Relationship with the AMO

Fig. 4. Cross-correlation functions between the PDO and AMO indices for unsmoothed values, 11-yr running averages, and residuals after removing the running averages.

The time series of SST averaged over the North Atlantic and linearly detrended to remove warming signal exhibits long-term changes, with cold and warm phases lasting 20-40 years. The alteration between these phases is known as the Atlantic Multidecadal Oscillation (AMO). For the annual unfiltered values, the correlation between the PDO and AMO indices reaches r = -0.53 (significant at p < 0.05) when the AMO is leading the PDO by 18 years (Fig. 4). If both indices are smoothed by 11-yr running averages, the correlation coefficient reaches r = -0.86, when the AMO is leading by 16 years (Fig. 4). The cross-correlation function in Fig. 4 does not necessarily indicate a causal relationship between the PDO and AMO; it just emphasizes that both indices have strong 70-yr components in their fluctuations, which are roughly in quadrature with respect to each other. Zhang and Delworth (2007) proposed a mechanism for the influence of the AMO on the North Pacific multidecadal variability. Their modeling results suggest that the AMO can contribute to the component of the PDO that is linearly independent of ENSO. Dima and Lohmann (2007) proposed a different conceptual model, in which the multidecadal signal is transferred from the Atlantic to the Pacific through the Tropics.

Fig. 5. Annual AMO and PDO indices smoothed by 11-yr running averages, with the AMO leading PDO by 16 years. Years on the abscissa are those of the PDO.

Whatever the mechanism may be (or lack thereof), the lagged AMO-PDO statistical relationship can be used to estimate further progression of the PDO. As shown in Fig. 5, the PDO will probably be decreasing until about 2017, although this may be just a manifestation of the 70-yr cycle in the PDO itself. Numerical experiments suggest that the 70-yr cycle is not generated by external forcing and is likely to be an internal cycle mediated by ocean-atmosphere interactions (Andronova and Schlesinger, 2000).

The 70-yr cycle is not the only cycle common for the North Pacific and North Atlantic. When the running 11-yr averages are removed from the PDO and AMO series, the cross-correlation function between the residuals reveals a distinct quasi-decadal cycle (Fig. 4). The magnitude of the correlation between the residuals reaches -0.39 (p < 0.05, data 1905-2002), when the AMO is leading the PDO by 11 years.

Fig. 6. The residuals in the annual PDO and AMO indices after removing the 11-yr running averages and smoothing by 3-yr running averages.

When the residuals are smoothed by running 3-yr averages, the correlation between the two time series at the 11-yr lead time jumps to -0.75 for the period 1952-2001. Figure 6 shows the time series of the residuals (with the AMO leading by 11 years), along with the PDO forecast values based on the regression between the AMO. As one can see from this figure, the decadal component of the PDO index will likely to decline by 2009 and then increase by 2012. This is generally consistent with rule 351, which suggests that the North Pacific index is expected to increase until 2010. Also shown in Fig. 6 are annual (unfiltered) values of the PDO for 2002-2007 and forecast PDO values based on the regression with the AMO.