the opposite correlations, indicating that WPSH had different effects on RX1day at different times.
