Correlations between El Niño-Southern Oscillation (ENSO) and large-scale precipitation have been found for many regions. In the 1920s to 1930s, research on El Niño events was carried out by Walker and his colleagues (Walker, 1923, 1925, 1928; Walker and Bliss, 1932). These pioneering works attempted to understand and predict variation in Indian monsoon precipitation and to extend these predictions to study global precipitation. Since then, numerous studies were carried out to reveal specific relationship between ENSO and mid-latitude precipitation anomaly (Hastenrath, 1978; Douglas and Englehart, 1981; Rasmusson and Carpenter, 1983; Rasmusson and Wallace, 1983; Shukla and Paolino, 1983; Kousky et al., 1984; Ropelewski and Halpert, 1989). For example, precipitation anomalies in different regions of America, Europe and Asia are linked to ENSO activities (Hoerling and Kumar, 1997). In research that focused on regional climate, evidence suggested that the Indian summer monsoon precipitation will be less than normal during an El Niño year (Rasmusson and Carpenter, 1982; Shukla and Paolino, 1983), while precipitation in the central equatorial Pacific islands will increase (Horel and Wallace, 1981). A series of studies revealed a strong seasonal and regional correlation between precipitation and ENSO (Ropelewski and Halpert, 1986, 1987, 1989). In autumn, winter and spring of the Northern Hemisphere, El Niño can cause a southwesterly wind anomaly over the East Asia coast (Gershunov and Barnett, 1998a, 1998b), resulting in a significant increase of precipitation in South China. The mechanism may be because of the Rossby wave in the lower atmosphere being enhanced by a convective cooling of air over the tropical western Pacific. As a result, the water vapour transport to the East Asia coast will be enhanced through anti-cyclonic circulation and convergence will occur in South China, leading to precipitation anomalies. In the meantime, El Niño can also cause weaker Indian summer monsoon, resulting in a reduction of northward water vapour transport. Thus, summer precipitation will be significantly reduced in North China (Zhang et al., 1999), while there is more than normal precipitation in the Yangtze–Huaihe Basin. On the contrary, precipitation is less in the Yangtze–Huaihe Basin during the El Niño weakening stage, while it is more abundant in the Yellow River Basin, North China and south of Yangtze River (Huang and Wu, 1989).
Linear correlation between the Southern Oscillation (SO) index and precipitation was proposed in many studies. However, constraints existed in the conventional correlation analysis of extreme precipitation, such as the constraint because of discontinuity in precipitation observations. Numerical models may be a good tool, but high model resolution is required for the simulation of regional extreme climate. Instead, we can use a model based on the extreme value theory (EVT) to simulate extreme climates. However, an EVT-based model dealing with a time series at a point in space is insufficient to reveal spatial distribution of regional extreme climate. It is therefore necessary to design an EVT-based simulation method with the capability of representing spatial distribution. A spatial model of generalized Pareto distribution (GPD) is such a model that will be used in this study. A detailed description of the GPD can be found from our recent work (Zhou et al., 2012). This study revealed an interesting relationship between global warming and regional extreme temperature, and indicated that patterns of extreme monthly low temperatures (EMLT) in China are related to global warming.
The datasets used in this study are daily observations of 740 weather stations in China, provided by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA). This is a gridded daily dataset of the quality-controlled and adjusted station data, as used by Feng et al. (2004) but with longer time series for the period of 1960–2007. The monthly precipitation in each 1° × 1° grid is calculated using a modified Cressman (1959) scheme (Glahn et al., 1985; Charba et al., 1992). The SO index is downloaded from the website at http://www.cgd.ucar.edu/cas/catalog/climind/soi.html.
2.2. Spatial model for GPD
The GPD is one of the most useful extreme value distribution (EVD) models and can be written as in the work of Coles (2001),
where µ, σ and ξ are position, scale, and shape parameters, respectively. When µ = 0, Equation (1) serves as a standard GPD model. Many methods, such as moment estimation, Bayes estimation and maximum likelihood estimation (MLE), can be used to estimate parameters, while MLE is very suitable to estimate parameters of different EVD model. It has good large sample characteristics and can give uncertainty metric of estimation method. The likelihood function of MLE is
where f(xi;θ) is probability density function, xi are independent samples (but not identically distributed), m is the sample size and θ is a model parameter. For convenience, we usually adopt its logarithmic form
Putting the standard GPD density function into Equation (3) gives us a relevant log-likelihood function,
where xi∈[0, ∞), ξ> 0 or xi∈[0, − σ/ξ), ξ< 0. and cannot be analytically solved, but can be numerically calculated.
The GPD can describe most of the extreme value information with proper pre-determined threshold (Coles, 2001). In other words, in order to describe the extreme events, a balance between defined extreme values and sufficient extreme samples should be considered. If a threshold is too large, there will be only a few useful data, and estimated error will be high. If a threshold is too small, it cannot satisfy the GPD conditions, and the estimate will become unsuitable. Observation variations, such as long-term variation trend and periodic effect of average climate, yield negative effect on analogue capacity of the model. Thus, dynamic timing threshold is adopted to avoid disadvantageous factors and to ensure a sensible choice of threshold value. The time-varying threshold is defined as in the work of Coelho et al. (2008):
where Ly, m is a long-term trend component, y and m are year and month, respectively, Sm is mean cycle variation, and ε is a constant increment to ensure α% of the observed values above the time-varying threshold uy, m is computed. The test performed has shown that the fractile (α%) is 75% (Zhou et al., 2010). If the exceedance over threshold is Z = Ty, m − uy, m, where Ty, m > uy, m is monthly averaged precipitation, then
where Z > 0, σ is a scale parameter, 1 + ξZ/σ> 0 and σ> 0, ξ is a shape parameter. Because the spatial distribution characteristics of the subject are investigated, the spatial relevance should be considered in the extreme value model. σr and ξr denote scale parameter and shape parameter of grid point r, respectively. If it is relevant to the next grid point s and the neighbourhood N(s), then, according to Coelho et al. (2008), we have
where x is covariant, and σ1r is covariant coefficient. N(s) is a neighbourhood of which we are interested in at grid point s, say, the eight immediately neighbouring grid points of a central grid point of interest. Use logσr to ensure the scale parameters are all positive, and set the scale parameters as bilinear function to smooth it spatially (Coelho et al., 2008).
where λr and δr are latitude and longitude of grid point r, λs and δs are latitude and longitude of grid point s, scale parameters σor and σ1r are relevant to spatial variation N(s). Shape parameter ξor is smoothened by setting ξor = ξos, r∈N(s).
3. Spatial distribution of EMP
This section presents GPD parameters of EMP. Given the GPD model with smooth parameters, setting x = 0 in Equation (7) leads to a stationary spatial GPD model:
The model parameters are estimated using MLE method (Coles, 2001), and the logarithm likelihood function is
where , i = 1, …, m, Zi is exceedance over threshold.
Model fitting, such as goodness-of-fittest, can be used to determine if the sample is from a known theoretic distribution F(x). A common method is Kolmogrov–Smirnow (K–S) test. Set H0:F(x) = F0(x, θ) as null hypothesis and H1:F(x)≠ F0(x, θ) as alternative hypothesis, where F0(x, θ) is a specific distribution, θ is parameter vector, which is generally unknown and can be replaced by estimation vector . When
where n is sample size, and the distribution of Dn is related to F0. If Dn is large, null hypothesis H0 will be rejected. Generally, 0.95 quantile of Dn is a threshold level, and then p = 0.05. In Figure 1, K–S test of GPD fitting shows that p value is far greater than 0.05 in most regions for all seasons, therefore, all the exceedances over thresholds meet distribution of generalized Pareto.
3.1. Spatial distribution of EMP variability
Scale parameter representing extreme values' frequency and variation may be used to describe the variability of the EMP distribution in time. The greater the scale parameter is, the larger the range of EMP variability is. The values of and can be obtained through numerical iterative computation using Equation (7). Figure 2(a) shows the scale parameter distribution of EMP in spring. It can be seen that the scale parameter decreased from south to north in China, or more precisely decreasing from southeast to northwest. The high-value centre of the scale parameter was located at the coast of South China with a maximum of 100. The physical significance of the scale parameter shows that there was a large variation in the EMP in this region. This coverage extends northwards to the Yangtze–Huaihe Basin and westwards to the eastern Yunnan–Guizhou Plateau, covering the southern part of the eastern reaches of the Yellow River, including the Yangtze River Basin and its southern region. Figure 2(b) shows the distribution in summer. The EMP centre moved northwards with its edge extending to North China, and the pattern of EMP coverage is much larger than that in spring. Compared with Figure 2(a), the lower limit of the scale parameter was larger than that in spring, i.e. the average EMP in summer was higher than that in spring. This result implies that the EMP record-breaking level in summer was higher than that in spring in terms of spatial coverage and strength. The centre of scale parameter was located in southeastern China, and the value dropped northwestwards. However, a large region of high value appeared in the southern part of the lower reaches of the Yangtze River, indicating that June was the flood season in South China. Meanwhile, the main rainfall belt in June/July moved to the middle and lower reaches of the Yangtze River. Obviously, precipitation extremes or flood events were likely to occur in the Yangtze River Basin in summer (Shi and Chen, 2002). Figure 2(c) shows that the coverage of scale parameter in autumn was much smaller than that in summer but is somewhat bigger than that in spring. This result indicates that the EMP in autumn had a higher upper limit level of record-breaking, which was related to greater influence of more frequent typhoons in autumn (Ren et al., 2002), that is, there was a higher probability of heavy rainfall in autumn, but a much lower one is in winter (Figure 2(d)), meaning the EMP variability in winter is the smallest spatially of all seasons. The reasons are that there was a stable westerly trough influence from India and Burma during this period, the major rainfall belt retreated to southeastern China, and climate in the Yangtze River basin was usually controlled by northwesterly air airflow (Shi, 1996). Thus, the same magnitude of precipitation extreme became exceptionally small, and the probability of continuous and extreme precipitation was reduced. In summary, there was a maximum for record-breaking probability of EMP in summer, followed by this value in spring and autumn, and a minimum was in winter.
3.2. Spatial distribution of EMP record-breaking probability
As the second important parameter of EVD, the shape parameter is used to explore extremal properties in the tails of the distribution. Different shapes show different levels of record-breaking, representing different record-breaking probability. A positive scale parameter indicates the EMP has a greater record-breaking probability and a lower upper limit of record-breaking. In contrast, a negative parameter indicates a lower probability and a higher upper limit for EMP. Figure 3(a) shows the EMP shape parameter in spring. The distribution with positive value was mainly located in a non-monsoon zone, i.e. the arid area from Northeast China, North China to the Qinghai–Tibet Plateau. The probability of EMP record-breaking in these regions was greater than that in the other regions. The areas with a negative shape parameter were mainly located in the central and eastern China, including the middle-lower reaches of the Yangtze River and the Yellow River. The record-breaking probability of precipitation in these regions was relatively small, corresponding to distribution characteristics of scale parameter in spring, i.e. corresponding to the pattern located where the EMP had greater variability. In other words, the greater the variability, the smaller the record-breaking probability for EMP, which is consistent with the principle that the longer the wavelength, the smaller the frequency. Figure 3(b) shows the distribution of shape parameter in summer. In general, the record-breaking probability of EMP in summer was relatively small, and the shape parameter was negative in most regions. The areas with positive values were mainly located in non-monsoon arid areas, with the centre in the Tarim basin. In this area, record-breaking easily occurred because of the small amount of precipitation. Figure 3(c) shows the shape parameter distribution of EMP in autumn, which is very similar to that in spring. According to the scale parameter in autumn (Figure 2(c)), it can be seen that the more frequent the precipitation was in a region, the lower the record-breaking probability in this region would appear. In winter, the coverage with positive value, mainly located in North China and West China, was the largest among all the seasons (Figure 3(d)). As viewed from temporal evolution, the shape parameter corresponded to the scale parameter, i.e. the more frequent the precipitation was in a region (such as a monsoon zone) or a season (such as summer), the smaller the probability of the record-breaking would be (lower than that located in arid areas or in the dry season). Since probability of precipitation is usually lower in arid areas, the probability of breaking the historical record of precipitation should be relatively higher.
4. EMP dependence on SO
The dependence of extreme climate on factors such as time and ENSO can be easily examined by modelling the shape and scale parameters of the GPD as functions of these factors (Coelho et al., 2008). According to Equations (7) and (8) in Section 2, three cases (nonstationary spatial model) have been chosen to study the impacts of SO on EMP based on Equation (7), namely,
where t is time, and σ1r and ξ1r are linear coefficients (gradients). Considering scale parameter σr influenced by SO in GPD1, linear increment σ1rt is added as covariant, and shape parameter ξr is fixed. Similarly, considering shape parameter ξr impacted by SO in GPD2, ξ1rt is set as covariant and scale parameter σr is fixed. In GPD3, scale and shape parameters affected by the SO are considered. The three cases are used to simulate the responses of EMP distribution to the SO. Thus, a GPD model  is set without the SO effect, and another GPD model  is set with SO parameters, where and are parameter vectors and M0⊂M1. Deviant statistic
where ℓ0(M0) and ℓ1(M1) are the log-likelihood function maxima in models of M0 and M1 respectively. Then D is in conformity with Chi-squared distribution of , where the effective degree is , i.e. the parameter difference of the two models (k is integer). With significance level α(α = 5%), if D > c1−α, where c1−α is (1 − α) fractile of distribution, (null hypothesis) shall be refused, and alternative hypothesis (alternative hypothesis) with a better analogue capability shall be accepted. Generally, p as another form of probability value shall be used to judge status of the hypothesis, where
and p-value is larger than the confidence interval α. Then, null hypothesis shall be accepted; otherwise alternative hypothesis shall be accepted. This test is called likelihood ratio test (LRT). Here, we set GPD0 as null hypothesis and GPD1—GPD3 as alternative hypothesis.
4.1. Response of EMP's variability to SO
According to Equation (12), Figure 4 maps the p-value of LRT from spring to winter. The alternative hypothesis cannot be rejected at the 5% significance level over regions where the p-value was lower than 0.05. This indicates that over oceanic regions, such as the subtropical Pacific, Indian Ocean and Atlantic, the model with shape and scale parameters affected by the SO index is to fit the excesses above the 75% time-varying threshold. The dependence of EMP on SO can be easily examined by modelling the shape and scale parameters of the GPD as functions of these factors (Coelho et al., 2008). On the other hand, Figure 4 shows the regions in China where the p-value was less than 0.05. Over these regions the null hypothesis can be rejected at the 5% significance level in favour of the alternative hypothesis, and there were different spatial distributions in different seasons. These results suggest that the SO index is a statistically significant factor for modulating the EMP variability over these spatial distributions. In other words, the variability of EMP over these regions was affected by the SO via atmospheric teleconnection.
It can be seen that EMP was influenced little by the SO during spring (Figure 4(a)), and few areas passed the LRT test. However, a completely different situation occurred during summer, when the SO influence was enhanced significantly (Figure 4(b)). The forced centre (p-value less than 0.05) was located at the Qinghai–Tibet Plateau and its eastern region between the Yangtze and Yellow Rivers, extending to the Yellow–Huaihe Basin. Another spatial pattern covered the majority of Northeast China. In summer, the SO influence on the spatial distribution of EMP was enhanced significantly in these regions. In autumn, change occurred because of the distribution pattern (Figure 4(c)), i.e. the SO influence extended northwards and retreated eastwards in the Qinghai–Tibet Plateau. The forced coverage between the Yangtze River and the Yellow River disappeared and moved northwards to North China. The coverage became smaller in winter spatially (Figure 4(d)). In summary, the regions significantly forced by the SO in Northeast China in summer shrank in size, and they moved northwards. It can be seen that China's EMP variability dependence on the SO mainly appeared in summer and autumn, because it reached minimum in winter and spring.
4.2. Response of EMP's record-breaking probability to SO
Similarly, the SO effects on the shape parameter can be obtained (Figure 5), according to Equation (13). Figure 5(a) shows that the spatial distribution of EMP's dependence on the SO is concentrated in Southeast China in spring, which extended north to the reaches of the Yellow River and west to the Yunnan–Guizhou Plateau. However, most of the regions were forced by the SO in the main flood season of summer (Figure 5(b)), indicating that the SO as a constraint factor had a large effect on the record-breaking probability of EMP in summer. In autumn (Figure 5(c)), the situation was different from that of the scale parameter (Figure 4(c)). The dependence region on the SO shrank southwards rather than expanding northwards, and the coverage was located in the Inner Mongolia. The SO impact on EMP has kept decreasing in the western part of North China and Tibet. In winter, the coverage was mainly located from Northwest China to Southeast China (Figure 5(d)), which may be related to the direction of movement of winter monsoon. Thus, we conclude that the record-breaking probability of EMP in summer was significantly controlled by the SO in general. Abnormal floods in these regions were caused by abnormal ENSO activities. However, a normal strength of SO activity should not lead to the highest level of precipitation (namely unable to lead to a new historical record).
4.3. SO's global effects on EMP
To investigate SO's global influences on the EMP using Equation (14), we added SO index to the two controlling parameters (i.e. scale and shape parameters) in the GPD model. The results are shown in Figure 6. By comparing Figure 5 and Figure 6, it can be seen that SO's global effects on two parameters were greater than that of SO's effects on a single one, because the spatial coverage depending on the SO expanded, i.e. the areas without any dependence for the scale and shape parameters extended. This was especially evident in spring and winter.
A spatial GPD model is able to simulate the distribution of EMP. The model's dynamic timing threshold can properly eliminate seasonal effects and long-term trend in the observations. Importantly, the spatial scheme of model parameters can effectively consider regional correlations of extreme spatial values by smoothing out the noise in the data and improving the accuracy of the model. The results revealed that the EMP variability and record-breaking probability in China had significant regional differences and unique spatial patterns. The EMP variability showed a lager spatial pattern in Southeast China (monsoon area) but a smaller pattern in Northwest China (arid region), while both regions showed a temporal distribution pattern with a maximum in summer (May–August) and a minimum in spring. The EMP record-breaking probability showed a different spatial pattern with a maximum in the arid areas, especially in wet–dry transition crossing zones, and a minimum in the regions located in the monsoon areas (e.g. south of the Yangtze River). Different from the variability (scale parameter), the record-breaking probability (shape parameter) showed a temporal distribution pattern with a minimum in summer and a maximum in spring and autumn.
ENSO played an important role in shaping the spatial pattern of the EMP, and had different effects on EMP variability and record-breaking probability. At the temporal scale, the EMP variability forced by the SO was mainly distributed in summer, when the corresponding spatial pattern covered the Qinghai–Tibet Plateau and the region between the Yangtze and Yellow Rivers as well as the Southern part of Northeast China. In autumn, the pattern moved northwards with a decreasing coverage, mainly influencing the northeastern and northern parts of the Qinghai–Tibet Plateau as well as the northern part of Northeast China and central North China. Almost no influences existed in spring and winter where the p-value is far greater than 0.05. The record-breaking probability was being forced by the SO mainly in summer, with a pattern of larger coverage than those in the other seasons. However, the SO has only a minimum influence in spring, and EMP's spatial pattern is mainly located south of the Yangtze River and the middle-lower reaches of the Yangtze River. In addition, the SO had more influence on the EMP with its impacts on both parameters instead of a single parameter.
The R Development Core Team (2008) is acknowledged for providing the statistics package ‘R’. This work has been supported by the National Natural Science Foundation of China (Grant Nos. 41005041, 40930952, 40875040, and 41005043), the National Basic Research Program of China (2012CB955203) and the Special Scientific Research Project for Public Interest (Grant No. GYHY201006021, GYHY201106015 and GYHY2011060 16) and the National Key Technologies R&D Program of China (Grant No. 2009BAC51B04).