3.1 A non-stationary relationship between PDO and IOBM
We first show the global patterns of PDO and IOBM, and their temporal variability for the period of 1900 to 2018 on a monthly timescale (Fig. 1). Figures 1a,b display the regressed SST anomalies against the monthly PDO and the IOBM indices, respectively. When the PDO phase is positive, the cold SST anomaly extends from the western North Pacific to the central North Pacific, and the warm SST anomaly along the western coast of North America wraps the cold anomaly in a horseshoe shape in the Pacific Ocean basin. When the IOBM phase is positive, basin scale warming is dominant in the entire Indian Ocean (Fig. 1b). In addition, the spatial structures of regressed SST anomalies are similar in the Pacific and Indian Ocean basins when the phases of PDO and IOBM are positive (Figs. 1a,b). The pattern correlation coefficient between the two regressed SST anomalies against the PDO and the IOBM indices is 0.75 in the globe. This result infers that the PDO index is positively correlated with the IOBM index. Figures 1c,d show the monthly variability in each index with a 11-year running mean. Both the PDO and IOBM indices fluctuate on low-frequency time scales and they are nearly in-phase relationship. The simultaneous correlation coefficient between the monthly PDO and IOBM indices for 1900–2018 is 0.36, which is statistically significant at a 95% confidence level. In addition, the correlation coefficient between the 11-year running mean time series is 0.55, which is also statistically significant at a 95% confidence level. While the correlation coefficient does not imply the causality, this result indicates that the PDO and the IOBM is simultaneously tied.
Hereafter, the analyzed period is limited to since 1948 because the reanalysis dataset is only available since 1948 and, unless stated otherwise, the results are for the boreal winter (DJF) only. Figures 2a,b are the same as in Figs. 1c,d except those during DJF for 1948–2018. While both the PDO and IOBM are dominant on the low frequency timescales, they also have the variability less than a decade (Supplementary Fig. 1). It is evident that the 31-year running correlations between the PDO and the IOBM indices fluctuate (Fig. 2c). Note that we remove the linear trend to eliminate the anthropogenic warming trend in every 31-year window and obtain the statistical significance considering the effective degrees of freedom. When we use a 41-year window length, the weakening of the PDO-IOBM relationship is also obtained (Supplementary Fig. 2).
While the PDO and IOBM indices are positively correlated significantly in most periods, there are some decades when two indices are poorly correlated with each other. This implies that the relationship between the PDO and IOBM is not stationary. In detail, the correlation is high until the early-1970s, and then it becomes weak and slowly recovers in the recent past. In particular, the correlation for 1954–1984 is the highest at 0.64, which is statistically significant above a 95% confidence level. In contrast, the correlation coefficient of 0.25 for 1976–2006 is the smallest, which is not statistically significant. While the PDO has gone through regime shifts in 1976 and 1998 (Hare and Mantua 2000; Peterson and Schwing 2003), the number of a positive and a negative phase of PDO is 19 and 12, respectively, during 1976–2006. This indicates that a single phase of PDO is not dominant in a period when the PDO-IOBM relationship is weak. To further understand the PDO-IOBM relationship, we also calculate the relationship of ENSO-IOBM. El Nino and Southern Oscillation (ENSO) is the most dominant SST variability in the tropical Pacific on interannual timescales, and it is known that ENSO interacts with the Indian Ocean (Alexander et al. 2002; Klein et al. 1999; Lau and Nath 1996; Saji et al. 2006). Figure 2d displays the time series of NINO3.4 SST index during DJF for 1948–2018. We find that the 31-year running correlation between the NINO3.4 index and the IOBM is nearly stationary during the entire analyzed period (Fig. 2e). We infer that the non-stationary relationship between the PDO and the IOBM could be from the PDO which is not related to the ENSO.
We further analyze a long term period (1,100 years) of simulation from a Community Earth System Model (CESM) (Kay et al. 2015) under a pre-industrial atmospheric condition to avoid a sampling issue of PDO-IOBM relationship. Following the same methodology applied to the observation, we obtain the PDO and IOBM indices from a CESM and then examine their relationship. Figures 3a,b display the regressed SST anomalies against the PDO and IOBM index, respectively, in a CESM, which are similar to the observation. To verify a non-stationary relationship of PDO-IOBM with a sufficiently long window, we calculate both the 31-year and 61-year running correlation between the PDO and the IOBM (Figs. 3c,d). We find that the relationship of PDO-IOBM fluctuates on the low-frequency timescales, indicating that a non-stationary relationship of PDO-IOBM is intrinsic in a climate system in a fixed anthropogenic forcing.
In addition, we analyze the CESM large ensemble (CESM-LE) simulations for 1948–2018 (Kay et al., 2015). The CESM-LE array contains 35 members that are used in the same model and with the same external forcing (i.e., RCP8.5). Each CESM-LE member has a unique climate trajectory due to small differences in rounding - approximately 10− 14 K - initial atmospheric conditions. Therefore, deviations in simulated PDO-IOBM relationship among ensemble members could be at least partly due to internal climate variability. We find that there is a large inter-member diversity to simulate the PDO-IOBM relationship (Fig. 4). While some models simulate a non-stationary relationship of PDO-IOBM like the observation, others simulate a stationary relationship of PDO-IOBM. This result implies that a non-stationary relationship of PDO-IOBM could be partly due to internal climate variability, which is consistent with the result from a long-term simulation of the pre-industrial run in a CESM.
3.2 Physical processes
To investigate the physical processes associated with the non-stationary relationship of PDO-IOBM, we select the period of 1976 to 2006, when the PDO-IOBM relationship is the weakest, and then we compare this with the results based on the entire period (1948–2018) to obtain a more reliable conclusion. It should be noted that all of the results obtained from the entire period are similar to those when the PDO-IOBM relationship was the highest during the period of 1954 to 1984 (figure not shown).
Figures 5a,b display the SST structure when the PDO phase was positive and negative, respectively, for the period from 1976 to 2006. Figures 5c,d are the same as in Figs. 5a,b except for the entire period. The spatial structures were similar to each other when the phase of PDO was positive in both for 1976–2006 and the entire period (Figs. 5a,c). Furthermore, basin scale warming in the Indian Ocean is also dominant for 1976–2006 and the entire period, respectively. However, the SST pattern during a negative phase of PDO for 1976–2006 (Fig. 5b) differs from that during the entire period (Fig. 5d). From 1976 to 2006, the anomalous warm SST is limited in the southern North Pacific and a triangular structure of anomalous cool SST is not as well shaped in the Pacific Ocean basin compared to that during the entire period. In particular, the anomalous warm and cool SSTs are mixed over the Indian Ocean basin for the period from 1976 to 2006 (Fig. 5b), which is in contrast to that during the negative phase of PDO for the entire period in which the anomalous cool SST is dominant (Fig. 5d). This result indicates that a weakening of the relationship between the PDO and IOBM for the period from 1976 to 2006 is primarily due to the negative phase of the PDO. In the subsequent analysis, we primarily focus on the physical processes associated with the negative phase of PDO for the period from 1976 to 2006 (hereafter, referred to as −PDO_76 − 06, and then compare the results with those for the entire period (hereafter, referred to as −PDO_ALL).
We hypothesize that the structure of tropical convection could be associated with the weakening of the PDO-IOBM relationship. To examine this, we conduct a composite analysis of precipitation in −PDO_ALL and −PDO_76 − 06 (Figs. 6a,b). In addition, we also display the composites of divergent wind and velocity potential at 200hPa during −PDO_ALL and −PDO_76 − 06, respectively (Figs. 6c,d). The normal structure of precipitation in −PDO_ALL is characterized by a dry-wet-dry structure from the Indian Ocean to the central tropical Pacific (Fig. 6a). Reduced precipitation in the western-to-central tropical Pacific is associated with an anomalous cool SST in the same region in −PDO_ALL (see also Fig. 5d). In contrast, the enhanced precipitation amount in the far western tropical Pacific as well as the Maritime Continent is associated with an upper level divergence (Fig. 6c), which indicates the strengthening of the ascending motion in Walker Circulation. Concurrently, reduced precipitation in the Indian Ocean is associated with an upper level convergence (Figs. 6a,c), which is associated with the enhancement of the descending motion of Walker Circulation in the same region. We emphasize that there is a divergence over the far western tropical Pacific as well as the Maritime Continent along with a convergence in the Indian Ocean basin in the upper level (i.e., 200hPa) (Fig. 6c), which represents the normal structure of atmospheric circulations associated with the Walker Circulation in −PDO_ALL
In −PDO_76 − 06 (Fig. 6b), in contrast, the precipitation structure is different compared to that of −PDO_ALL. It is characterized by a wet-dry-wet-dry structure from the Indian Ocean to the eastern tropical Pacific. In particular, the precipitation amount is reduced in the far western tropical Pacific as well as the Maritime Continent and it increases over the Indian Ocean basin. In addition, it is slightly increased in the central tropical Pacific. Therefore, the structure of the precipitation amount between −PDO_ALL and −PDO_76 − 06 is nearly opposite despite the same negative phase of PDO. In −PDO_76 − 06, the upper level convergence extends over the Maritime Continent (Fig. 6d), leading to suppressed precipitation amounts in the same region (Fig. 6b). This result is concurrent with the upper level divergence over the Indian Ocean (Fig. 6d), which is indicative of a strengthening of the ascending motion of Walker Circulation over the Indian Ocean. This suggests that the Walker Circulation in −PDO_76 − 06 is shifted more to the west than the normal structure in −PDO_ALL.
We argue that these circulation changes over the Indian Ocean, which might be induced by the upper level convergence over the Maritime Continent, caused the mixed pattern of the anomalous warm and cool SSTs in −PDO_76 − 06 (see Fig. 5b). This is in contrast to the basin cooling in the Indian Ocean in −PDO_ALL (see Fig. 5d). In −PDO_76 − 06, the upper level divergence caused an increase in precipitation as well as an anomalous cool SST via less penetration of shortwave radiation in the southern portion of the Indian Ocean in particular (Fig. 7a). Subsequently, the enhanced precipitation in the southern Indian Ocean causes the changes in the meridional circulation across the Indian Ocean basin, leading to the strengthening of downward motion in the northern Indian Ocean (Fig. 7b). These changes warm the Indian Ocean SST via more penetration of shortwave radiation (see Fig. 7a and Fig. 5b). It should be noted that, while the average downward shortwave radiation flux in the North Indian Ocean (0°N-20°N, 30°E-120°E) is 0.95 w/m2, the average in the South Indian Ocean (20°S-0°N, 30°E-120°E) is -0.02 w/m2 in −PDO_76 − 06. This result is consistent with the argument noted above. We infer that the structural change in tropical convection and its associated atmospheric circulation in the Indian Ocean, as well as the tropical Pacific, plays an important role in causing the weakening of PDO-IOBM relationship.
3.3 Pacemaker experiments
The results noted in the previous section suggest that the weakening of the PDO-IOBM relationship could have been associated with the changes in the tropical convection. To examine this argument, we conduct two pacemaker experiments using NESMv3 with four ensemble members as explained in Sect. 2. In one experiment, we nudge the monthly observed SST with a 3-day nudging timescale in the Pacific Ocean (120°E-280°E, 70°S-70°N) only for 1948 to 2013 in NESMv3, which is referred to as Pacific_Exp. In the other experiment, we do the same as for the Pacific_Exp except that the monthly observed SST is nudged in the Indian Ocean (40°E-110°E, 90°S-20°N) only for 1948 to 2013, which is referred to as Indian_Exp. We conduct the same analysis following the observations.
Figures 8a,b display the ensemble mean SST structure in −PDO_ALL and −PDO_76 − 06 in Pacific_Exp for 1948–2013. In the Pacific_Exp, the spatial structures of the composited SST in the Pacific Ocean are almost identical to the observations in both −PDO_ALL and −PDO_76 − 06 (Figs. 5b,d and Figs. 8a,b). The slight differences are due to the difference in horizontal resolution as well as the prescribed SST dataset. The most striking difference between −PDO_ALL and −PDO_76 − 06 in the Pacific_Exp is found in the SST structure in the Indian Ocean basin. While the composited SST in −PDO_ALL is dominant with a basin scale cooling, that in −PDO_76 − 06 is characterized by a basin scale warming except for the far eastern Indian Ocean. We emphasize that a positive relationship of PDO-IOBM in −PDO_76 − 06 is broken in the Pacific_Exp. This result indicates that the weakening of PDO-IOBM is primarily due to the difference in the SST forcing in the Pacific Ocean because the Indian Ocean SST is largely explained by the forcing of the Pacific Ocean SST in the Pacific_Exp. To further support this notion, we also calculate the 31-yr running correlation coefficient between the PDO and the IOBM indices in each four ensemble member of the Pacific_Exp (Fig. 8c). Similar to our observations (Fig. 2c), the relationship of PDO-IOBM is not stationary in all ensemble members. This result also indicates that the changes in the Pacific SST and its associated convection are responsible for the weakening of the PDO-IOBM relationship.
On the other hand, the results from the Indian_Exp are different from those from the Pacific_Exp. Figures 9a-c show the same as in Figs. 8a-c except for the Indian_Exp with four ensemble members. In the Indian_Exp, the spatial structures of the composited ensemble mean SST in the Indian Ocean are almost identical to the observations in both −PDO_ALL and −PDO_76 − 06 (Figs. 5b,d, and Figs. 9a,b). In contrast to the Pacific_Exp, however, the composited SSTs in the Pacific Ocean in both −PDO_ALL and −PDO_76 − 06 in Indian_Exp are different than those from the observations. The Indian_Exp does not simulate the SST structure in both −PDO_ALL and −PDO_76 − 06, that is, the triangular structure of the cool SST in the Pacific Ocean basin (Figs. 5b,d, and Figs. 9a,b). This result indicates that the Pacific Ocean SST in both −PDO_ALL and −PDO_76 − 06 is not forced by the Indian Ocean SST in the observations, because the Pacific Ocean SST is largely influenced by the forcing of the Indian Ocean SST in the Indian_Exp. Furthermore, the relationship of PDO-IOBM simulated in the Indian_Exp (Fig. 9c) is also different from the observations (Fig. 2c) and the Pacific_Exp (Fig. 9c), which supports the theory that the low-frequency fluctuations of the PDO-IOBM relationship is not due to the Indian Ocean SST forcing.