Open access peer-reviewed chapter

Threshold Recognition Based on Non-Stationarity of Extreme Rainfall in the Middle and Lower Reaches of the Yangtze River Basin

Written By

Yao Wang, Suning Liu, Zhaoqiang Zhou and Haiyun Shi

Submitted: 07 June 2022 Reviewed: 05 January 2023 Published: 01 February 2023

DOI: 10.5772/intechopen.109866

From the Edited Volume

Flood Risk in a Climate Change Context - Exploring Current and Emerging Drivers

Edited by Tiago Miguel Ferreira and Haiyun Shi

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Abstract

Analyzing the hydrological sequence from the non-stationary characteristics can better understand the responses of changes in extreme rainfall to climate change. Taking the plain area in the middle and lower reaches of the Yangtze River basin (MLRYRB) as the study area, this study adopted a set of extreme rainfall indices and used the Bernaola-Galvan Segmentation Algorithm (BGSA) method to test the non-stationarity of extreme rainfall events. The General Pareto Distribution (GPD) was used to fit extreme rainfall and was calculated to select the optimal threshold of extreme rainfall. In addition, the cross-wavelet technique was used to explore the correlations of extreme rainfall with El Niño-Southern Oscillation (ENSO) and Western Pacific Subtropical High (WPSH) events. The results showed that: (1) extreme rainfall under different thresholds had different non-stationary characteristics; (2) the GPD distribution could well fit the extreme rainfall in the MLRYRB, and 40–60 mm was considered as the suitable optimal threshold by comparing the uncertainty of the return period; and (3) ENSO and WPSH had significant periodic effects on extreme rainfall in the MLRYRB. These findings highlighted the significance of non-stationary assumptions in hydrological frequency analysis, which were of great importance for hydrological forecasting and water conservancy project management.

Keywords

  • yangtze river
  • non-stationarity
  • extreme rainfall
  • optimal threshold
  • ENSO
  • WPSH

1. Introduction

Extreme weather events can change local climate characteristics such as the mean values of temperature and precipitation, as well as their variabilities. As one of the most important climate variables, precipitation, has significant impacts on the hydrological processes and water resources management of a river basin [1]. In the context of climate change, the frequency of extreme weather events has increased, causing more serious natural water-related disasters such as floods and droughts [2, 3, 4, 5]. The increase in extreme rainfall always leads to floods, which have remarkable impacts on the local ecology, industry, and social economy. According to the statistics, more than 60% of floods are caused by extreme rainfall since the twentieth century [6, 7]. Therefore, more attention has been paid to studying the importance of extreme rainfall. However, extreme rainfall in different regions can vary greatly in spatial distribution, scope, frequency, duration, and severity [8, 9]. Moreover, the responses to extreme rainfall can vary greatly in different regions. Thus, it is of great importance to investigate the characteristics of extreme rainfall in a designated region.

The traditional hydrological frequency analysis of extreme rainfall and flooding is mainly based on stationary assumptions. However, several studies have shown that extreme rainfall is increasing in many parts of the world due to varying degrees of instability. Li et al. believed that the non-stationarity of the rainfall series could play an important role in the prediction and risk analysis of extreme rainfall [10]. Liu et al. observed that the non-stationarity of extreme rainfall in the Weihe River basin was sensitive to environmental changes [11]. Chen et al. studied the non-stationarity of the maximum daily rainfall in Taiwan and found that the high uncertainty of the non-stationarity of the maximum daily rainfall would lead to a difference in the predicted return period [12]. Beguería et al. established the General Pareto Distribution (GPD) model and found that extreme rainfall in Northwest Spain decreased significantly in winter but increased significantly in summer [13]. Sugahara et al. believed that, under non-stationary conditions, extreme rainfall in Sao Paulo, Brazil, showed a clear increasing trend [14]. Lee et al. found that the peak over threshold (POT)-GPD combined model would be more suitable for predicting future rainfall under non-stationary conditions [15]. Syafrina et al. proposed that the non-stationary extreme rainfall series is more suitable for Generalized Extreme Value Models (GEV) in Sabah [16]. Therefore, it has important significance to study the non-stationarity of extreme rainfall.

Currently, there is no clear definition of extreme rainfall. According to the World Meteorological Organization (WMO), most studies have used percentile rainfall or fixed rainfall as thresholds, such as 95% or 50 mm rainfall [17, 18, 19, 20]. However, in a non-stationary state, the difference in the choice of the threshold will generate a large amount of uncertainty, even based on stationary assumptions. Different threshold selections will also have impacts on modeling [7, 21]. Vu and Mishra demonstrated that the models and parameters selected under different thresholds would affect the non-stationarity of extreme rainfall, and a suitable extreme rainfall sequence needed to be selected [22]. Sugahara et al. studied the distribution of extreme rainfall under different thresholds in Sao Paulo and believed that 98% of the daily rainfall value was the most suitable for the extreme rainfall threshold in that region [14]. Liu et al. studied the extreme rainfall in the Weihe River basin and believed that 95% rainfall was suitable [11]. Therefore, it is necessary to study the non-stationarity of extreme rainfall under different thresholds and detect the specific extreme rainfall threshold in a designated region.

Among all, the climatic and non-climatic factors, large-scale climatic patterns, for example, El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Western Pacific Subtropical High (WPSH), and Arctic Oscillation (AO), are regarded as the most important factors affecting rainfall [23, 24, 25, 26, 27]. Villarini and Denniston showed that ENSO had a significant control effect on extreme rainfall in Australia [28]. Limsakul and Singhruck claimed that PDO was one of the most important factors affecting extreme rainfall changes in Thailand [29]. Fu et al. found that ENSO could affect China’s extreme rainfall trends and changes [30]. Zhang and Liu et al. demonstrated that WPSH was one of the main driving factors of the summer extreme rainfall in China [31, 32]. However, previous studies exploring the teleconnections between extreme rainfall and large-scale climatic patterns were usually based on trend analysis and correlation coefficients [33], which could not fully reveal their correlations.

The main purposes of this study are: (1) to divide the middle and lower reaches of the Yangtze River basin (MLRYRB) into sub-regions to perform the non-stationary detection of extreme rainfall, and to identify the non-stationarity of extreme rainfall with different thresholds; (2) to screen out the most suitable threshold range of extreme rainfall in each sub-region based on distribution fitting of extreme rainfall; and (3) to explore the teleconnections between extreme rainfall and large-scale climatic patterns. The main significance of this study is to explore the non-stationary pattern of extreme rainfall in the MLRYRB when the threshold changes. Combined with the non-stationarity of extreme rainfall in different sub-regions, the extreme rainfall threshold range in the region is accurately screened. In addition, the cross-wavelet analysis method will be used to comprehensively explore the relationships between ENSO, WPSH, and extreme rainfall in a different time and frequency domains.

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2. Data and methodology

2.1 Study area

The Yangtze River is the longest and largest river in China, which originates in the Tanggula Mountains, flows through 19 provinces from west to east, and finally flows into the East China Sea. The Yangtze River Basin (YRB; 24–35°N, 90–122°E), with a drainage area of about 1.8 million km2, is located in the subtropical and temperate climate zones dominated by the southeast monsoon. In this study, the MLRYRB (25–34°N, 108–122°E; Figure 1) is selected as the study area, which is one of the important water sources and an important economic center in East China. The average annual temperature is between 14 and 18°C, and the average annual precipitation is between 1000 and 1400 mm. Affected by factors such as subtropical monsoons and typhoons, the MLRYRB is one of China’s heavy rain-prone areas and areas with the highest flood intensity.

Figure 1.

Location and topography of the MLRYRB in China.

2.2 Data

The data used in this study are obtained from the China Meteorological Data Service Center (http://data.cma.cn/), and there are 62 meteorological stations with the complete sequence of daily rainfall from 1960 to 2020 in the MLRYRB (Figure 1). The meteorological stations selected in this study include all types of topography and climate regions in the MLRYRB (Figure 1).

To find out the impacts of climate change, the correlations between the extreme rainfall indices and ENSO/WPSH are studied. Here, the Nino3.4 index, which can be obtained from National Center for Atmospheric Research (NCAR) (https://climatedataguide.ucar.edu/climate-data), is used to express the ENSO phenomenon and its changes. The WPSH index, which can be obtained from the National Climate Center of China Meteorological Administration (https://cmdp.ncc-cma.net/Monitoring/cn_stp_wpshp.php), is used to analyze the strong effects of extreme rainfall in the MLRYRB [31, 32].

2.3 Methodology

2.3.1 K-mean clustering

The topography of the MLRYRB is complex and the Spatiotemporal distributions of rainfall are uneven due to the influence of the monsoon. Therefore, to reveal the steady changing process and regional differences of extreme rainfall more reasonably, the K-mean clustering method is used to identify similar rainfall characteristics and divide the whole study area into sub-regions. The K-mean clustering analysis is suitable for processing large data sets, which is a commonly used non-hierarchical clustering algorithm with high computational efficiency [11, 34]. This method can reduce the impacts of regional differences on extreme rainfall to a certain extent. For the specific calculation process, please refer to the study of Yang et al. [35].

The results of the K-means clustering analysis vary with the initial cluster centers and the number of selected clusters. Therefore, silhouette coefficient (SC) is usually selected to evaluate whether the number of clusters is reasonable. The value range of SC is from -1 to 1. Generally, the larger the SC value, the better the clustering effect. When the SC value is negative, the clustering result is incorrect. When the average SC value reaches the maximum and the number of negative values is the least, it is the optimal number of clustering. For the specific calculation process, please refer to the study of Liu et al. [19].

2.3.2 Bernaola-Galvan segmentation algorithm

Bernaola-Galvan Segmentation Algorithm (BGSA), a sequence segmentation method proposed by Bernaola-Galvan et al. based on the sliding T-test, is used to detect the mutation points of the extreme rainfall time series. Compared with traditional methods such as the sliding T/F test, the Mann-Kendall (MK) test, and the rank sum test, this method performs better in dealing with highly nonlinear time series [36].

X is a time series with a length of N. One of the segmentation points, i, slides from the left of the sequence to the right in turn. The average values of the left and right parts of the segmentation point are μ1(i) and μ2(i), and their standard deviations are s1(i) and s2(i), respectively. Then, the merged deviation SD(i) at the split point i can be expressed as Eq. (1).

SD=N11s12+N21s22N1+N221/21N1+1N212E1

In Eq. (1), N1 and N2 represent the sequence length on the left and right sides of the dividing point i, respectively. The difference between the subsequences on both sides of the split point can be represented by the T test statistic T(i) (Eq. (2)).

Ti=μ1iμ2iSDE2

In Eq. (2), the T value represents the difference between the subsequences on both sides of the split point. The statistical significance P(tmax) corresponding to the maximum T is calculated as Eq. (3).

Ptmax1Ivv+tmax2δvδηE3

In Eq. (3), Ix(a,b) is an incomplete beta function, where x corresponds to v/(v+t2 max), a corresponds to δv, and b corresponds to δ. According to the Monte Carlo simulation, η=4.19lnN-11.54, δ=0.40, v=N-2.

If P(tmax) is greater than or equal to the threshold of P0(0.95), the difference between the average values is considered to be statistically significant. Then, the time series will be split, and the iteration of the above process will continue until the effective value obtained is less than the threshold or the length of the acquired subsequence is less than the minimum length l0 (l0 ≥ 25). On the contrary, if P(tmax) is less than P0(0.95), the sequence will not be split.

2.3.3 Distribution fitting

In the identification of regional extreme rainfall, the POT method is currently used to screen the rainfall sequence, and then the parametric method is used to fit the filtered extreme rainfall sequence. The statistical distribution models used in this study for extreme rainfall research are the GPD and GEV. The distribution functions of GPD and GEV are as follows.

For the GPD in Eq. (4), k is the shape parameter, β is the threshold, and α is the scale parameter.

Fx=1α1+kxβα11kk0,βxαkE4

For the GEV in Eq. (5), μ is location parameter, α is scale parameter, and k is shape parameter.

Fx=1αexp1+kxμα1k1+kxμα11kk0E5

Klomogorov-Smirnov test (KS-test) is used to compare the results of different distributions. The larger the p value calculated by the KS-test, the better the fitting result. The standard uses a confidence level of 0.05 (p=0.05). After obtaining the distribution parameters, the corresponding return period in different years is Eq. (6).

R=β+αk(1yT)kk0E6

In Eq. (6), R is the rainfall value corresponding to the return period; y is the number of rainfalls exceeding the threshold in one year, taking the multi-year average value; T is the year of the return period; β is the threshold; α is the scale parameter; and k is the shape parameter.

2.3.4 Cross wavelet analysis

The cross wavelet analysis proposed by Hudgins et al. is an effective tool family for studying the correlation of time series [37]. Cross wavelet transform (CWT) combines wavelet transform and cross spectrum analysis, and can display two sets of time-correlated time-domain sequences. For two time series X and Y, their cross wavelet transform can be defined as Eq. (7).

Wnxys=WnxsWnysE7

In Eq. (7), W y* n(s) is the complex conjugate of W y n(s), and s is the time lag. The cross wavelet power spectrum is defined as |W xy n(s)|, and its value indicates the degree of correlation between the two time series.

For two time series X and Y, the expected spectra are Px k and Py k, then the cross wavelet power spectrum distribution is expressed as Eq. (8).

DWnxsWnysσxσy=zvpvPkxPkyE8

In Eq. (8), σx and σy are the standard deviations of the time series X and Y, respectively. zv (p) is the confidence level related to the probability p, and v is the degree of freedom. The calculation program of cross wavelet analysis can be found in the study of Torrence and Compo [38], and the code can be downloaded from http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence.

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3. Results

3.1 Classification of different sub-regions

The MLRYRB has different climatic characteristics, and different sub-regions can receive different influences from monsoon and large-scale climatic patterns. Therefore, it is necessary to determine the areas with the same changing characteristics for division. In this study, it is considered that the variations of extreme rainfall in different regions will be affected by the differences in regional characteristics. Therefore, the K-mean clustering was used to divide sub-regions with the same rainfall characteristics according to rainfall, terrain, longitude, and latitude, and the SC value was used to evaluate the results of clustering. When the SC reaches the maximum, the result is considered to be optimal. The numbers of clusters from 2 to 6 were calculated, and the corresponding SC values are shown in Table 1. When the number of clusters was 5, the SC value was the largest (i.e., 0.54). So, the MLRYRB could be divided into five sub-regions (Figure 2). Li et al. used Hierarchical Climate Regionalization to study the regionalization of the MLRYRB [39], and their results also showed that the division of five sub-regions was reasonable. After the clustering was completed, the homogeneity test was carried out on the rainfall sequences of the rain gauge stations in each sub-region. Then, the regional attribution of the boundary rain gauge stations was adjusted to ensure that the rainfall sequences of the meteorological stations in each sub-region could pass the homogeneity test.

K23456
SC0.2680.410.470.540.52

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.

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 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. 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 non-stationarity 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.

Figure 3.

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

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 Sub-region 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 Sub-region 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.

Figure 4.

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

It is shown that variation ranges of different design return periods in the five sub-regions 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 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 Sub-regions 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 Sub-region 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.

Figure 5.

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

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.

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.

Figure 6 illustrates the cross wavelet spectrum of RX1day and ENSO for each sub-region. 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 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 sub-regions. 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.

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4. Discussion

Figure 8 shows the BGSA test results of RX1day in the five sub-regions of the MLRYRB. The thin blue line represents the RX1day sequence, the thick line represents the average RX1day sequence, and the red line represents the split year. Since the BGSA method is based on the non-stationary detection of the mean value, the variation of RX1day will affect the non-stationarity of the extreme rainfall series to a certain extent. It can be considered that the non-stationarity for extreme rainfall series at a given threshold should be similar to the non-stationarity for the maximum rainfall series. After comparing the non-stationarity of the extreme rainfall series screened by different thresholds and RX1day series, the extreme rainfall threshold obtained would have a certain reference. Comparing the non-stationary split point years of extreme rainfall series under different thresholds, the extreme rainfall thresholds in the MLRYRB should be between 40 and 60 mm.

Figure 8.

BGSA test results of RX1day in the five sub-regions of the MLRYRB.

After selecting a more reasonable threshold range, this study compared the non-stationarity and the p-value of the extreme rainfall series under different thresholds. When the extreme rainfall series tends to be relatively stable, the corresponding p-value will also respond higher. Combined with the threshold uncertainty under different return periods, when the threshold was selected below 40 mm, the extreme rainfall series were in a strong non-stationary state, the fitting results were relatively poor, and the calculated design return years could not be distinguished very well. Therefore, below 40 mm was not a suitable threshold of extreme rainfall to screen the rainfall sequence, which is also consistent with the conclusion drawn by the BGSA method. When the rainfall threshold was greater than 60 mm, the p value in Sub-regions II, IV, and V begins to decline. For Sub-regions I and III, although the fitting effect was the best when the threshold was greater than 60 mm, the corresponding return period was not within a reasonable range. Therefore, based on the above findings, the reasonable range of the extreme rainfall threshold of each sub-region in the MLRYRB should be between 40 and 60 mm with the largest p value. Therefore, the extreme rainfall thresholds of the five sub-basins were 45, 60, 50, 45, and 60 mm, respectively. It is found that the extreme rainfall thresholds of the sub-regions close to the coast were higher than those far from the coast, which might be due to that the sub-regions close to the coast are more susceptible to typhoons. Regarding the whole MLRYRB, the thresholds of 40 and 60 mm corresponds to the 95% quantile and 99% quantile of the daily rainfall. So, the range of 40–60 mm is reasonable when screening and calculating extreme rainfall and different thresholds can be selected for the screening of extreme rainfall sequences for different computing requirements. Due to climate change, the definition of regional extreme rainfall is of great significance for precipitation forecasting and flood protection. The method presented in this study can judge the extreme rainfall thresholds of regions under changing environments and obtain the most suitable thresholds. When the threshold of extreme rainfall is low, it often does not work; when the threshold of extreme rainfall is high, rainfall forecasting tends to increase the risk of local flood disasters. Therefore, the extreme rainfall threshold with regional characteristics is also more reasonable. Moreover, this study adopts a generalized method and has no regional limitations, which means that it will be applicable to other regions and future climate model simulations. For different regions and different environmental backgrounds, the choice of extreme rainfall needs to consider the local specific conditions.

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5. Conclusions

This study conducted the threshold recognition based on non-stationarity of extreme rainfall in the MLRYRB. The main conclusions can be summarized as follows:

First, five sub-regions with similar rainfall characteristics were identified. Using the BGSA method to detect the non-stationarity of extreme rainfall events under different thresholds in each region, it is found that the non-stationarity of extreme rainfall events in the MLRYRB would change with the selection of threshold. When the threshold was selected as 40–60 mm, the non-stationarity of extreme rainfall was similar to the non-stationarity of RX1day series, indicating that 40–60 mm should be a reasonable threshold interval of extreme rainfall.

Second, this study performed distribution fitting on the extreme rainfall screened by different thresholds. The fitting of the General Pareto Distribution (GPD) was much better than that of the Generalized Extreme Value Models (GEV) regardless of the threshold selection. Then, the GPD with different design return periods was calculated, and the uncertainty of the threshold in Sub-region V was slightly larger than those in the other four sub-regions. Combined with the uncertainty of the threshold in each sub-region, the extreme rainfall thresholds in the five sub-regions were 45, 60, 50, 45, and 60 mm, respectively. Moreover, the extreme rainfall thresholds of the sub-regions close to the coast were higher than those far away from the coast.

Third, this study investigated the correlations of extreme rainfall with large-scale climatic patterns and found significant correlations between extreme rainfall and ENSO/WPSH. It is worth noting that WPSH is a large-scale climatic pattern that affects the rainfall in the entire YRB, and the impact of WPSH on the heavy rainfall is significantly stronger than that of ENSO. This suggests that accurate outputs from large-scale climate models can help to improve the extreme rainfall predictions in the MLRYRB.

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Acknowledgments

This study was supported by National Natural Science Foundation of China (51909117) and Natural Science Foundation of Shenzhen (JCYJ20210324105014039).

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Conflict of interest

The authors declare no conflict of interest.

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Written By

Yao Wang, Suning Liu, Zhaoqiang Zhou and Haiyun Shi

Submitted: 07 June 2022 Reviewed: 05 January 2023 Published: 01 February 2023