近似熵对气候突变检测的适用性研究
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摘要
近似熵是一种定量度量时间序列复杂性的非线性动力学指数,已被用于时间序列的动力学结构突变检测中,但已有的研究仅仅针对理想模型的时间序列进行了性能测试,对于其在实际观测资料中的适用性问题尚未系统地进行研究。鉴于此,本文开展了近似熵的适用性研究,系统地测试了近似熵在气候突变检测中的性能。许多观测资料中存在着各种各样的趋势,如季节变化引起的周期性趋势、全球变暖所造成的线性趋势、多项式趋势等。并且观测数据中经常包含噪声和扰动等一些虚假的信息。因此,本文首先研究了各种趋势和不同噪声对滑动移除近似熵的影响。其次,利用天气发生器模拟产生了大量长时间序列的温度和降水资料,研究了滑动移除近似熵在气温、降水等气象要素动力学结构突变检测中的适用性。最后,应用滑动移除近似熵方法对中国西北地区的降水量、PDO指数等资料进行了气候突变检测,测试了滑动移除近似熵方法在实际观测资料中的突变检测性能。主要研究结果如下：
(1)各种趋势对滑动移除近似熵突变检测结果的影响较小。通过大量数值试验,测试了非线性理想时间序列中的周期趋势、线性趋势、二阶多项式趋势以及更高阶多项式趋势信号对于滑动移除近似熵方法突变检测结果的影响程度,发现这些平稳和非平稳趋势信号对滑动移除近似熵检测结果的影响较小。
(2)滑动移除近似熵具有较强的抗干扰能力。通过分析尖峰噪声、高斯白噪声对滑动移除近似熵突变检测的影响,发现时间序列中所含尖峰噪声的数目占原序列长度的比例和尖峰噪声的大小对滑动移除近似熵的突变检测结果影响较小,表明滑动移除近似熵方法对尖峰噪声具有较强的抗噪能力。当对长度为2000的非线性理想时间序列加入高斯白噪声,对于不同长度的滑动子序列,可检测到突变点的信噪比临界值均约为22dB,这可能与样本量的大小有关系,表明滑动移除近似熵对高斯白噪声也具有较强的抗干扰能力。
(3)无论是对于大量的模拟资料,还是对于实际观测资料,滑动移除近似熵方法均能够有效地检测气候突变。探讨滑动移除近似熵对不同气象要素动力学结构突变检测的适用性,基于天气发生器产生了逐日最高气温、逐日最低气温、逐日降水量三种气象要素,并分别对三种气象要素构造了1000条具有动力学结构突变的序列。用滑动移除近似熵对各气象要素的1000条序列分别进行了突变检测,并结合滑动t-检验方法对检测得到的近似熵序列进行了诊断分析,结果显示三种气象要素的1000条序列中绝大多数序列的突变点均可被滑动移除近似熵方法准确地检测到,表明滑动移除近似熵方法适用于逐日最高气温、逐日最低气温、逐日降水量等三种气象要素动力学结构突变的检测。同时,滑动移除近似熵方法对我国西北地区榆中、临夏等气象观测站1960-2006年的逐日降水资料和1960-2006年的逐月PDO指数资料的突变检测结果均与已有研究结论一致,这进一步证实了滑动移除近似熵检测突变的可靠性,为该方法的广泛应用打下了坚实的基础。
Approximate entropy is a nonlinear dynamics index of quantitatively measuring the complex of the time series and it has been used for abrupt dynamic detection of time series, but the existing researches are only for the performance tests of ideal model time series and the applicability in the actual observations has not been systematically studied. In view of this, we develop the applicability of approximate entropy and test the performance of approximate entropy in the detection of abrupt climate change. Various trends exist in many observation data, such as periodical trends caused by seasonal variation, linear trends and polynomial trends brought about by global warming. In addition, observational data often contains noises, disturbances and some other false information. In order to research the applicability of abrupt climatic change detection of the approximate entropy, in present paper, firstly the effects of various trends and different noises on moving cut data-Approximate Entropy are investigated. Secondly, we use weather generator to simulate a large number of long time series of temperature and precipitation data and study the applicability of moving cut data-Approximate Entropy in abrupt changes detection in dynamics structures of main meteorological elements, such as temperature, precipitation, etc. At last, the abrupt climatic changes of the precipitation of China's northwestern region and the PDO index are detected by moving cut data-Approximate Entropy. We test the abrupt detection performance of moving cut data-Approximate Entropy method in the actual observation data. The main results are as follows:
(1) The detection results of moving cut data-Approximate Entropy are little affected by various trends. By doing a large number of numerical tests on model time series, we test the degree of effects of periodical trends, linear trends, second order polynomial trends and higher order polynomial trends in nonlinear ideal time series on abrupt change detection results of moving cut data-Approximate Entropy. It is indicated that the detection results of moving cut data-Approximate Entropy are little affected by these signals of stationary and non-stationary trends.
(2) Moving cut data-Approximate Entropy has strong anti-interference ability for noises. By analyzing the effects of random spikes and Gaussian white noise on abrupt change detection results of moving cut data-Approximate Entropy, we find that the abrupt change detection results of moving cut data-Approximate Entropy are little affected by the number of random spikes accounted for the length of the original time series and the size of random spikes. It is indicated that moving cut data-Approximate Entropy has strong anti-noise ability for random spikes. When Gaussian white noise is added to the nonlinear ideal time series IS1of which the length is2000, for the different lengths of sliding subsequence, the critical value of SNR at which the abrupt change points can be detected is about SNR=22dB, that may has something to do with the size of the sample. It is showed that moving cut data-Approximate Entropy also has strong anti-interference ability for Gaussian white noise.
(3) Whether for a large number of simulation data, or for the actual observation data, moving cut data-Approximate Entropy method can detect climate mutation effectively.The applicability of moving cut data-Approximate Entropy in abrupt changes detection in dynamics structures of different meteorological elements is studied. We use weather generator to generate three kinds of meteorological elements, which are daily maximum temperature, daily minimum temperature and daily precipitation, and build1000time series of three kinds of meteorological elements separately, which have abrupt changes in dynamics structures.1000time series of various meteorological elements are detected by moving cut data-Approximate Entropy separately. Then the ApEn series detected by moving cut data-Approximate Entropy are diagnostic analyzed by MTT method. The results show that vast majority of abrupt change points of the1000series of the three meteorological elements can be accurately detected by moving cut data-Approximate Entropy method, indicating that the moving cut data-Approximate Entropy method applies to abrupt changes detection in dynamics structures of three meteorological elements, such as daily maximum temperature, daily minimum temperature, daily precipitation, etc. Meanwhile, the abrupt changes detection results by moving cut data-Approximate Entropy method of daily precipitation data of the Yuzhong, Linxia meteorological observation station in Northwest China from1960to2006and monthly PDO index data from1960to2006are with the previous studies the same conclusion, which will further confirm the reliability of the moving cut data-Approximate Entropy to detect abrupt changes and lay a solid foundation for the wide applications of the present method in observational data.
(1)各种趋势对滑动移除近似熵突变检测结果的影响较小。通过大量数值试验,测试了非线性理想时间序列中的周期趋势、线性趋势、二阶多项式趋势以及更高阶多项式趋势信号对于滑动移除近似熵方法突变检测结果的影响程度,发现这些平稳和非平稳趋势信号对滑动移除近似熵检测结果的影响较小。
(2)滑动移除近似熵具有较强的抗干扰能力。通过分析尖峰噪声、高斯白噪声对滑动移除近似熵突变检测的影响,发现时间序列中所含尖峰噪声的数目占原序列长度的比例和尖峰噪声的大小对滑动移除近似熵的突变检测结果影响较小,表明滑动移除近似熵方法对尖峰噪声具有较强的抗噪能力。当对长度为2000的非线性理想时间序列加入高斯白噪声,对于不同长度的滑动子序列,可检测到突变点的信噪比临界值均约为22dB,这可能与样本量的大小有关系,表明滑动移除近似熵对高斯白噪声也具有较强的抗干扰能力。
(3)无论是对于大量的模拟资料,还是对于实际观测资料,滑动移除近似熵方法均能够有效地检测气候突变。探讨滑动移除近似熵对不同气象要素动力学结构突变检测的适用性,基于天气发生器产生了逐日最高气温、逐日最低气温、逐日降水量三种气象要素,并分别对三种气象要素构造了1000条具有动力学结构突变的序列。用滑动移除近似熵对各气象要素的1000条序列分别进行了突变检测,并结合滑动t-检验方法对检测得到的近似熵序列进行了诊断分析,结果显示三种气象要素的1000条序列中绝大多数序列的突变点均可被滑动移除近似熵方法准确地检测到,表明滑动移除近似熵方法适用于逐日最高气温、逐日最低气温、逐日降水量等三种气象要素动力学结构突变的检测。同时,滑动移除近似熵方法对我国西北地区榆中、临夏等气象观测站1960-2006年的逐日降水资料和1960-2006年的逐月PDO指数资料的突变检测结果均与已有研究结论一致,这进一步证实了滑动移除近似熵检测突变的可靠性,为该方法的广泛应用打下了坚实的基础。
Approximate entropy is a nonlinear dynamics index of quantitatively measuring the complex of the time series and it has been used for abrupt dynamic detection of time series, but the existing researches are only for the performance tests of ideal model time series and the applicability in the actual observations has not been systematically studied. In view of this, we develop the applicability of approximate entropy and test the performance of approximate entropy in the detection of abrupt climate change. Various trends exist in many observation data, such as periodical trends caused by seasonal variation, linear trends and polynomial trends brought about by global warming. In addition, observational data often contains noises, disturbances and some other false information. In order to research the applicability of abrupt climatic change detection of the approximate entropy, in present paper, firstly the effects of various trends and different noises on moving cut data-Approximate Entropy are investigated. Secondly, we use weather generator to simulate a large number of long time series of temperature and precipitation data and study the applicability of moving cut data-Approximate Entropy in abrupt changes detection in dynamics structures of main meteorological elements, such as temperature, precipitation, etc. At last, the abrupt climatic changes of the precipitation of China's northwestern region and the PDO index are detected by moving cut data-Approximate Entropy. We test the abrupt detection performance of moving cut data-Approximate Entropy method in the actual observation data. The main results are as follows:
(1) The detection results of moving cut data-Approximate Entropy are little affected by various trends. By doing a large number of numerical tests on model time series, we test the degree of effects of periodical trends, linear trends, second order polynomial trends and higher order polynomial trends in nonlinear ideal time series on abrupt change detection results of moving cut data-Approximate Entropy. It is indicated that the detection results of moving cut data-Approximate Entropy are little affected by these signals of stationary and non-stationary trends.
(2) Moving cut data-Approximate Entropy has strong anti-interference ability for noises. By analyzing the effects of random spikes and Gaussian white noise on abrupt change detection results of moving cut data-Approximate Entropy, we find that the abrupt change detection results of moving cut data-Approximate Entropy are little affected by the number of random spikes accounted for the length of the original time series and the size of random spikes. It is indicated that moving cut data-Approximate Entropy has strong anti-noise ability for random spikes. When Gaussian white noise is added to the nonlinear ideal time series IS1of which the length is2000, for the different lengths of sliding subsequence, the critical value of SNR at which the abrupt change points can be detected is about SNR=22dB, that may has something to do with the size of the sample. It is showed that moving cut data-Approximate Entropy also has strong anti-interference ability for Gaussian white noise.
(3) Whether for a large number of simulation data, or for the actual observation data, moving cut data-Approximate Entropy method can detect climate mutation effectively.The applicability of moving cut data-Approximate Entropy in abrupt changes detection in dynamics structures of different meteorological elements is studied. We use weather generator to generate three kinds of meteorological elements, which are daily maximum temperature, daily minimum temperature and daily precipitation, and build1000time series of three kinds of meteorological elements separately, which have abrupt changes in dynamics structures.1000time series of various meteorological elements are detected by moving cut data-Approximate Entropy separately. Then the ApEn series detected by moving cut data-Approximate Entropy are diagnostic analyzed by MTT method. The results show that vast majority of abrupt change points of the1000series of the three meteorological elements can be accurately detected by moving cut data-Approximate Entropy method, indicating that the moving cut data-Approximate Entropy method applies to abrupt changes detection in dynamics structures of three meteorological elements, such as daily maximum temperature, daily minimum temperature, daily precipitation, etc. Meanwhile, the abrupt changes detection results by moving cut data-Approximate Entropy method of daily precipitation data of the Yuzhong, Linxia meteorological observation station in Northwest China from1960to2006and monthly PDO index data from1960to2006are with the previous studies the same conclusion, which will further confirm the reliability of the moving cut data-Approximate Entropy to detect abrupt changes and lay a solid foundation for the wide applications of the present method in observational data.
引文
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[1]符淙斌,王强.气候突变的定义和检测方法[J].大气科学.1992,16：482-493.
[2]Alley R B, Marotzke J, Nordhaus W D, Overpeck J T. Abrupt Climate Change[J].Science.2005,299:1081056.
[3]雷内·托姆.结构稳定性与形态发生学[M].四川：四川教育出版社.1992.
[4]封国林.董文杰,龚志强,侯威,万仕全,支蓉.观测数据非线性时空分布理论和方法[M].北京：气象出版社.2006.
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[4]何文平,何涛,成海英,张文,吴琼.基于近似熵的突变检测新方法[J].物理学报.2011·60(4)：049202.
[5]Pinus S M. Approximate entropy as a measure of system complexity[J]. Proc. Natl. Acad. Sci. USA.1991,88:2297.
[6]Pincus S M, Goldberger A L. Physiological time-series analysis:what does regularity quantify? [J]. Am. J. Physiol.1994,266:H1643-H1656.
[7]Pinus S M. Approximate entropy(ApEn) as a complexity measure[J].Chaos.1995, 5(1):110-117.
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