Quantitative decomposition of the interdecadal change in the correlation coefficient between the El Ni?o-Southern Oscillation and South Asian summer monsoon

Interdecadal change in the correlation coefficient between two variables is an important scientific issue since it can affect climate predictions. A new statistical method is proposed for the quantitative decomposition of the difference in the correlation coefficient, and its derivation is based only on the first-order Taylor expansion. Particularly, the difference in the correlation of two time series between two specific periods is divided into three linear terms, which are only related to the changes in the covariance and variances. This method is illustrated in detail with an example of the recently recovered relationship between El Nino-Southern Oscillation (ENSO) and the South Asian summer monsoon (SASM). For the two periods of 1979-2000 and 2001-2022, the correlation between ENSO and the SASM is - 0.29 and - 0.60. The difference in the correlation coefficient (- 0.31) is mainly resulted from the enhanced covariance of ENSO and SASM (- 0.26) and decreased variance of ENSO (- 0.15), and is partly offset by the increased variance of SASM (+ 0.11). These three terms contribute to 84%, 48%, and - 36% of the interdecadal change in the correlation coefficient, respectively. The summation of these three terms accounts for 96% of the difference in the correlation, which indicates a nearly neglecting contribution from the high-order term. A similar decomposition has been applied to the correlation maps, such as the correlation between ENSO and the velocity potential at the upper troposphere. This statistical method is suggested to be a useful tool, which can potentially promote our understanding of the interdecadal changes in the correlation coefficients.