3.1 The response of PDO to PNA in observation and model simulation
To measure the observed North Pacific SST variability generated by PNA, we first use the seasonal cycle of cross correlation between PDO (HadISST1 dataset) and PNA (20CRv2c dataset) monthly expansion coefficient (EC) time series (both are filtered with 3-month running mean, Fig. 1b). The observed correlations show that atmospheric variations generally lead SST variations (e.g., Davis 1976; Deser and Timlin 1997). The springtime PDO has a high correlation with prior wintertime PNA variability. The maximum correlation value appears between January PNA and February SST, indicating that the PNA during its dominating season has a strong influence on the North Pacific SST variability in the later month. To confirm how dose PDO with a 1-month delay (JMF) change by PNA forcing in wintertime (DJF), we calculate the regression of the Pacific SSTa (30°S-70°N, 110°E-60°W) in JFM onto the observed PNA index in DJF (as shown in Fig. 2c). Unless otherwise noted, the season is fixed on DJF for atmospheric field and JFM for oceanic field through the paper. The regression pattern is similar to the observed PDO pattern (Fig. 2a), except for the weaker amplitude in SST variation. Note that the tropical Pacific SSTa excites atmospheric Rossby wave trains during ENSO events which force extratropical large-scale atmospheric teleconnections (e.g., Trenberth et al. 1998; Liu and Alexander 2007). And the PDO-like SST variations are effected by ENSO as well. Figure 1a shows that the observed PDO and ENSO index (here, defined as the Niño 3.4 index) are simultaneously correlated throughout the year. The high correlations at the lags from − 6 to 6 suggest significant interactions between ENSO and PDO. These results indicate that the ENSO signal entangles in both PNA and PDO signals.
To illustrate the PNA-induced SST variations, the PLS regression is employed to eliminate the ENSO effect (Fig. 2e). To further inspect the relationship between the PDO and the PNA-forced SSTa, we compare the time evolution of the intensities of the North Pacific center of the PDO (defined as the absolute regression coefficients averaged over the box in Fig. 2a) and the PNA-forced SSTa (the same as the former, but in Fig. 2e) as shown in Fig. 1c. The time evolutions of the intensities are constructed over 33 80-yr sliding windows (i.e., 1901–1980, 1902–1981, …, 1933–2012). The red (blue) line represents the time evolution of the North Pacific center intensity of the PDO (PNA-forced North Pacific SSTa). Here the time evolution of PNAb (the North Pacific center of PNA) intensity (green line in Fig. 1c) is constructed using the same methods as in Chen et al. (2018). The results show a robust connection between PDO and PNA-forced SSTa (Corr. =0.76, p = 0.01). Also PNAb and PDO reveal the significant correlations 0.69 with p-value 0.02. Percentages in black at the lower right corner of the graphs indicate the contribution of PNA-forced SSTa to PDO intensity, which is defined as \(\text{P}=\left({\sum }_{i}^{n}{|x}_{i}|/\sum _{i}^{n}{|y}_{i}|\right)\bullet r\times 100\%\), where \({x}_{i}\left({y}_{i}\right)\) is the PNA-forced SSTa (PDO) intensity in the i-th year and r is the correlation coefficient between these two variables. For example, if P reaches 100%, which means the variable x is exactly the same as y (there is no energy loss from x to y) and x is the only factor to cause the change of variable y. It shows that the wintertime PNA affects the North Pacific SST within one month, and it impacts on the PDO variability via the PNA-forced North Pacific SSTa.
Similar phenomenon also appears in the patterns (Fig. 2b, d, and f) of multi-model ensemble mean (MEM, see Table 1 for the details of the selected models), which demonstrate the model capability to simulate the observed atmospheric and oceanic variability in the tropical and North Pacific. When compared with the observe patterns, the amplitudes in Alaska Current area are overestimated for all the MEM patterns of Fig. 2. Besides that, the SST variations in Kuroshio Extension are also over-amplification in multi-model simulation (Fig. 2b), which may affect the position of the North Pacific center of PDO. In this case, we avoid the Kuroshio Extension area and set the maximum value of SSTa as the North Pacific center of PDO in each selected CMIP5 model (as shown in Fig. 3).
3.2 Projected future changes of PDO and the contribution of PNA under global warming
Based on the statistics of PDO patterns in CMIP5 models, we find that the location of the North Pacific center is different from model to model. Thus we choose variable boxes to accommodate the different locations of the North Pacific center in different models. For all of the 12 models except the HadGEM2-ES model, the pattern difference between the RCP8.5 and historical scenario (Fig. 3) show an enhancement of the North Pacific center of the PDO under the global warming consistently. Besides, the overestimated Kuroshio Extension variability becomes weaker than historical scenario except NorESM1-ME model.
To measure the magnitude of the North Pacific SST response to the intensification of PNA under the warming scenario, the historical PLS regression pattern of each model along with the pattern difference between the RCP8.5 and Historical scenarios are drawn in Fig. 4. The multi-model collectively shows the PDO-like SSTa response under the forcing of PNA. However, the inter-model diversity promotes us to design tailored box for each model to measure the intensities of PNAb and its forced SSTa centers. Most of the selected models present good performance and show enhanced PNA-forced SSTa centers.
We have confirmed in our previous study that the PNA in these 12 models are enhanced in RCP8.5 scenario as well (also shown by the dashed lines of Fig. 4). The central location of PNAb in each model is denoted in the green box, and the PNAb intensity is defined as the area-averaged regression coefficients in that box.
The PNA-forced SSTa of the models only contribute to the negative (positive) value of SSTa in the North Pacific (Alaska Current). We use the same location (magenta boxes) as the PDO center to measure the intensity of the PNA-forced SSTa. The intensities differences between RCP8.5 and Historical scenario are calculated for PNAb (green bars), PDO (red bars) and PNA-forced SSTa (blue bars), as shown in Fig. 5. It suggests that the intensities of the North Pacific center of the PDO and the PNA-forced SSTa are intensified under global warming in models with enhanced PNAb except the HadGEM2-ES model. The projected change is considered significant when the magnitude exceeds the unforced internal variability which is measured based on the PI-control run. All the changes have passed significance test except PNA-forced SSTa change in CMCC-CESM model. Note that most of the intensity changes are more than twice the internal variability, but the only model (HadGEM2-ES) with a weakened PDO shows that the PNAb and the PNA-forced SSTa intensity changes are close to their internal variability. In general, through the numerical statistics of the North Pacific SSTa variability, the PDO will intensify in a warming climate and the enhancement of the PNA-forced SSTa is the main cause.
Although the enhancement of the North Pacific center of PDO in future projection (RCP8.5 scenario) is robust in the multiple models, the difference between individual models is primarily in magnitude. A naturally raised issue is, to what extent the inter-model differences in the North Pacific center of PDO are related to the PNA variability and associated SST responses.
As shown in Fig. 6, we find a close inter-model relationship among the intensity changes of the PDO, the PNAb and the PNA-forced SSTa in multi-model projections. For these three variables, we examined the correlations between them, which are 0.78, 0.75, and 0.8, which are all significant at the 0.01 significance level. The MEM of the PDO intensity change shows an increase of 0.13°C with the 95% confidence interval of 0.06°C to 0.20°C (Fig. 6a), and the signal-to-noise ratio (i.e., change value divided by the estimation of unforced internal variability) is 2.22. Such an intimate linkage also holds for the MEM result, which shows an increase of 0.10°C with the 95% confidence interval of 0.05°C to 0.15°C (Fig. 6c), and the signal-to-noise ratio is 3.59. Meanwhile the enhanced PNA in warming projection also shows an increase of 11.74 gpm with the 95% confidence range of ± 2.71 gpm, and the signal-to-noise ratio is 2.8. Apparently, the changes among the future projections of the selected models will enhance consistently. High correlations with the models indicate little difference in the inter-model diversity. It gives us a robust conclusion on the cause of the PDO enhancement under global warming. The deepened trough of the PNAb will force a PDO-like SSTa pattern, and thus enhance the PDO.
3.3 Possible mechanism of the changes in North Pacific SSTa
To further inspect the evolution of the PDO intensity enhancement and the contribution of the PNA-forced SSTa to it under global warming, we examine the relationship between the North Pacific center of PDO and the PNA-forced SSTa with their projected intensity changes. The time evolution of the PDO intensity is constructed over 107 95-yr sliding windows (i.e., 1900–1994, 1901–1995, …, 2006–2100). Here the PDO intensity in each sliding window is derived from the area-averaged absolute regressions coefficients of the specific 95-yr late winter (JFM) SSTa against the PDO index in the selected boxes (the same boxes as in Fig. 3). Likewise, the time evolution of PNA and the PNA-forced SSTa intensity are calculated based on the area-averaged absolute regressions of winter (DJF) 500-hPa GPHa and JFM SSTa against the normalized PNA indices in the respective green and magenta boxes (Fig. 4) of each model. Note that similar results are obtained when using larger boxes. Here the statistical significance of correlation coefficient between the time series based on 95 years sliding window is tested with a two-tailed Student’s t-test using the effective sample size, which takes into account the serial autocorrelation (Bretherton et al. 1999). The effective sample size (Ne) is defined as \({N}_{e}=N\times (1-{r}_{x}\times {r}_{y})/(1+{r}_{x}\times {r}_{y})\), where N is the length of time series and rx(ry) is the autocorrelation coefficient of the time series for variable x (y) at lag one.
As shown in Fig. 7, the MEM result clearly illustrates that the long-term evolution of the North Pacific center of PDO is in line with that of the PNA and the PNA-forced SSTa. All the intensities are increased gradually, particularly from 2030 and onward. It is obvious that there is a close association between the multidecadal evolution of the PDO intensity and PNA-forced SSTa, with high correlation coefficient of 0.96 at 0.01 significance levels. Also the PDO intensity has a close relationship with the PNAb intensity (correlation coefficient 0.93). Note that the time coverage of the RCP8.5 data of CMCC-CESM is up to the year 2095 while that of the other models are all up to the year 2100, and the MEM timeline adjust to the shortest one. The definition of the percentages at the lower right corner of the graphs are the same as in Fig. 1c (see Sect. 3.1 for details)..
Figure 7 shows that all models except HadGEM2-ES can capture the close relationship between the time evolutions of the PDO North Pacific center intensity and the PNA along with its forced SSTa intensity. It is notable that PDO intensity is more correlated to the PNA-forced SSTa than it is to PNA. The percentage of contribution in each model ranges from 46.3–72.8%. Therefore, the PNA and the North Pacific SSTa forced by it will indeed intensify with global warming, and the PNA contributes about 67% of the intensification of PDO intensity.
Overall, the above results suggest that, on average, models with stronger intensification of PNA variability tend to have larger magnitude of PNA-forced SSTa response, which contributes more to the enhancement of PDO in a warmer climate.