基于分数阶导数的天气和气候要素时间序列关系分析
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摘要
天气和气候要素时间序列特征及关系的研究,对于提高极端天气和极端气候事件影响的认识,以及提高模拟及预报预测极端天气气候事件,都会起到积极的作用。利用沈阳市1951~2010年的日平均气温资料,经处理后得到不同时间尺度(日、月和年)的平均气温距平时间序列,分别代表着平均气温距平的时间序列和气候序列,运用自相关函数和归一化概率密度函数分析了上述时间序列的自相关性和概率密度函数的长尾特征,在此基础上,利用二阶结构函数建立了月、年平均气温距平与日平均气温距平的分数阶导数关系,即气候时间序列和天气时间序列之间的分数阶导数关系。研究结果表明:沈阳日、月、年平均气温距平时间序列分别呈现出无记忆性、短期记忆性和长期记忆性的特征;相比日、月平均气温距平序列,年平均气温距平序列的归一化概率密度函数呈现出明显的长尾特征,意味着气候极端事件发生的概率要大于天气极端事件发生的概率。这些结果表明,月、年平均气温距平序列(气候要素时间序列)与日平均气温距平序列(天气要素时间序列)之间存在着分数阶导数关系,计算出相应的导数阶数分别为0.524和0.83。
Research on characteristics of time series of weather and climate factors and theirrelationship will improve our understanding on effect of weather and climate extreme events, and willenhance our abilityon simulation and prediction of weather and climate extreme events. In this paper, the average air temperature anomaly time series with different time scales(daily,monthly and yearly scales) from 1951 to 2010 in Shenyang city were selected,which represents the time series of weather and climate factors. The characteristics of autocorrelation and long-trail probability distribution for these time series was analyzed by using the autocorrelation function and the normalized probability density function. Furthermore, thefractional derivative relationships between monthly, yearly average air temperature anomaly and daily average air temperature anomaly were established by using second order structure function,i.e., the fractional order derivative relationship between the time series of climate and weather factors. The results showed that the time series of daily, monthly, and yearly average air temperature anomaly in Shenyang city presented the characteristics of non-memory, short-term memory and long-term memory, respectively. The normalized probability function of yearlyaverage air temperature anomaly series showed obvious long-tail trait, compared to that of daily and monthly air average temperature anomaly series. Which means that the probability of climate extreme events is greater than that of weather extreme events.These results suggested that there were fractional derivative relationships between the monthly,yearlyaverage air temperature anomaly series(time series of climate elements)and daily average air temperature anomaly series(time series of weather elements), the calculated order ofderivative were 0.524 and 0.83,respectively.
Research on characteristics of time series of weather and climate factors and theirrelationship will improve our understanding on effect of weather and climate extreme events, and willenhance our abilityon simulation and prediction of weather and climate extreme events. In this paper, the average air temperature anomaly time series with different time scales(daily,monthly and yearly scales) from 1951 to 2010 in Shenyang city were selected,which represents the time series of weather and climate factors. The characteristics of autocorrelation and long-trail probability distribution for these time series was analyzed by using the autocorrelation function and the normalized probability density function. Furthermore, thefractional derivative relationships between monthly, yearly average air temperature anomaly and daily average air temperature anomaly were established by using second order structure function,i.e., the fractional order derivative relationship between the time series of climate and weather factors. The results showed that the time series of daily, monthly, and yearly average air temperature anomaly in Shenyang city presented the characteristics of non-memory, short-term memory and long-term memory, respectively. The normalized probability function of yearlyaverage air temperature anomaly series showed obvious long-tail trait, compared to that of daily and monthly air average temperature anomaly series. Which means that the probability of climate extreme events is greater than that of weather extreme events.These results suggested that there were fractional derivative relationships between the monthly,yearlyaverage air temperature anomaly series(time series of climate elements)and daily average air temperature anomaly series(time series of weather elements), the calculated order ofderivative were 0.524 and 0.83,respectively.
引文
[1]时少英,刘式达,付遵涛,等.天气和气候的时间序列特征分析[J].地球物理学报,2005,48(2):259-264.
[2]DMOW SKA R,SALTZMAN B.Advance in Geophysics:Long-range Persistence in Geophysical Time Series[M].San Diego,London.Boston,New York,Sydney,Tokyo,Toronto:Academic Press,1999:14-16.
[3]LORENZ E N.Deterministic nonperiodicflow[J].J Atmos Sci,1963,20(22):130-141.
[4]刘式达,时少英,刘式适,等.天气和气候之间的桥梁—分数阶导数[J].气象科技,2007,35(1):15-19.
[5]HASSELMANN K.Stochastic climate model Part I,Theory[J].Tellus,1976,28:473-485.
[6]刘式达,刘式适.物理学中的分形[M].北京:北京大学出版社,2014:263-267.
[7]刘式达,袁乃明,付遵涛,等.气候变化的长期记忆性[J].中国科学,2013,13(10):1327-1331.
[8]王在华.分数阶微积分:描述记忆特性与中间过程的数学工具[J].科学中国人,2011(3):76-78.
[9]徐明瑜,谭文长.中间过程、临界现象——分数阶算子理论、方法、进展及其在现代力学中的应用[J].中国科学G辑,2006,36(3):225-238.
[10]丁裕国,江志红.气象数据时间序列信号处理[M].南京:气象出版社,1998:26-28.
[11]陈昭.时序非平稳性ADF检验法的理论与应用[J].广州大学学报(自然科学版),2008(5):5-10.
[12]董祺.近似白噪声序列的一种判别方法[J].火控技术,1981(1):1-3.
[13]梁光明,唐玉鹏,孙即祥,等.基于概率分布均衡技术的归一化算法及在模式识别中的应用[J].信号处理,2009,25(4):636-638.
[14]陈文,孙洪广,李西成,等.力学与工程问题的分数阶导数建模[M].北京:科学出版社,2010:3-6.
[2]DMOW SKA R,SALTZMAN B.Advance in Geophysics:Long-range Persistence in Geophysical Time Series[M].San Diego,London.Boston,New York,Sydney,Tokyo,Toronto:Academic Press,1999:14-16.
[3]LORENZ E N.Deterministic nonperiodicflow[J].J Atmos Sci,1963,20(22):130-141.
[4]刘式达,时少英,刘式适,等.天气和气候之间的桥梁—分数阶导数[J].气象科技,2007,35(1):15-19.
[5]HASSELMANN K.Stochastic climate model Part I,Theory[J].Tellus,1976,28:473-485.
[6]刘式达,刘式适.物理学中的分形[M].北京:北京大学出版社,2014:263-267.
[7]刘式达,袁乃明,付遵涛,等.气候变化的长期记忆性[J].中国科学,2013,13(10):1327-1331.
[8]王在华.分数阶微积分:描述记忆特性与中间过程的数学工具[J].科学中国人,2011(3):76-78.
[9]徐明瑜,谭文长.中间过程、临界现象——分数阶算子理论、方法、进展及其在现代力学中的应用[J].中国科学G辑,2006,36(3):225-238.
[10]丁裕国,江志红.气象数据时间序列信号处理[M].南京:气象出版社,1998:26-28.
[11]陈昭.时序非平稳性ADF检验法的理论与应用[J].广州大学学报(自然科学版),2008(5):5-10.
[12]董祺.近似白噪声序列的一种判别方法[J].火控技术,1981(1):1-3.
[13]梁光明,唐玉鹏,孙即祥,等.基于概率分布均衡技术的归一化算法及在模式识别中的应用[J].信号处理,2009,25(4):636-638.
[14]陈文,孙洪广,李西成,等.力学与工程问题的分数阶导数建模[M].北京:科学出版社,2010:3-6.