ORIGINAL PAPER Factor analysis for El Niño signals in sea surface temperature and precipitation Christine K. Lee & Samuel S. P. Shen & Barbara Bailey & Gerald R. North Received: 24 February 2008 / Accepted: 12 August 2008 # Springer-Verlag 2008 Abstract Maximum likelihood factor analysis (MLFA) is applied to investigate the variables of monthly Tropical Pacific sea surface temperatures (SST) from Niño 1+2, Niño 3, Niño 3.4, and Niño 4 and precipitation over New South Wales and Queensland of eastern Australia, Kali- mantan Island of Indonesia, and California and Oregon of the west coast of the United States. The monthly data used were from 1950 to 1999. The November-February SST with time leads of 0, 1, 2, and 3 months to precipitation are considered for both El Niño warm phases and non El Niño seasons. Interpretations of the factor loadings are made to diagnose relationships between the SST and precipitation variables. For El Niño signals, the rotated FA loadings can efficiently group the SST and precipitation variables with interpretable physical meanings. When the time lag is 0 or 1 month, the November–February El Niño SST explains much of the drought signals over eastern Australia and Kalimantan. However, when the time lag is 2 or 3 months, the same SST cannot adequately explain the precipitation during January–May over the two regions. Communality results of five factors for precipitation indicate nearly 100% explanation of variances for Queensland and California, but the percentages are reduced to only about 30% for Oregon and Kalimantan. Factor scores clearly identify the strongest El Niño relevant to precipitation variations. Principal component factor analysis (PCFA) is also investigated, and its results are compared with MLFA. The comparison indicates that MLFA can better group SST data relevant to precipitation. The residuals of MLFA are always smaller than the PCFA. Thus, MLFA may become a useful tool for improving potential predictability of precipitation from SST predictors. 1 Introduction Factor analysis (FA) is a multivariate statistical analysis method that decomposes a covariance or correlation matrix and reduces the dimension of data (Gorsuch 1983). It has often been used in social sciences, marketing, and oper- ations research. However, its use in climate research is still rare, although some successful applications have effectively demonstrated its value. Examples include identification of dynamical modes (Walters 1999) and correlation patterns (Bartzokas and Metaxas 1995; Dinpashoh et al. 2004). The commonly used FA decomposition methods are the empirical orthogonal function (EOF) approach and the maximum likelihood (ML) approach (Johnson and Wichern 1992; Bartzokas and Metaxas 1995; Wilks 2006). The purpose of this paper is to explore the advantages of using ML factor analysis (MLFA) in climate data analysis. In the process, we further introduce the fundamentals of the method to climate research. As a computational example, MLFA is used to investigate the relationships between the Tropical Pacific sea surface temperature (SST) in Niño 1+2, Niño 3, Niño 3.4, and Niño 4 and precipitation data of five 5°×5° land grid boxes over Kalimantan of Indonesia, New South Wales and Queensland of Australia, and California and Oregon of the United States. Theor Appl Climatol DOI 10.1007/s00704-008-0056-y C. K. Lee : S. S. P. Shen (*) : B. Bailey Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA e-mail: shen@math.sdsu.edu G. R. North Department of Atmospheric Sciences, Texas A&M University, College Station, Texas 77843, USA