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Statistics of Solar Cycle–La Niña Connection: Correlation of Two Autocorrelated Time Series

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  • 1 Department of Applied Mathematics, Harvard University, Cambridge, Massachusetts, and Department of Applied Mathematics, University of Washington, Seattle, Washington
  • | 2 Department of Applied Mathematics, University of Washington, Seattle, Washington
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Abstract

Both the 11-yr solar cycle and the El Niño–Southern Oscillation (ENSO) phenomena are quasi periodic, with periods of 9–11 and 3–4 yr, respectively. There have been claims that the two are correlated, with the sun at its peak in sunspot number presumably forcing a cold event in the equatorial Pacific. However, both phenomena are also highly autocorrelated. Caution should be exercised when testing for the statistical significance of the correlation of two autocorrelated time series. The solar peak years can coincide with cold ENSO by chance, even if the two time series are independent, and the coincidence then persists for many cycles due to their autocorrelation, before drifting apart. This study demonstrates that this is indeed the case using the Quinn El Niño index (1525–1987), which is a chronicle of observations of El Niño–related events, and the sunspot number (SSN) series going back to 1750. Appropriate statistical tests are suggested that can test for correlation, taking into account autocorrelation applicable to the shorter instrumental records. There is so far no solar peak–La Niña connection found that is statistically significant.

Corresponding author address: Eddie Haam, School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138. E-mail: keh@eecs.harvard.edu

Abstract

Both the 11-yr solar cycle and the El Niño–Southern Oscillation (ENSO) phenomena are quasi periodic, with periods of 9–11 and 3–4 yr, respectively. There have been claims that the two are correlated, with the sun at its peak in sunspot number presumably forcing a cold event in the equatorial Pacific. However, both phenomena are also highly autocorrelated. Caution should be exercised when testing for the statistical significance of the correlation of two autocorrelated time series. The solar peak years can coincide with cold ENSO by chance, even if the two time series are independent, and the coincidence then persists for many cycles due to their autocorrelation, before drifting apart. This study demonstrates that this is indeed the case using the Quinn El Niño index (1525–1987), which is a chronicle of observations of El Niño–related events, and the sunspot number (SSN) series going back to 1750. Appropriate statistical tests are suggested that can test for correlation, taking into account autocorrelation applicable to the shorter instrumental records. There is so far no solar peak–La Niña connection found that is statistically significant.

Corresponding author address: Eddie Haam, School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138. E-mail: keh@eecs.harvard.edu
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