Stochastic Environmental Research and Risk Assessment

, Volume 15, Issue 2, pp 153-172

First online:

A statistical measure of severity of El Niño events

  • S. YueAffiliated withMeteorological Service of Canada – Ontario Region, Environment Canada, 867 Lakeshore Rd., P. O. Box 5050, Burlington, Ontario, L7R 4A6, Canada, e-mail:

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 El Niño exerts a significant influence on climate, and hence tremendously affects human activities. The monthly Southern Oscillation Index (SOI) is used to quantify El Niño events. The severity of El Niño is determined by a combination of its maximum intensity, magnitude, and duration that may be mutually correlated. However, the past analyses on the statistical properties of El Niño events either only take into account their occurrences or non-occurrences, or simply rank El Niño events by a few categories such as most severe, severe, and less severe. Apparently, these analyses can not give a complete description of El Niño events. This article sheds new light on the statistical properties of El Niño events. The Gumbel logistic model, a bivariate extreme value distribution with Gumbel marginals is employed to analyze joint probability distributions of El Niño maximum intensity and magnitude, El Niño magnitude and duration, as well as El Niño maximum intensity and duration. Based on the marginal distributions of El Niño maximum intensity, magnitude, and duration, the joint distributions, conditional distributions, and associated return periods of two of these El Niño characteristics can be readily obtained. Results indicate that statistics of El Niño events can be represented by the proposed method. The proposed method provides a much more detailed description of the properties of El Niño events than do the past approaches. It is also prior to single-variable frequency analysis.

Key words: El Niño Southern Oscillation Index (SOI) bivariate extreme distribution Gumbel logistic model joint distribution conditional distribution correlation.