Precipitation In China's Power-law Tail Distribution Characteristics

Global climate change has received more and more attention from the governments, scientists, and the public. For the special monsoon climatology of China, variation of precipitation caused by climate change is significant, thus the study of precipitation is important to the development of economy and society. The precipitation is to some extent random, multiscale, hierarchical and non-stationary, it makes the traditional analytical methods that based on the linear, stationary theries not suitable for precipitation. In additation, because of the limitation of the observational data and inhomogenity of the observation station's location, the mechanics and prediction of precipitation has been always a difficult problem. For some extreme precipitation events, we can only analysis the particular rains and can not obtaion a bird's eye view of the whole precipitaton process. In this paper, we study the precipitation of China according to the research achievements in complexity science, and the main content is as follows:(1) We analyze 20 time serieses of 10 days'moving mean vaule of 20 stations'daily precipitation records based on BG algorithm, statistical results show that the distribution of cumulative probability of finding a segment, cutted by BG algorithm, with length larger than l are well fitted by power-law decay P ( L> l)~l?γ, i.e. scaling law characteristic. Considering present research of sequences of temperature and human heart rate, the scaling law characteristic might be a common property of all the nonstationary time series. The power-law tail exponents for 10 stations in north China varied between 1.6~2.0, which are somewhat larger than the exponents of stations in south China. South and north China respectively belong to different climate regions, which might be the reason for that the exponent of north China is greater than that of south China. From this point, the power-law tail exponents might to some extent denote the basic characters of original time series. Moving calculated the power-law tail exponents of the mean value precipitation sequences of south and north China in a 10a window with step 1a, then divided the power-law tail exponents into four grades, results show that close to 1970a, 1980a and 1990a there might be homochronous distinct abrupt change points in the precipitation of south and north China under the climate change background of our country, and the power-law tail exponents might be another effective way to study the abrupt changes contained in nonlinear and nonstationary time series.(2) The daily precipitation observational data of 740 stations from 1960a to 2000a of China are divided in sections and statistical analyzed. A common feature is revealed——the power-law distribution, and different precipitation corresponds to different power-law exponent; this to a certain extent reflects that different precipitation have different climate backgrounds and control systems. The power-law exponents of the seven climate regions of China show the trend of increase from southeast to northwest, this corresponds to the spatial character of precipitation of China—more in east and less in west, more in south and less in north. The analyses on the character of the temporal evolvement of the power-law exponent shows that: the abruption points of the power-law exponent of northeast, east, and northwest of China correspond to the drying trend of northern China starting from 1970s.(3) Based on the daily precipitation observations of 740 stations in China from 1960 to 2000a, this chapter reveals the power-law tail distributive character of the daily precipitation≥30mm in 7 climate characteristic regions, and the power-law exponentγ>3.0 in most part of China. This indicates that the daily precipitation≥30mm is a non-stationary process, and it makes the long-term prediction of heavy rainfall very difficult. It is found from further investigation using the filtering method that the power-law tail distributive character is resulted from the interaction of atmospheric systems of various scales, among them the one-week scale system had the most important influence on power-law tail exponent of the daily precipitation≥30mm.(4) We study the temporally evolutional character of power-law exponents for daily precipitation with the sliding window length being 10 years, and evaluateγto the last year in the window. and by doing so, we can not locate the abrupt change point of northen China precisely. In this section, we study in an'inverse direction'way and find that the abrupt change point of northen China located exactly between 1979 and 1980. We conclude that the large-scale climate system has changed at that time, and it has close relation with the index MEI. This maybe one of the main reasons for the drying trend of northern China. 0-29mm daily precipitation is to some extent a ststionary process, and the daily precipitation≥30mm is obviously non-stationary, it makes the long-term prediction of heavy rainfall very difficult.(5) Reconstruction and analysis of proxy series is an important program of climate research.using methods of wavelet transformation and power spectrum, the main periods of Dulan tree ring and other 7 temperature proxy series are analyzed in this paper. Through filtering, the 8 original series were divided into many components with different scales, the components'similarities of dynamics and external features on each scale are studied based on the dynamical correlation factor exponent and correlation coefficient. Research results show that, quasi 100a scale might be the common period of these proxy series, meanwhile, both dynamics and external features of these proxy series are similar on the quasi 100a and higher scales. This means that the quasi 100a and higher scales components meet with the comparable condition on those two sides. More attention must be paid to this scale when analyzing proxy series. We also find that the similarities of dynamics and external features of these proxy series descend as the scale of the components degrade; On quasi 60-70a scale, the components'similarities of dynamics features disappeared; On quasi 30a and lower scale, the similarities of external features also disappeared.