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Characteristics and Evolutions of Probability Distribution of Summer Extreme High Temperatures in China
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摘要: 针对夏季高温极值分布存在偏态性，利用Box-Cox变换，得到一种偏态概率分布拟合函数。基于偏态分布函数中的偏态指数和最概然高温极值，揭示了我国夏季高温极值的概率分布特征及其在20世纪80年代前后的变化规律，发现我国夏季高温极值的概率分布主要呈正偏分布型，最概然高温极值变化较好地反映了分布型的改变。研究不同时间尺度内极值对偏态指数和最概然高温极值的影响发现，最概然高温极值较为稳定，10年尺度内受极值影响较小，而偏态指数所受影响随着时间尺度的增大而越发显著。Abstract: In view of the non-normal distribution existed in summer extreme high temperature (SEHT) in China, a skewed probability distribution function is proposed to study the SEHT, which derived from Box-Cox Transformation of SEHT data. Based on a skewness index (SI) and the most probable extreme high temperature (MPEHT), the characteristics and evolutionary rules of the probability distributions in the SEHT are described before and after 1980s. The results show that from 1961 to 2008, the probability distributions of the SEHT at most meteorological stations are positive skew, and particularly in the southeastern Southwest China. While the probability distributions show negative skewness in most areas of the south to the middle and lower reaches of the Yangtze River. The highest magnitudes of the SEHT lie in the central-eastern China and the western Northwest China, secondary magnitudes lie in Northeast China and most of Inner Mongolia, and the smallest magnitudes in the central Northwest China and most parts of Southwest China.Before and after 1980s, the probability distribution changes greatly in most parts of central-eastern China, central Southeast China, most of Xinjiang, and northeastern Inner Mongolia, respectively. The results indicate that there are some weakening trends for both positive skewed distribution pattern and negative skewed distribution pattern, and the MPEHT has a common trend to approximate the mean values of the SEHT, which show that the changes of the distribution patterns can reflect some change direction of the MPEHT. There is a significant cooling trend in those areas especially for the MPEHT, while in the secondary or smallest magnitudes regions, obvious warming trend is found.Further study on the responses of SI and MPEMT to different time scales of SHET suggests that sliding removing some sequential SEHT has influences on SI and MPEMT.The SI is affected obviously to south of the Yangtze River, but changes relatively less in other areas. The larger time scale of SEHT is removed, the more significant impact appears on the probability distribution. MPEMT nearly remains the same when removing different time scale of SHET, so it is a relatively stable value, and can be regarded as a possible new way to define a threshold of extreme high temperature events.
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图 1 我国夏季高温极值的正偏、负偏、高斯分布
(直方图对应夏季高温极值的概率统计分布，圈点线为高斯拟合，实点线为偏态函数拟合)(a) 海南东方站，(b) 浙江杭州站，(c) 内蒙古化德站
Fig. 1 The positive skew, negative skew, and normal distribution of summer extreme high temperatures in China
(the histogram is experience distribution, with Gaussian fitting in hollow points line, skewness fitting in solid points line) (a) Dongfang station in Hainan, (b) Hangzhou station in Zhejiang, (c) Huade station in Inner Mongolia
图 2 1961—2008年我国夏季高温极值的偏态指数分布图
Fig. 2 The skewness index of summer extreme high temperatures in China during 1961—2008
图 3 1961—2008年我国夏季最概然高温极值的分布图
Fig. 3 The most probable extreme high temperature in China during 1961—2008
图 4 20世纪80年代前后我国夏季高温极值偏态指数变化分布
Fig. 4 The changes of the skewness index of extreme high temperatures in China before and after 1980s
图 5 20世纪80年代前后我国夏季最概然高温极值变化分布
Fig. 5 The changes of the most probable extreme high temperature in China before and after 1980s
图 6 剔除不同尺度极值后偏态指数变化的均值分布图 (a) 剔除2年尺度，(b) 剔除5年尺度，(c) 剔除10年尺度
Fig. 6 The changes in skewness index after removing different scales extreme high temperatures
(a) removing 2-year imescale, (b) removing 5-year timescale, (c) removing 10-year timescale
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