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Yu-Chiao Liang, Matthew R. Mazloff, Isabella Rosso, Shih-Wei Fang, and Jin-Yi Yu

data, such as optimal interpolation ( Reynolds and Smith 1994 ; Schneider 2001 ), model-based gap-filling techniques (e.g., data assimilation; Stammer et al. 2002 ; Wunsch and Heimbach 2007 ; Mazloff et al. 2010 ; Verdy and Mazloff 2017 ), and empirical orthogonal function (EOF)-based methods (e.g., Smith et al. 1996 ; Kaplan et al. 1997 ; Beckers and Rixen 2003 ; Alvera-Azcárate et al. 2005 ; Kondrashov and Ghil 2006 ; Alvera-Azcárate et al. 2007 ; Alvera-Azcárate et al. 2011

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Christopher Dupuis and Courtney Schumacher

1. Introduction Empirical orthogonal functions (EOFs) are an important part of spatial analysis of oscillations and have been an especially popular technique in the atmospheric sciences since the 1950s ( North et al. 1982 ). However, EOFs have more frequently been applied to model datasets since there is currently no theoretically exact way to connect EOF analysis to nonequispaced data. “Nonequispaced” (alternatively “gappy,” “irregularly spaced,” or “unevenly spaced”) in this context refers to

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Yuxin Zhao, Dequan Yang, Wei Li, Chang Liu, Xiong Deng, Rixu Hao, and Zhongjie He

, the amount of data available for ocean regions has increased dramatically, providing support for the application of statistical forecast methods in ocean regions. The empirical orthogonal function (EOF) analysis method, also known as principal component analysis (PCA), is used to extract dominant feature vectors from feature structures in analysis matrix data ( Jolliffe 2002 ; Pearson 1901 ). Lorenz (1963) introduced the EOF into meteorological research for the first time in the 1950s, and

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Marc H. Taylor, Martin Losch, Manfred Wenzel, and Jens Schröter

1. Introduction Empirical orthogonal function (EOF) analysis, called principal component analysis (PCA) in other disciplines, is commonly used in climate research as a tool to analyze meteorological fields with high spatiotemporal dimensionality. The leading EOF modes will typically describe large-scale dynamical features in the field, and reconstruction of the field using a truncated subset of EOFs can filter out small-scale features or noise. Furthermore, EOF truncation may be useful for

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Jung-Eun Chu, Bin Wang, June-Yi Lee, and Kyung-Ja Ha

interacts with the ISM and the East Asian summer monsoon (EASM). A number of statistical studies have attempted to explain the characteristics of the BSISO in terms of their spatial patterns and propagation. By using empirical orthogonal function (EOF) analysis, Lau and Chan (1986) found that the dominant EOF modes of outgoing longwave radiation (OLR) over the Indian Ocean–western Pacific region during the northern summer showed a dipole pattern with the convection centered over the Indian Ocean and

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Adam H. Monahan, John C. Fyfe, Maarten H. P. Ambaum, David B. Stephenson, and Gerald R. North

1. Introduction Since its introduction to meteorology by Edward Lorenz ( Lorenz 1956 ), empirical orthogonal function (EOF) analysis—also known as principal component analysis (PCA), the Karhunen–Loève transform, or proper orthogonal decomposition—has become a statistical tool of fundamental importance in atmosphere, ocean, and climate science for exploratory data analysis and dynamical mode reduction (e.g., the recent review by Hannachi et al. 2007 ). In particular, it has become common to

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Tao Lian and Dake Chen

1. Introduction Since the introduction of empirical orthogonal function (EOF) analysis in atmospheric science by Lorenz (1956) , this simple yet effective method has been used extensively in atmospheric, oceanic, and climatic research. The essence of EOF analysis is to identify and extract the spatiotemporal modes that are ordered in terms of their representations of data variance. Because a small number of leading modes usually account for most of the total variance, EOF analysis enables one

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Gerald R. North

I MARCH 1984 GERALD R. NORTH 879Empirical Orthogonal Functions and Normal Modes GERALD R. NORTHGoddard Laboratory for Atmospheric Sciences, NASA/Goddard Space Flight Center, Greenbelt, MD 20771(Manuscript received 9 September 1983, in final form 16 November 1983) ABSTRACT An attempt to provide ~hysical

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Bryan C. Weare and John S. Nasstrom

JUNE 1982 BRYAN C. WEARE AND JOHN S. NASSTROM 481Examples of Extended Empirical Orthogonal Function Analyses BRYAN C. WEARE AND JOHN S. NASSTROMDepartment of Land, Air and Water Resources, University of California, Davis 95616(Manuscript received 23 November 1981, in final form 21 January 1982)ABSTRACT An extended empirical orthogonal function analysis technique is described which expands a data set

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Roberta Quadrelli, Christopher S. Bretherton, and John M. Wallace

1. Introduction It is known that the eigenvalues and empirical orthogonal functions (EOFs) for a finite sample are only estimates of the “true” eigenvalues and eigenvectors that would be perfectly recovered from an infinite size dataset. North et al. (1982) derived an explicit form for the first-order errors in the eigenvalues λ i of the covariance matrix for a sample of T independent realizations in time. The resulting formula, where ε = T  −1/2 , has been extensively used to estimate

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