  The El Ni\~no Southern Oscillation (ENSO) is the Earth's strongest climate
fluctuation on inter-annual time-scales and has global impacts although
originating in the tropical Pacific. Many point indices have been developed to
describe ENSO but the Multivariate ENSO Index (MEI) is considered the most
representative since it links six different meteorological parameters measured
over the tropical Pacific. Extreme values of MEI are correlated to the extreme
values of atmospheric CO2 concentration rate variations and negatively
correlated to equivalent scale extreme values of the length of day (LOD) rate
variation. We evaluate a first order conversion function between MEI and the
other two indexes using their annual rate of variation. The quantification of
the strength of the coupling herein evaluated provides a quantitative measure
to test the accuracy of theoretical model predictions. Our results further
confirm the idea that the major local and global Earth-atmosphere system
mechanisms are significantly coupled and synchronized to each other at multiple
scales.
