A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

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Ensemble empirical mode decomposition: a noise-assisted data analysis method

The Analysis of Time Series: An Introduction, 4th edn. By C. Chatfield. ISBN 0 412 31820 2. Chapman and Hall, London, 1989. 242 pp. £13.50.

The Analysis of Time Series: An Introduction

Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.

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A study of the characteristics of white noise using the empirical mode decomposition method

[1] We review evidence for climate change over the past several millennia from instrumental and high-resolution climate “proxy” data sources and climate modeling studies. We focus on changes over the past 1 to 2 millennia. We assess reconstructions and modeling studies analyzing a number of different climate fields, including atmospheric circulation diagnostics, precipitation, and drought. We devote particular attention to proxy-based reconstructions of temperature patterns in past centuries, which place recent large-scale warming in an appropriate longer-term context. Our assessment affirms the conclusion that late 20th century warmth is unprecedented at hemispheric and, likely, global scales. There is more tentative evidence that particular modes of climate variability, such as the El Nino/Southern Oscillation and the North Atlantic Oscillation, may have exhibited late 20th century behavior that is anomalous in a long-term context. Regional conclusions, particularly for the Southern Hemisphere and parts of the tropics where high-resolution proxy data are sparse, are more circumspect. The dramatic differences between regional and hemispheric/global past trends, and the distinction between changes in surface temperature and precipitation/drought fields, underscore the limited utility in the use of terms such as the “Little Ice Age” and “Medieval Warm Period” for describing past climate epochs during the last millennium. Comparison of empirical evidence with proxy-based reconstructions demonstrates that natural factors appear to explain relatively well the major surface temperature changes of the past millennium through the 19th century (including hemispheric means and some spatial patterns). Only anthropogenic forcing of climate, however, can explain the recent anomalous warming in the late 20th century.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2003RG000143

Climate over past millennia

Climate and weather constitute a typical example where high dimensional and complex phenomena meet. The atmospheric system is the result of highly complex interactions between many degrees of freedom or modes. In order to gain insight in understanding the dynamical/physical behaviour involved it is useful to attempt to understand their interactions in terms of a much smaller number of prominent modes of variability. This has led to the development by atmospheric researchers of methods that give a space display and a time display of large space-time atmospheric data.



Empirical orthogonal functions (EOFs) were first used in meteorology in the late 1940s. The method, which decomposes a space-time field into spatial patterns and associated time indices, contributed much in advancing our knowledge of the atmosphere. However, since the atmosphere contains all sorts of features, e.g. stationary and propagating, EOFs are unable to provide a full picture. For example, EOFs tend, in general, to be difficult to interpret because of their geometric properties, such as their global feature, and their orthogonality in space and time. To obtain more localised features, modifications, e.g. rotated EOFs (REOFs), have been introduced. At the same time, because these methods cannot deal with propagating features, since they only use spatial correlation of the field, it was necessary to use both spatial and time information in order to identify such features. Extended and complex EOFs were introduced to serve that purpose.



Because of the importance of EOFs and closely related methods in atmospheric science, and because the existing reviews of the subject are slightly out of date, there seems to be a need to update our knowledge by including new developments that could not be presented in previous reviews. This review proposes to achieve precisely this goal. The basic theory of the main types of EOFs is reviewed, and a wide range of applications using various data sets are also provided. Copyright © 2007 Royal Meteorological Society

Empirical orthogonal functions and related techniques in atmospheric science: A review

[1] The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

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A. Saunders

Papers

Advanced spectral methods for climatic time series