In the original manuscript of Vecchi et al. (2013), Eq. (6), which is used to quantify the effective number of degrees of freedom in two autocorrelated time series Neff, was incorrectly transcribed from Bretherton et al. (1999). The correct equation is, where N is the number of samples in each time series, and rτX and rτY are the biased estimates of the autocorrelation of each time series at lag τ. We evaluated whether the equation was incorrectly transcribed in the text of Vecchi et al. (2013), or whether the incorrect equation in the published paper was implemented in the calculations for the manuscript (which would have led to a substantial overestimate of the effective degrees of freedom). We found that the equation had been incorrectly transcribed. However, in reviewing the implementation of the equation an error was found. This error stemmed from an indexing mistake when referencing an array, in which the lag-1 autocorrelation term in the summation in the denominator (which is always less than 1) was summed once instead of twice, while the lag-0 autocorrelation term (which is exactly 1) was summed twice. Therefore, the degrees of freedom were underestimated in the original Vecchi et al. (2013) manuscript; this led to an overestimation in the size of the error bars in Figs. 2, 4, and 9. For Figs. 2 and 4, because the lag-1 autocorrelation of both the time series was close to 1, the underestimation in Neff was generally between 1 and 2, and resulted in only minor changes to the error bars, without impacting the validity of the statements about statistical significance.
All Science Journal Classification (ASJC) codes
- Atmospheric Science