基于非线性时间序列分析方法的气候突变检测研究

【作者】 龚志强；

【导师】 封国林；

【作者基本信息】 扬州大学 ， 理论物理， 2006， 硕士

【摘要】 全球变化已成为当代科学界瞩目的新领域,气候变化是其研究的核心内容之一,它受到各国政府的极大重视。气候突变是气候变化的重要表现形式之一,是一个典型的物理学与气候学的交叉性科学研究课题,是非线性科学研究的重要领域。目前对气候突变的研究主要针对代用资料,运用传统的统计学方法进行处理,尽管取得了不少进展,但气候系统的非线性、多层次性和非平稳性对分析和检测气候突变的方法提出了较高的要求。基于非线性科学的最新研究成果,本文的主要研究内容如下:(1)本文介绍了经验模态分解(Empirical Mode Decomposition , EMD)、希尔伯特变换(Hilbert Transformation,HT)、小波分解(Wavelet Decomposition,WD)和小波变换(Wavelet Transformation,WT)的主要思想,并利用理想时间序列和青藏高原古里雅冰芯18O时间序列,系统地分析比较了EMD和小波分解(Wavelet Decomposition ,WD)以及HT和小波变换(Wavelet Transformation ,WT)处理非线性时间序列时的优缺点,并针对它们的分解结果中均存在虚假分量这一问题,提出了基于两种分解结果的相关性分析方法,在一定程度上实现了去除虚假分量并找到包含原序列最显著信息的主要分量。研究结果表明,将基于EMD的方法和基于WD的方法有机结合起来应用,可以更有效地识别原时间序列不同尺度(周期)的主要特征信息。(2)在上述工作的基础上,引入Bernaola Galvan等提出的能够将非平稳序列分割为多个不同尺度的自平稳子序列的启发式分割算法(下文简称BG算法),并应用于非平稳时间序列的突变检测。通过数值试验验证了BG算法处理非平稳时间序列的有效性和尖峰噪声、随机扰动等对检测结果的影响较小。同时,基于滤波方法对近2000年北半球树木年轮宽度和北京石花洞石笋微层厚度距平序列进行以100a尺度为界限的高低频信号分离处理,并应用BG算法对高频和低频信号分别进行处理,试图检测和分析其中包含的各种尺度的气候突变事件,区分不同性质的突变,并揭示其变化的物理机制。定义了新的物理量-突变密度,对比前后千年内更多还原

【Abstract】 Global change science is a new research domain nowadays, and one of the most imp ortant studies of which is the climate change, to which great attention is paid by all governments in world. Abrupt climate change (ACC) is one of most important manifestation of climate change, is a integrative science of physics and climatology. Nowadays, studies on ACC are mainly based on proxy data using traditional statistical methods and have made some progresses, however, the non-linearity, multi-hierarchies and nonstationarity of climate system make it more difficult to analyze and detect ACC and put forward much higher requirement for the detecting methods. Based on the newest research production of nonlinear science, the main content of this thesis is as follows:1. This thesis introduced the main idea of the Hilbert transformation (HT), empirical mode decomposition (EMD), wavelet decomposition (WD) and wavelet transformation (WT), then, in the context of an ideal time series and the Guliya (located in Tibetan plateau) ice core (GIC)δ18O time series, merits and defects of EMD and WD as well as HT and WT in the nonlinear time series analysis are systematically analyzed, and aiming at the generation of the false components during their decomposing process, the author presented the method of correlation analysis based on their decomposing results, on which the false components might be wiped off and the remarkable signals of the original time series concentrate be picked out. Research results show that the combination of the EMD and the WD is able to more effectively identify the characteristic signals of the original series.2. This thesis introduced a new method-heuristic segmentation algorithm (briefly BG algorithm) which can divide a nonstationary time series into a series of self-stationary subsets, and appliedthis method to detect abrupt changes of nonstationary time series. Numerical test show that spike noise or random white noise had little更多还原