doi:10.1016/S0378-4371(02)00812-9 
Copyright © 2002 Elsevier Science B.V. All rights reserved.
MEI, SOI and mid-range correlations in the onset of El Niño–Southern Oscillation
Eduardo Ortiz-Tánchez
, 
, a, Werner Ebelinga, b and Karl Laniusb
a Institute of Physics, Humboldt University, Invalidenstrasse 110, 10115 Berlin, Germany
b Leibniz Sozietät, P.O. Box 840126, 12531 Berlin, Germany
Received 22 February 2002.
Available online 8 May 2002.
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Abstract
Entropy analysis and wavelet transforms are used to study the Southern Oscillation index (SOI) and multivariate ENSO index (MEI) indexes for the El Niño–Southern Oscillation. Trends to large decreasing symbolic chains responsible for La Niña and interrupted increasing chains for El Niño are found in the MEI persistence series. These are all located in regions where the wavelet transforms of both indexes reveal the existence of mid-range correlations. The SOI and MEI indexes are mutually correlated in a non-trivial manner in the time.
Author Keywords: Entropy analysis; Mid-range correlations
PACS classification codes: 92.10.Gk; 02.50.Ga
Fig. 1. Time series of the: (a) SOI; and (b) MEI indicators of the Southern Oscillation since 1950.
Fig. 2. Monthly trends for: (a) MEI index time series; (b) SOI time series; (c) MEI persistence time series; and (d) SOI persistence time series, with their respective deviations.
Fig. 3. Local entropy of the SOI time series between 1950 and 2000.
Fig. 4. (a) Local entropy of the MEI persistence series between 1950 and 20001; (b) Localization of the “000” blocks in the MEI index time series; solid lines represent blocks as large or larger than “00000” at the onset of a La Niña; (c) Localization of the “222” blocks in the MEI series; solid lines represent separated couples of “222” at the onset of an El Niño.
Fig. 5. Local conditional entropy and Paul wavelet power spectra of the MEI and SOI ENSO quantifiers since 1950. The solid contours are the 10% significance level, the inferior solid line is the “cone of influence”, where finite-size effects predomine.
Fig. 6. Kullback information and crossinformation of the MEI and SOI symbolic series.
Table 1. Representative 3-blocks for the MEI persistence series, conditional entropy, expected (most probable) symbol after the block and empirical probability of the expected symbol
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