Assessing the significance of changes in ENSO amplitude using variance metrics

The variance of time-series records relating to ENSO, such as the inter-annual anomalies or bandpass filtered components of equatorial Pacific SST indices, provides one approach to quantifying changes in ENSO amplitude. Robust assessment of the significance of changes in amplitude defined in this way is, however, hampered by uncertainty regarding the sampling distributions of such variance metrics within an unforced climate system. The present study shows that the empirical constraints on these sampling distributions provided by a range of unforced CGCM simulations are consistent with the expected parametric form, suggesting that standard parametric testing strategies can be robustly applied, even in the case of the non-linear ENSO system. Under such an approach the sampling distribution of unforced relative changes in variance may be constrained by a single parameter, τd, the value of which depends on the choice of method used to extract the ENSO-related component of time-series variability. In the case of inter-annual anomaly records, the value of τd is also substantially dependent of the overall spectral properties of the climatic variable under consideration. In contrast, the τd value for bandpass filtered records can be conservatively constrained from the lower edge of the filter passband, allowing for the direct, but robust assessment of the significance of relative changes in ENSO amplitude, regardless of the climatic variable under consideration. Example applications of this approach confirm marginally significant F-test p-values for multi-decadal changes in central Pacific instrumental SST variance and highly significant ones for centennial changes in central Pacific coral δ18O variance.