气候统计的新武器——集合经验模态分解EEMD（官方matlab版、民间fortran版）

hillside

     据网帖（http://www.ilovematlab.cn/thread-163985-1-1.html）介绍，EEMD是针对EMD方法的不足,提出了一种噪声辅助数据分析方法。EEMD分解原理为:当附加的白噪声均匀分布在整个时频空间时,该时频空间就由滤波器组分割成的不同尺度成分组成。当信号加上均匀分布的白噪声背景时,不同尺度的信号区域将自动映射到与背景白噪声相关的适当尺度上去。当然,每个独立的测试都可能会产生非常嘈杂的结果,这是因为每个附加噪声的成分都包括了信号和附加的白噪声。既然在每个独立的测试中噪声是不同的,当使用足够测试的全体均值时,噪声将会被消除。全体的均值最后将会被认为是真正的结果,唯一持久稳固的部分是信号本身,所 加入的多次测试是为了消除附加的噪声。
　　EEMD的全称为Ensemble Empirical Mode Decomposition (集合经验模分解)(Wu and Huang, 2009)，它是EMD（经验模分解）(Huang et al. 1998; Huang and Wu, 2008)的改进算法，有效地解决了EMD的混频现象。

        魏凤英《现代气候统计诊断与预测技术》仅介绍了EMD与EMD-HTT方法。
       EEMD在气候学中的应用正逐渐增加。国内的研究还比较薄弱，相信将会继续增加。

                                                                                EEMD在气候学研究中的一些实例
实例1：
Franzke, Christian, 2012: Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature. J. Climate, 25, 4172–4183.
doi: http://dx.doi.org/10.1175/JCLI-D-11-00293.1
Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Christian Franzke

British Antarctic Survey, Cambridge, United Kingdom

Abstract

This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

Keywords: Climate change, Climate variability, Time series, Trends

Received: May 26, 2011; Final Form: December 5, 2011

Corresponding author address: Dr. C. Franzke, British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, United Kingdom. E-mail: chan1@bas.ac.uk

实例2：台湾“气候变迁研究联盟”（http://cclics.rcec.sinica.edu.tw/home/index.php?f=contentShow&id=464&courseID=43）在《自然年代際變化與人為暖化氣候變遷》研究计划页面介绍了所用方法：
     所用資料與方法如下。
    利用EOF、SVD、wavelet、HHT（EEMD）等方法，分析下列資料診斷年代（際）變化的特徵：

• NCEP、ERA40、20 Century Reanalysis 等大氣資料
• CRU、HadISST、APHRODITE 等由測站資料整理出的全球或大區域網格資料
• SODA、GFDL、OFES 等利用海洋模式同化系統產出的海表與海下的長期資料
• CCSM/CESM 長期（數百年）模擬資料
• CMIP3/CMIP5 模擬資料，包括工業革命前與20 世紀模擬，以及情境模擬資料
  

     本項研究將以滾動的方式進行，不易分年切割研究項目，將視需要隨時比對觀測與模擬資料以及進行必要的數值機制模擬。

       EEMD目前的主流网页是台湾中央大学数据分析方法研究中心（http://rcada.ncu.edu.tw/research1_clip_ex.htm）提供的MATLAB版本，国内的PUDN、CSDN多是如此。fortran版难寻踪影。然而，对于FORTRAN程序的爱好者来说，fortran程序的价值是无可替代的，再说MATLAB是商业软件，比不上fortran程序用得舒坦。

                                                                     EEMD唯一官方版-matlab

官网地址：

http://rcada.ncu.edu.tw/research1_clip_program.htm

HHT MATLAB program   runcode package [download]

The current MATLAB program of HHT includes the following modules:

1)      eemd.m. The module that performs EMD/EEMD;

2)      ifndq.m. The module that calculates an instantaneous frequency for a given IMF; and

3)      extrema.m. A supporting module that is used by the previous two modules.

4)    significance.m This is used to obtain the "percenta" line based on Wu and Huang  (2004).

5)    dist_value.m  This is a utility program being called by "significance.m".

6)    nnspe.m Compute the Hilbert-Huang Spectrum of energy

7)    significanceIMF  

The modules of the program are suggested to be in a folder (for example folder “EEMD”) under the MATLAB “toolbox” folder (C:\MATLAB6p5\toolbox\EEMD). By adding the MATLAB path to that directory, the programs are ready to be used. Some interface related information is given in each program. The “help” command can be used to get these information.

The above programs are the preliminary version of an HHT software. In future, more modules that provide more features such statistical test, calculation of marginal spectrum, and visualization in time-frequency-energy domain, will be added.

2014年10月26日增补：因近期台湾中央大学原网址无法访问，一网友希望上传原始文件。现将本人曾下载的中文大学网站原有文件打包为“EEMD(下载于台湾中央大学)”，链接见附件。

                                                                     EEMD难得一见的民间版-fortran版

     经过搜索，本人找到了一个fortran版本，现飨有意一阅与可能使用的网友。
https://github.com/mathnathan/EEMD/tree/master/eemdf90
EEMD / eemdf90 /

Fixed the show function. Working on bug in F90 Spline code

latest commit 3b18046d95

                               
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mathnathan authored 2 months ago

	..
	test	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	CMakeLists.txt	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	cppcall.cpp	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	cppeemd	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	eemd.common	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	eemd.f90	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	gasdev.f90	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	gsta.dat	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	libf90eemd.a	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	makefile	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	min_max.f90	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	natural_spline.f90	2 months ago	Fixed the show function. Working on bug in F90 Spline code [mathnathan]
	newfort.txt	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	runEEMD.f90	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	standev.f90	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	tempEEMD.ctl	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	tempEEMD.dat	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]
	tempTS.dat	3 months ago	Added Fortran90 eemd backend and finished meemd prototype [Nathan Crock]

注：上述程序看来似乎是一些子例程，我未使用过，仅供参考。

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晚晴山

来个全套的撒~

budapestw

正在学习研究中 楼主辛苦了

www237036

集合数量多少算合理呢？

a平和a

谢谢楼主，正在学习中

congxiaochong

太给力了  正好马上要开始学习这个方法了~~谢谢楼主分享

vip545

哇  太感谢了

2006202788

是很有用   留着以后慢慢消化

冋菿{棉花糖}

上面“EEMD唯一官方版-matlab”中的M文件点击进去无法显示网页，请问您已经下载好了吗？可否上传以便下载呢？非常感谢

hillside

冋菿{棉花糖} 发表于 2014-10-25 10:57
上面“EEMD唯一官方版-matlab”中的M文件点击进去无法显示网页，请问您已经下载好了吗？可否上传以便下载呢 ...

已上传，需要的网友可下载本帖附件。