L. Yang, State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Room 334, New Hydraulic Building, Tsinghua University, Beijing 10084, China. E-mail: firstname.lastname@example.org
Extreme rainfall and flooding events are the subjects of intense scientific investigation because of their large societal and economic impacts (e.g., Karl and Easterling, 1999; Easterling et al., 2000). Their effects may be exacerbated in a changing climate, with modelling studies projecting large changes in the frequency and magnitude of extreme events in a warmer climate (e.g., Voss et al., 2002; Milly et al., 2005).
China has experienced an increased frequency of extreme rainfall and flooding events over the last century (e.g., Wang and Zhou, 2005; Pan et al., 2012; Xu et al., 2011). Extreme rainfall is the most destructive of the natural hazards in China, and is responsible for substantial damage to property and infrastructure. Numerous studies have investigated possible changes in the temporal and spatial characteristics of extreme precipitation over China. Xu et al. (2011) found that annual mean precipitation and extreme precipitation days have increased by 10.9 mm and 0.12 d, respectively, during 1990–2007, with most of the observed increases concentrated in the mid-lower Yangtze River valley and northwest China. Slight variations in precipitation extremes in northern and northeastern China have also been detected. Qian and Lin (2005) analysed several indices of precipitation and found that the mid-lower Yellow River and the upper Yangtze River valley tend to have lower precipitation intensity and frequency of persistent wet days, while both indices increased in the Xinjiang region (northwest China) and southeastern China. Jiang et al. (2011) found a significant decrease in extreme summer rainfall in few areas of the Circum-Bohai-Sea region during 1961–2008. Other studies focussed on Chinese sub-regions, such as the eastern and central Tibetan Plateau (You et al., 2008), northeastern (Liang et al., 2011a) and southeastern China (Zhang et al., 2009, 2010), the Yellow-Huaihe River basins (Dong et al., 2011), the Yangtze River basin (Zhang et al., 2008) and Poyang lake (Zhang et al., 2011a).
Owing to the seasonal changes in the rainfall process (Yao et al., 2009), the validity of the stationarity assumption should be examined both at seasonal and annual scales (e.g., Villarini, 2011). In this study, we focus on the temporal changes in extreme rainfall in individual seasons, and test whether stationarity is a reasonable assumption. A stationary time series is a time series for which the probability distribution is invariant to temporal translation (Brillinger, 2001), indicating a lack of periodicities, abrupt and slowly varying changes (Salas, 1993). The validity of the stationarity assumption is generally examined by focussing only on slowly varying changes (e.g., Zhang et al., 2011b), or the presence of abrupt changes is tested after the trend test (Liu et al., 2008). As discussed in Villarini et al. (2009), this approach may lead to misleading results. In this study, we first test the records for the presence of abrupt changes, followed by trend tests. If a change point in mean is detected, the time series is divided into two sub-series and trend analysis is carried out for each of the two sub-series separately. Otherwise, we test the entire series for the presence of trends. We use the nonparametric Pettitt test (Pettitt, 1979) to detect abrupt changes, and the Mann-Kendall (MK) test (Mann, 1945; Kendall, 1975) and Sen's slope estimator (Sen, 1968) to detect slowly varying changes and trend magnitude, respectively. More details about these methods are provided in Section '3. Methodology'.
Apart from the evaluation of the stationarity assumption, we examine the upper tail properties of seasonal extreme rainfall using the Generalized Extreme Value (GEV) distribution (e.g., Coles, 2001) as a modelling framework. Feng et al. (2007) fitted 651 time series of annual maximum precipitation in China with the non-stationary GEV distribution. Previous studies examined upper tail properties of rainfall using the GEV distribution for other areas of the world (Chu et al., 2009; Villarini et al., 2011; Villarini 2011). Particular emphasis was given to the dependence of the GEV parameters on elevation. Based on previous studies, no strong link between the GEV parameters and elevation was detected. We assess whether we can draw the same conclusions for China, and examine whether orography can explain the spatial variability of the GEV parameters.
As extreme summer rainfall is the most destructive natural hazard affecting China (Ding, 1994), we examine whether it is possible to link extreme anomalies in warm season rainfall to the East Asia Summer Monsoon (EASM; Ding and Chan, 2005). These results will provide valuable information on the relation between extreme rainfall and climate variability, and shed more light on the water resources status in China under the influences of a changing environment.
The paper is organized as follows. Description of the data and quality control procedures are provided in the next section. We briefly introduce the methods used to perform change-point and monotonic trend tests, GEV modelling and correlation analysis in Section '3. Methodology'. The results of our analysis will be presented in Section '4. Results', followed by the conclusions in Section '5. Conclusions'.
The data used in this study are daily precipitation series from 754 meteorological stations during the period 1961–2006, provided by the National Climate Center (NCC) of Chinese Meteorology Administration (CMA). Strict quality control procedures were performed: (1) stations without complete record from 1961 to 2006 are discarded, even if only one daily record is missing; (2) stations with erroneous records (negative or anomalously large daily precipitation, e.g., over 2000 mm) are also removed from the dataset. There are 485 stations satisfying these criteria, and they are used in our analyses. The locations of all the 485 stations are shown in Figure 1.
To facilitate the presentation and interpretation of the results, we have divided the study area into three main sub-regions: north, south and west China (Figure 1). The density of the stations is not uniform, with a sparse distribution in northwest China and the Tibetan Plateau (‘West’ region in Figure 1), while the density is much higher in eastern China (‘North’ and ‘South’ regions in Figure 1). To account for seasonal changes in extreme rainfall, we focus on the following four seasons: spring (March–April–May, MAM), summer (June–July–August, JJA), autumn (September–October–November, SON) and winter (December–January–February of the following year, DJF). The seasonal extreme precipitation represents the maximum daily precipitation in each season (block maximum, e.g., Coles, 2001).
We examine the link between summer extreme rainfall and large-scale forcing using the East Asia Monsoon (EAM), and, more specifically its summer component (EASM). It describes the variability of the westerly jet stream in the upper-troposphere over East Asia (e.g., Yao et al., 2009), and is one of the most important atmospheric circulation features over eastern China. For most of the stations, extreme rainfall is concentrated during the summer (Ding, 1994), and this is the reason why we focus on this season. For some coastal stations affected by tropical cyclones, the heaviest rainfall of the year can occur in early autumn (Wu, 2005a). The EASM index used in this study is defined as an area-average seasonally (JJA) dynamical normalized seasonality (DNS) at 850 hPa within the East Asian monsoon domain (10°–40°N, 110°–140°E; Li and Zeng, 2002, 2003), and was downloaded from http://web.lasg.ac.cn/staff/ljp/data-monsoon/EASMI.htm.
In this section, we provide an overview of the methods used to perform change-point and trend analysis, as well as correlation analysis. GEV distribution modelling is also briefly described in this section. All the calculations are performed in R (R Development Core Team, 2010).
3.1. Change point and trend analysis
The validity of the stationarity assumption is examined by testing the data for the presence of abrupt and slowly varying changes. The main difference between these two modes of violation of the stationarity assumption is that changes would continue in the future in the presence of trends. On the other hand, when an abrupt change occurs, it remains in that regime until a new shift occurs.
We use the nonparametric Pettitt test (Pettitt, 1979) to test the data for the presence of abrupt changes in the seasonal maximum rainfall distributions. This is a rank-based test that uses a version of the Mann–Whitney statistic to test whether two samples come from the same population, and it allows for the detection of a single change point in the mean at an unknown point in time. The main advantages of this test are that it is nonparametric (no distributional assumptions are made), which makes it less sensitive to outliers and skewed distributions, and that the test significance can also be computed using the formulation in Pettitt (1979).
Most change-point tests are designed to detect abrupt changes in the mean of the distribution of the variable of interest. Fewer tests are designed to detect abrupt changes in variance, even though they can have a large impact on the distribution of the extremes (e.g., Katz and Brown, 1992; Ferro et al., 2005). In this study, similar to what is suggested in Pegram (2000), we test the seasonal records for the presence of abrupt changes in variance by applying the Pettitt test on the squared residuals computed with respect to the local polynomial regression line (loess function; Cleveland, 1979 with a span of 0.75). We set the significance level for the change-point analysis to 5%.
The presence of monotonically increasing or decreasing trends is tested using the nonparametric Mann–Kendall test (e.g., Mann, 1945; Kendall, 1975; Helsel and Hirsch, 1993). This test is widely used in studies of this kind and its power is similar to the Spearman's test (Yue et al., 2002). We also use the Sen's slope estimator (Sen, 1968) to quantify the magnitude of the trend. This estimator can be considered as the nonparametric counterpart of the ordinary least squares method. Because of their widespread use, we do not describe them in detail but point the interested reader to the literature (e.g., Helsel and Hirsch, 1993; Liang et al., 2011b; You et al., 2011). We set a 5% significance levels for the trend analysis.
3.2. Generalized Extreme Value distribution
The GEV distribution is used to statistically model the distribution of seasonal extreme precipitation (e.g., Coles, 2001). The cumulative distribution function of the GEV takes the form:
where µ∈(−∞, + ∞) is the location parameter (related to the record magnitude; units are mm), σ> 0 is the scale parameter (related to the record variability; units are mm) and ξ∈(−∞, + ∞) is the shape parameter (related to the tail of the distribution). If ξ> 0, the distribution is heavy tailed and with no upper bound (Frechet distribution). If ξ< 0, the distribution is light tailed and bounded above by an upper bound given by µ− σ/ξ (Weibull distribution). The Gumbel distribution is the special case for ξ→0 and corresponds to unbounded distributions with light upper tails. Parameter estimation is performed using maximum likelihood estimators (see Hosking 1990; Coles 2001; Morrison and Smith 2002 for other estimation techniques).
We fit the GEV distribution only to those stations without statistically significant abrupt changes in mean and variance and monotonic trends. We also assess the quality of the fit using three goodness-of-fit tests: Kolmogorov–Smirnov, Anderson–Darling and Cramer–von Mises (e.g., Laio, 2004; Kottegoda and Rosso, 2008; Serinaldi, 2009). We use a Monte Carlo approach to compute the critical values of the test statistics, under the null hypothesis that the sample comes from the fitted GEV distribution, because we estimate the GEV parameters directly from the data. We set the significance level to 0.05.
Previous studies investigated the dependence of the GEV parameters on elevation (Chu et al., 2009; Villarini et al., 2011; Villarini, 2011) without finding a strong relation. In this study, we examine whether elevation can explain the variability of the GEV parameters, shedding some light on the transferability of the previous findings to other areas of the world.
3.3. Correlation analysis
Correlation analysis is used to examine the association of summer extreme precipitation with large-scale climate forcings. We focus on the EASM because it was found to be a relevant predictor in examining the variability in summer rainfall (e.g., Wang and Zhou, 2005; Yao et al., 2009; Zhou et al., 2010, 2011). The Spearman correlation coefficient is computed between each summer precipitation time series and the normalized EASM index. We use Spearman correlation coefficient because it does not require assuming a linear dependence between quantities, but allows testing for more general monotonic relations. It is rank based and corresponds to computing the Pearson correlation coefficient on the ranks (e.g., Conover, 1998).
4.1. Change-point analysis
Figure 2 and Table 1 summarize the results of the change-point analyses based on the Pettitt test. When examining all the seasonal results together, there is a tendency towards a larger number of stations with change points in variance (208) than in mean (68), indicating that abrupt changes in the second rather than the first moment of the distribution are a more common mode of violation of the stationarity assumption. More stations tend to show larger values in mean and/or variance after the change point. The years of the change points tend to concentrate in the 1980s, possibly related to the changes of observation standards in the observational network around 1980 (Wu, 2005b). There is no strong spatially coherent pattern associated with the results of the change-point analysis, possibly with the exception of the winter season (Figure 2(d)). During winter, the values of the mean and variance become larger after the year of the change point over almost the entire study area, with the exception of a cluster of stations in the Circum-Bohai-Sea region, which includes the Beijing metropolitan area.
Table 1. Summary statistics of the change point analysis based on the Pettitt test (significant at the 5% level)
The number in brackets represents the counts of stations with a smaller value of the mean or variance after the year of the change point.
The existence of change points can be attributed to several reasons, such as relocation of stations, changes in the time and frequency of the measurements, changing measuring devices and land use changes due to anthropogenic activities (Potter, 1979; Peterson et al., 1998; Liu et al., 2011). In some instances, it is also possible that these step changes are associated with shifts in climate regime (Karl and Knight, 1998; Alley et al., 2003; Swanson and Tsonis, 2009). As an example, in northwestern China the measuring devices were changed to mitigate the wind effects in the 1960s, possibly affecting the measured rainfall distribution (Liu and Sun, 1995). The Yellow River basin has also undergone tremendous land use and land cover changes due to human activities, particularly during the period 1975–1985 (Liu et al., 2008). For the cluster of stations in the Circum-Bohai-Sea region with change points in winter extreme precipitation series, the reason is not clear. Circum-Bohai-Sea region is one of the most developed areas in China, and some of the largest cities (Beijing and Tianjin) are located there. Whether the change points can be associated with human activities or changes in climate regime still remains an open question.
4.2. Trend analysis
The presence of monotonic trends is examined by means of the Mann–Kendall test. We show the location of the stations with statistically significant trends in Figure 3, while Table 2 summarizes the results concerning the sign of the change. There is a general tendency towards increasing trends, in particular during winter, spring and summer, although most of them are not statistically significant (Table 2). When we focus on the statistically significant stations (Figure 3), 26 out of 27 have increasing trends during winter. The picture is less clear for summer and autumn. For summer, the number of stations with significant increasing (8) or decreasing (6) trends is comparable, while autumn exhibit more stations with significant decreasing (9) than increasing (4) trends. Given the small fraction of stations with statistically significant trends, it is not possible to make conclusive statements about the presence of a climate change signal. This could be due to a lack of signal, or to a low signal-to-noise ratio due to the nature of these rare events (Frei and Schär, 2001).
Table 2. Summary statistics of the trend analysis based on the Mann–Kendall test
The number in brackets represents the counts of stations with statistically significant trends at the 5% level.
To complement the results of the Mann–Kendall test, we use the Sen's estimator, which provides information about the slope of the regression line, regardless of its statistical significance (Figure 4). As expected from the Mann–Kendall results, there is a tendency towards increasing trends during spring and winter, and a tendency towards decreasing trends during autumn. In the summer, which is also the season with the largest rainfall accumulation of the year, there is a dipole-like pattern, with extreme precipitation increasing in the southern part of the study region and decreasing in northern one. This rainfall regime in Eastern China is known as ‘southern flood, northern drought’ (e.g., Hu, 1997; Chen et al., 2004; Li et al., 2011). We repeated the same analysis focussing on the 1985–2006 period to examine changes in extreme rainfall over the most recent decades (Figure 5). The changes in slope over the most recent period are much more dramatic, with a much more distinct differentiation between areas with increasing and decreasing rainfall. This is particularly true for the summer season, in which the differences between the northern and southern regions are exacerbated. Xia et al. (2007) found that aerosol loading significantly increased over northern China during 1980–2005, and Zhao et al. (2006) identified the positive feedback of increased aerosols loading on rainfall reduction.
4.3. Generalized Extreme Value distribution
In this section, we describe the results concerning the modelling of the seasonal extreme rainfall using the GEV distribution. We focus only on the stations without change points in mean or variance, and without statistically significant monotonic trends. There are 452 (spring), 451 (summer), 439 (autumn) and 451 (winter) stations that satisfy these requirements. We also excluded stations for which the results of the goodness-of-fit tests (Kolmogorov–Smirnov, Anderson–Darling and Cramer–von Mises tests) lead to the rejection of the null hypothesis that the data were generated by the GEV distribution.
Because of the sparsity of the rain gage network in West China, we only focus on eastern China, stratifying the data into ‘North’ and ‘South’ (Figure 1). Figure 6 shows the dependence of the GEV parameters on elevation for the four seasons. Location and scale parameters are negatively correlated with elevation in the log–log domain. With the exception of the ‘South’ spring location parameter, the slopes are all statistically significant at the 5% level, pointing to a dependence of these parameters on elevation. This is different from results in Villarini et al. (2011) and Villarini (2011), and suggests that the GEV parameters depend on elevation in certain geographic settings. The shape parameter generally decreases with elevation in the log-linear domain, even though the dependence is weak and not statistically significant. Compared to the shape parameters, the largest difference between northern and southern stations are for the location and scale parameters. More specifically, these two parameters are larger in the south than the north (Figure 6), reflecting the climatology of extreme rainfall. There is also a stronger linear dependence (in the log–log domain) between elevation and location and scale parameters in North rather than South China, especially for spring and summer (Table 3).
Table 3. Summary statistics of the relations between the three parameters of the GEV distribution and elevation
Numbers in bold denote a statistically significant relation (at the 5% level) between elevation and the GEV parameter.
The spatial patterns of the three GEV parameters are illustrated in Figure 7 for the four seasons. If we focus on the location and scale parameters, there is a very good visual agreement between elevation and location and scale parameters in the northern part. This should not come as a surprise, given the dependence of these parameters on elevation (Figure 6). For South China, the location and scale parameters vary smoothly, with generally decreasing values moving from the coast to the inland. As expected, the spatial variability of the shape parameter does not mimic the topography, and is less spatially coherent. The only exceptions are the areas of light tails in the Yangtze River and pockets of heavy tails in the Circum-Bohai-Sea region.
The relation of the three GEV parameters to elevation and its spatial patterns indicates that the controlling factors of extreme precipitation distribution are different for different regions over eastern China. In the north, elevation is an important factor, especially for spring and summer extreme precipitation distribution. On the other hand, additional predictors (e.g. rainfall associated with landfalling tropical cyclones) may play a significant role in explaining the spatial variability of extreme rainfall in Southern China.
4.4. Association between summer extreme precipitation and EASM
In addition to the examination of the stationarity assumption, we also investigate whether summer extreme rainfall can be described in terms of large-scale atmospheric circulation forcings. China has a typical monsoon climate (Ding, 1994) and previous studies discuss the relation between changes in the monsoon and annual and seasonal properties of rainfall (Wang and Zhou, 2005; Wang et al., 2011; You et al., 2011). In this section, we examine the association between summer extreme precipitation and EASM, using the Spearman correlation coefficient as our metric.
The correlation coefficient between summer precipitation and EASM is generally negative in southern China, especially in the mid-lower Yangtze River basin, while it is positive in the northern part (Figure 8). EASM exhibits an oscillatory behaviour over the past 60 years, with a tendency towards a weakening trend over the most recent period (Figure 9). Yu et al. (2004) also indentified the weakening trend of EASM in the same time period, which they further attributed to the tropospheric cooling effect around 300 hPa over the northeast of the Tibet Plateau. The trend could provide a physical interpretation of the results in Figure 3(b), with the weakening of EASM possibly associated with the decreasing (increasing) trends of summer extreme precipitation in northern (southern) China. One possible explanation for this phenomenon is the following: due to the weakened EASM, the rain belt (known as Meiyu fronts in China), which is supposed to move northward, tends to remain over southern China (especially in the mid-lower Yangtze River basin) for longer periods during late June to August. Thus, southern China experiences heavier summer rainfall totals and extreme precipitation, while the opposite holds for northern China (Tu et al., 2010; Zhang et al., 2011b).
Some stations along the southeastern coast of China, however, exhibit statistically significant positive correlations with EASM, which differs from the general pattern of negative correlations in the south. Because the southeastern coastal region is vulnerable to tropical cyclones (Ren et al., 2006; Ying et al., 2011), it is possible that these events control extreme rainfall over this area rather than the EASM.
In this study, we analysed seasonal extreme precipitation series for 485 stations over China during the period 1961–2006. The main conclusions are summarized as follows.
We checked the validity of the stationarity assumption by testing the seasonal maximum precipitation time series for the presence of abrupt and slowly varying changes using nonparametric tests. The violation of the stationarity assumption was mostly associated with abrupt changes. There are more stations with change points in variance than in mean for all the four seasons. Most of the change points tend to occur in the 1980s, when China underwent a remarkable socio-economic change. No strong spatially coherent pattern was detected for the results of the change-point analysis with the exception of winter. During winter, there is an overall tendency towards larger mean and variance after the year of the change point, while the variance tends to be smaller after the year of the change point in the Circum-Bohai-Sea region. These results are consistent with previous studies (e.g., Liu et al., 2008; Zhang et al., 2009). In some cases, we were able to explain these abrupt changes in terms of human activity. It is possible, however, that some of these detected step changes are related to shifts from one climate regime to another. Future studies should examine in more details the physical nature of these changes.
There is a tendency towards increasing (decreasing) precipitation trends in spring, summer and winter (autumn), even though only a very limited number of them are statistically significant at the 5% level. The results for northern and southern China qualitatively point to increasing trends during spring and winter, and decreasing trends during autumn. During summer we found a ‘dipole-like’ structure, with extreme precipitation increasing in the southern and decreasing in the northern part. Our results are generally consistent with the analysis of Wang and Zhou (2005), with the exception of spring. According to Wang and Zhou (2005), the number of spring extreme rainfall days decreased over most of the country, which is different from the increasing trend of spring maximum precipitation in our study. This suggests less frequent, but more intense precipitation during spring. We examined the trend magnitude over the entire period and over the most recent two decades (1985–2006). During the period 1985–2006, the magnitude of the changes is much larger, resulting in a stronger spatial contrast among the different parts of China. These results may suggest an increased rate of change over the most recent period. Whether these changes are related to natural variability or to human modifications of the climate system should be examined in future studies.
We fitted the GEV distribution to the stationary precipitation series, and examined the dependence of its parameters on elevation. The location and scale parameters are negatively correlated with elevation, while the shape parameter does not strongly depend on it. The strength of the dependence varies seasonally and regionally. Location and scale parameters in the south tend to be larger than in the north reflecting the climatology of extreme rainfall. Extreme precipitation distribution in the north is mainly controlled by elevation, especially for spring and summer. On the other hand, some other factors (e.g., landfalling tropical cyclones) may play a significant role in explaining the rainfall variability over southern China.
We have examined the association between summer extreme precipitation and the EASM. EASM tends to be negatively correlated in some regions of South China and positively correlated elsewhere. This spatial structure provided insight in explaining the observed changes in summer extreme rainfall in North and South China. More specifically, because of the weakening trend of EASM over the recent decades, the rain belt, which is supposed to move northward, tends to remain longer than normal over South China (especially over the mid-lower Yangtze River basin). This study connected summer rainfall variability over eastern China directly to EASM, which further confirmed the results of other researchers (e.g., Yu et al., 2004; Wang and Zhou, 2005). The consequences of the increasing (decreasing) trend in summer rainfall in the south (north) will potentially further increase water shortage in the North China Plain and cause more floods in the south. Thus, more effective and integrated water resources management and higher adaptability to flood events are in great urgency.
This research was funded by the National Science Foundation of China (NSFC 51179084, 51190092), the special foundation of Ministry of Water Resources, China (Project No.201001004), the foundation of State Key Laboratory of Hydroscience and Engineering of Tsinghua University (2012-KY-03), the Willis Research Network and a generous gift from Mr. and Mrs. Thomas Ou. The authors would like to acknowledge Chinese Meteorology Agency and Prof. Jianping Li for providing the meteorological data and EASM index used in the analysis. Two anonymous reviewers made insightful comments on the early version of the manuscript, which greatly improved the paper.