  Understanding current global climate requires an understanding of trends both
in Earth's atmospheric temperature and the El Nino-Southern Oscillation (ENSO),
a characteristic large-scale distribution of warm water in the tropical Pacific
Ocean and the dominant mode of year-to-year climate variability (Holbrook et
al. 2009. However, despite much effort, the average projection of current
climate models has become statistically significantly different from the
observed 21st century global surface temperature trend (Fyfe 2013)and has
failed to reflect the statistically significant evidence that annual-mean
global temperature has not risen in the 21st century (Fyfe 2013, Kosaka 2013).
Modelling also provides a wide range of predictions for future ENSO
variability, some showing an increase, others a decrease and some no change
(Guilyardi, et al. 2012; Bellenger, 2013). Here we present correlations which
include the current era and do not have these drawbacks. The correlations arise
as follows. First it has been shown (Kuo 1990, Wang W. et al. 2013) that the
rate of change of the level of atmospheric CO2 (expressed as its first
derivative) has a time-trend signature which is statistically significantly
similar to that for global surface temperature. Second, we show here that the
rate of this change - the second derivative of the level of atmospheric CO2 -
is statistically significantly correlated with the separate signature displayed
by the El Nino-Southern Oscillation. Third, we show that second-derivative
atmospheric CO2 leads ENSO, first-derivative CO2 and temperature. Taken
together the foregoing three points provide further lines of evidence for the
key role of atmospheric CO2 as a driver of global climate. The results may also
contribute to more accurate prediction of future global climate.
