Signal Versus Noise in the Southern Oscillation

Abstract

The utility of a simple index for monitoring the Southern Oscillation signal is explored in detail. Based upon sea level pressure data at the two stations Tahiti (T) and Darwin (D), an optimal index, in the sense that it combines the Southern Oscillation variance into one series is the combination [Tn + Dn] where the subscript n denotes normalization by the overall standard deviation of each series. A direct measure of the noise due to small-scale or transient phenomena that are not a part of the large-scale coherent Southern Oscillation fluctuations is the index [Tn + Dn]. It is recommended that this index of noise also should be monitored in order to determine the representativeness of the Southern Oscillation index. The signal-to-noise ratio is shown to depend upon the cross correlation between Darwin and Tahiti, and can be increased by applying weighted moving average low-pass filters to the data. Monthly data exhibit a signal-to-noise ratio, defined as the ratio of the standard deviations, of 1.44 and this increases to 1.97 for seasonal data. An 11-term low-pass filter is designed that increases the signal-to-noise ratio to 2.70 without adversely reducing the variance in frequencies that are important in the Southern Oscillation. Resulting time series plots are presented.