The Index Cycle: a Cross-spectral Analysis of Zonal Index Data

I n order to examine quantitatively the evidence for an index cycle, 21 years of daily 700-mb. zonal index data for the western longitudes of the Northern Hemisphere were subjected to cross-spectral analyses. The annual variation of the mean and standard deviation of the three zonal indices (polar, temperate, and subtropical) was removed by a standardizing procedure utilizing time-smoothed annual curves. The variance (power) spectra of the individual indices indicated’that their correlation structure can be closely approximated by a first-order Markov scheme. No evidence was found for an excess of variance in the range of period (3 to 8 weeks) assigned to the index cycle by subjective means. The cospectra all indicated negative covariability among the indices as would be expected from circulation patterns characteristic of index-cycle-like behavior, but none showed an excess of negative covariability within the period range of interest. Coherence values, indicating the degree of relationship among the various indices, also did not show maxima in the required period range. The distributions of the standardized indices were found to be slightly skewed in the case of the subtropical and temperate indices and normal in the case of the polar index. In addition, a significant seasonal variation in the correlation and cross-correlation structure of the indices was found. Such nonstationarity complicates the interpretation of the cross spectra. The conclusion of the statistical study of the zonal index data is tha t there is 110 evidence for sequential variations and covariations of the strength of the westerlies at various latitudes with any preferred range of period. Rather, significant relationships hold over a very broad range of period.