[mathjax]The Southern Oscillation embedded with the ENSO behavior is what is called a dipole [1], or in other vernacular, a standing wave. Whenever the atmospheric pressure at Tahiti is high, the pressure at Darwin is low, and vice-versa. Of course the standing wave is not perfect and far from being a classic sine wave.
To characterize the quality of the dipole, we can use a measure such as a correlation coefficient applied to the two time series. Flipping the sign of Tahiti and applying a correlation coefficient to SOI, we get Figure 1 below:
Fig 1 : Anti-correlation between Tahiti and Darwin. The sign of Tahiti is reversed to see better the correlation. The correlation coefficient is calculated to be 0.55 or 55/100.
Note that this correlation coefficient is “only” 0.55 when comparing the two time-series, yet the two sets of data are clearly aligned. What this tells us is that other factors, such as noise in the measurements, can easily drop correlated waveforms well below unity.
This is what we have to keep in mind when evaluating correlations of data with models as we can see in the following examples.
GeoEnergy Math 
