基于分形理论的安庆气候变化分析
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摘要
在当今的世界格局下,对全球气候变化的趋势的研究逐渐成为国际社会关注的焦点。气候变化在人类社会的发展过程占据着重要位置,它直接影响着人类的生存生产,它的任何变化都将直接影响到自然系统和社会生态系统的平衡。如今,以全球气候变暖为中心的氛围下,气候变化将会给人类社会发展带来严重的影响和危害,这也必然影响和制约着我国推行的可持续发展战略。
近些年来,人们尝试着用各种方法来研究城市的气候变化趋势,并且取得了重要成果。本文运用了多重分形、联合多重分形以及多重分形消除趋势波动分析法分析安徽省安庆市的部分气象数据资料,得到一些结论如下：
(1)运用多重分形理论分析,发现安庆近四十几年的日平均气温与日平均气压均存在多重分形现象,具有分形特性；并且,在过去几十年,日平均气温的多重分形特性强于日平均气压的多重分形特性,日平均气温的波动程度比日平均气压的波动程度强；安庆处在日平均气温较高的机会比处在较低的机会大,处在日平均气压较低的机会比处在较高的机会大,两者的关系是相反的。
(2)运用联合多重分形分析安庆的日平均气温与日平均气压的关系,发现当气温较高时,气压处在较低的可能性比较大；当气温较低时,气压处在较高的可能性比较大,这一结论与大气热力环流理论是一致的。
(3)采用多重分形消除趋势波动分析法(MF-DFA法)分析安庆最近四十多年的四个季度的日平均气温,发现安庆春秋两季的日平均气温具有较弱的短程相关性,夏冬两个季度的日平均气温具有一定的长程相关性。未来一段时间内安庆的春季和秋季的日平均气温上升的趋势不太明显,与过去有较弱的相反性；未来一段时间内夏季和冬季的日平均气温将可能保持继续上升的状态。简而言之,未来几十年里安庆的春秋两季可能会变的比较凉爽,夏季会变得更加炎热,冬季会变得越来越暖和。
Under the modern world pattern, the international society pays great attention to the research of global weather change in trend. The weather variety relates to the mankind's existence and production, which also has serious impact on the mankind social development process, and any varieties of the weather will directly infect the natural system and the social eco-system. Now, under the central atmosphere of that the global weather is becoming warm, the weather variety will bring serious influence and bane to the social development, and it will also infect and limit the sustainable development strategy in our country.
In recent several decades, people have tried various useful methods to study the weather variety in trend, and obtained many succeed results. In this paper, it has used multifractal theoy、joint multifractal theory and R/S analysis to analyses the weather data in Anhui province of Anqing city, and has got some useful conclusion to the weathers forecast, which can be listed as follows.
(1) Based on multifractal analysis, we find that the air temperature and atmospheric pressure of Anqing have multifractality. Beside that, the multifractality of day average air temperature is stronger than the multifractality of day average atmospheric pressure, and the fluctuation extent of day average air temperature is stronger than the multifractality of day average atmospheric pressure; it also means that the opportunity of Anqing being in high temperature is more possible than Anqing being in low temperature, and the opportunity of Anqing being in low atmospheric pressure is more possible than Anqing being in high atmospheric pressure, both of them are contrary.
(2) Based on joint multifractal analysis, it has got the relationship between air temperature and atmospheric pressure, and this conclusion is consistent with thermodynamics theory. When the air temperature is high, the atmospheric pressure is more possible to be low; when the air temperature is low, the atmospheric pressure is more possible to be high.
(3)It has used multifractal and detrended fluctuation analysis method, to analyses the seasonal average temperature of Anqing in recent several decades, and find that the day average air temperature in spring and autumn has short range correlation, and in summer and winter has long range correlation. In other words, the trend of temperature in spring and autumn of future is weakly opposite to the past, the temperature in them will not be possible to rise. The trend of temperature in summer and winter of future will continue to rise. In a word, in the future of several decades, the weather of Anqing in spring and autumn will become cooler, in summer will become hotter and in winter will become warmer.
近些年来,人们尝试着用各种方法来研究城市的气候变化趋势,并且取得了重要成果。本文运用了多重分形、联合多重分形以及多重分形消除趋势波动分析法分析安徽省安庆市的部分气象数据资料,得到一些结论如下：
(1)运用多重分形理论分析,发现安庆近四十几年的日平均气温与日平均气压均存在多重分形现象,具有分形特性；并且,在过去几十年,日平均气温的多重分形特性强于日平均气压的多重分形特性,日平均气温的波动程度比日平均气压的波动程度强；安庆处在日平均气温较高的机会比处在较低的机会大,处在日平均气压较低的机会比处在较高的机会大,两者的关系是相反的。
(2)运用联合多重分形分析安庆的日平均气温与日平均气压的关系,发现当气温较高时,气压处在较低的可能性比较大；当气温较低时,气压处在较高的可能性比较大,这一结论与大气热力环流理论是一致的。
(3)采用多重分形消除趋势波动分析法(MF-DFA法)分析安庆最近四十多年的四个季度的日平均气温,发现安庆春秋两季的日平均气温具有较弱的短程相关性,夏冬两个季度的日平均气温具有一定的长程相关性。未来一段时间内安庆的春季和秋季的日平均气温上升的趋势不太明显,与过去有较弱的相反性；未来一段时间内夏季和冬季的日平均气温将可能保持继续上升的状态。简而言之,未来几十年里安庆的春秋两季可能会变的比较凉爽,夏季会变得更加炎热,冬季会变得越来越暖和。
Under the modern world pattern, the international society pays great attention to the research of global weather change in trend. The weather variety relates to the mankind's existence and production, which also has serious impact on the mankind social development process, and any varieties of the weather will directly infect the natural system and the social eco-system. Now, under the central atmosphere of that the global weather is becoming warm, the weather variety will bring serious influence and bane to the social development, and it will also infect and limit the sustainable development strategy in our country.
In recent several decades, people have tried various useful methods to study the weather variety in trend, and obtained many succeed results. In this paper, it has used multifractal theoy、joint multifractal theory and R/S analysis to analyses the weather data in Anhui province of Anqing city, and has got some useful conclusion to the weathers forecast, which can be listed as follows.
(1) Based on multifractal analysis, we find that the air temperature and atmospheric pressure of Anqing have multifractality. Beside that, the multifractality of day average air temperature is stronger than the multifractality of day average atmospheric pressure, and the fluctuation extent of day average air temperature is stronger than the multifractality of day average atmospheric pressure; it also means that the opportunity of Anqing being in high temperature is more possible than Anqing being in low temperature, and the opportunity of Anqing being in low atmospheric pressure is more possible than Anqing being in high atmospheric pressure, both of them are contrary.
(2) Based on joint multifractal analysis, it has got the relationship between air temperature and atmospheric pressure, and this conclusion is consistent with thermodynamics theory. When the air temperature is high, the atmospheric pressure is more possible to be low; when the air temperature is low, the atmospheric pressure is more possible to be high.
(3)It has used multifractal and detrended fluctuation analysis method, to analyses the seasonal average temperature of Anqing in recent several decades, and find that the day average air temperature in spring and autumn has short range correlation, and in summer and winter has long range correlation. In other words, the trend of temperature in spring and autumn of future is weakly opposite to the past, the temperature in them will not be possible to rise. The trend of temperature in summer and winter of future will continue to rise. In a word, in the future of several decades, the weather of Anqing in spring and autumn will become cooler, in summer will become hotter and in winter will become warmer.
引文
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[2]孙霞,吴自勤等.分型原理及其应用(第一版)[M].合肥：中国科学技术大学出版社,2003.10：23-88.
[3]沙震,阮火军.分形与拟合(第一版)[M].杭州：浙江大学出版社,2005.3：1-188.
[4]曾文曲,王向阳等译.分形几何中的技巧(第一版)[M].沈阳：东北大学出版社,1999.6：22-242.
[5]徐新阳,康雁等.分形漫步(第一版)[M].沈阳：东北大学出版社1994.12：1-189.
[6]刘丹.实用分形图像学(第一版)[M].大连：大连海事大学出版社,2001.6：1-146.
[7]谢和平.分形最新进展与力学中的分形[J].力学与实践,1993,15(2)：9-18.
[8]卢方元.中国股市收益率的多重分形分析[J].系统工程理论与实践,2004.6：50-52.
[9]施锡铨,艾克风.股票市场风险的多重分形分析[J].统计研究,2004.9：33-35
[10]于宁莉,易东云.基于股市交易数据流的场景记忆模型[J].系统工程,2006,10：13-14.
[11]何建敏,常松.中国股票市场多重分形游走及其预测[J].中国管理科学,2002,10(3)：11-17.
[12]郑婷婷,毛军军等.蛋白质序列中的多重分形分析[J].计算机工程与应用,2007,43(20)：46-48.
[13]Zu-Guo Yu, Vo Anh, Ka-Sing Lau. Chaos game representation of proteim sequences based on the detailed HP model and their multifractal and correlation analyses[J]. Journal of Theoretical Biology 2004.226:341-348.
[14]Zu-Guo Yu, Vo Anh, Ka-Sing Lau. Fractal analysis of measure representation of large proteins based on the detailed HP model[J].Physica A,2004.337:171-184.
[15]许娜,商朋见等.气温变化时间序列的复杂性分析[J].北京交通大学学 报,2008,32(3)：98-101.
[16]冯德益,刘喜兰等.大地震活动的模糊时间分维特征[J].中国地震,1991,7(4)：1-10.
[17]冯德益,刘喜兰等.模糊分维及其在地震研究中的某些应用[J].地球物理学报,1992,35(4)：459-467.
[18]张永平,谢和平.模糊分形与动态分形[J].自然杂志,2010,13(02)：67-69
[19]李彤,商朋见.多重分形在掌纹识别中的研究[J].物理学报,2007.56(08)：4393-4397.
[20]卓晴,王文渊等.一种利用分形压缩指纹图像的方法[J].中国图像图形学报,1989,4(03)：215-218.
[21]蒋爱平,杨悦华等.基于多重加权法的多重分形图像分割研究[J].中国图像图形学报,2007,12(10)：1889-1892.
[22]Multifractal Characteristics of Palmprint and Its Extracted Algorithm[J].Applied Mathematical Modelling.2009,33(12):4378-4380.
[23]周厚云,刁桂仪.用海岸线分形计算方法对气候变化复杂性的初步研究[J].地球化学,1999,28(01)：80-86.
[24]陈伟,周株妹.基于气象卫星分形纹理的云雾分离研究[J].自然灾害学报,2003,12,(02)：133-139.
[25]江田汗.我国近百年气温的非趋势波动分析[J].气象科学,2004.24(2)：200-204.
[26]江田汗.全球气温变化的多重分形谱[J].热带气象学报,2004,20(6)：673-678.
[27]冯新灵,罗隆诚.中国雨日变化趋势的分形研究[J]. 自然灾害学报,2009,18,(06)：112-117
[28]冯新灵,冯自立等.青藏高原气候变化趋势的R/S分析及Hurst指数实验研究[J].干旱区地理,2008,31(2)：175-179.
[29]许娜,商朋见等.气温变化时间序列的复杂性分析[J].北京交通大学学报,2008,32(3)：98-101.
[30]Qiang Zhang, Chong-YuXu. Multi fractal analysis of streamflow records of the East River basin (Pearl River), China [J].Physica A,2009,388:927-934.
[31]Jonas Olsson, Janusz Niemczynowicz. Multifractal analysis of daily spatial rainfall distributions[J].Journal of Hydrology,1996,187:29-43.
[32]M.C.Breslin, J.ABelward. Fractal dimensions for rainfall time series[J].Mathematics and Computer in Simulation,1999,48:437-446.
[33]S.Lovejoy, D.Schertzer. Multifractals, cloud radiances and rain [J].Journal of Hydrology,2006,322,59-88.
[34]F.J.Jimenez-Hornero, P.Pavon-Dominguez. Joint multifulfractal description of the relationship between wind patterns and land surface air temperature[J].Atmospheric Research,2011,99:366-376.
[35]Charles Meneveau, K.R.Sreenivasan, et al Joint multifractal measures:Theory and applications to turbulence[J].Physical Review A,1990,41 (2):894-913.
[36]陈双平,韩凯等.染色体碱基序列的联合多重分形分析[J].电子与信息学报,2008,30(02)：298-301.
[37]Alexandra N.Kravchenko, Donald G.Bullodk.Joint Multifractal Analysis of Crop Yield and Terrain slope[J].Agronomy Journal,2000,11-12(92):1279-1290.
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