Understanding the Weakening Relationship of the Pacic Decadal Oscillation and Indian Ocean Basin Mode During Boreal Winter

While it is known that the Pacic Decadal Oscillation (PDO) leads the Indian Ocean Basin Mode (IOBM) with the same phase via the atmospheric bridge, we found that the relationship of PDO-IOBM during boreal winter is not stationary. Here, we investigated the PDO-IOBM relationship changes on low-frequency timescales by analyzing the observations, a long-term simulation of climate model with its large ensembles as well as the pacemaker experiments. A long-term simulation of climate model with its large ensemble simulations indicated that the non-stationary relationship of PDO-IOBM is intrinsic in a climate system and it could be at least partly due to internal climate variability. In details, we compared the PDO structures during the entire period with those during the period when the PDO-IOBM relationship was weak (i.e., 1976-2006). We found that the structures of sea surface temperature (SST) as well as its associated tropical Pacic convective forcing during the negative phase of PDO for 1976-2006 are far away from the typical structures of the negative PDO phase during the entire period, which were responsible for the weakening relationship of the PDO-IOBM in the observation. The results of the two pacemaker experiments support that a non-stationary relationship of PDO-IOBM is primarily due to the SST forcing in the Pacic.

Statistically, the PDO/IPO is positively correlated with the IOBM, i.e., a positive phase of PDO/IPO is concurrent with a basin-wide warming of the Indian Ocean, and vice versa (Klein et al. 1999). However, recent studies suggest the changes in the relationship of PDO/IOBM and IOBM. For example, Dong; argued that the relationship between IPO and IOBM has been weakened by external anthropogenic forcing. By analyzing Coupled Model Intercomparison Phase 5 climate models, they suggested that the external forcing strongly in uenced the Indian Ocean basin warming more than IPO, resulting in a strengthening of the out-of-phase relationship of IPO-IOBM. This result indicated that the relationship of IPO and IOBM could be modulated by anthropogenic forcing. Han et al. (2014a) suggested that a strengthening of the out-of-phase relationship between the IPO and IOBM since 1985 led to an intensi ed sea-level variability in the western tropical Paci c. Cai et al. (2019) and Wang (2019) also suggested that understanding the ocean basin interactions including the Paci c, Indian, and Atlantic is important for improving climate prediction and future climate projections. These require a further understanding of the changes in the relationship of PDO/IPO and IOBM. In this study, we investigated the relationship of PDO and IOBM, and we found that their relationship is not stationary on low-frequency timescales. The main purpose of this study is to investigate the mechanisms associated with the weakening relationship of PDO and IOBM in the observation, which received less attention compared to the relationship of IPO and IOBM as mentioned above.
This paper is organized as follows. Section 2 describes the data, de nitions, and model design used in the analysis. Section 3 examines the causes of the weakening of the PDO-IOBM relationships from observation, reanalysis, and model results. Section 4 includes the summary and discussion.

Data And Methodology a. Dataset
We used monthly SST from the Hadley Centre Global Sea Ice and SST version 1.1 (HadISST1.1), gridded at a 1° latitude x 1° longitude resolution (Rayner et al. 2003) and the Extended Reconstructed Sea Surface Temperature version 4 (ERSSTv4), gridded at a 2° latitude x 2° longitude resolution (Huang et al. 2015;Liu et al. 2015). The atmospheric datasets including air temperature, omega, and wind are obtained from the National Center for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR) Reanalysis-1 dataset, gridded at a 2.5° latitude x 2.5° longitude resolution (Kalnay et al. 1996). For the precipitation dataset, NOAA's Precipitation Reconstruction (PREC) at a 1° latitude x 1°l ongitude was used (Chen et al. 2004). We primarily focused on the boreal winter season (December, January, February, hereafter, DJF), when both the PDO and the IOBM are dominant (Alexander et al. 2002;Huang et al. 2019;Schott et al. 2009). All of the datasets covered the period of 1948 to 2018 and the DJF mean was calculated from the monthly data from December to February. The seasonal anomaly was obtained by subtracting the winter-mean from the total winter-mean eld and the linear trend was removed.
b. De nition of PDO, IOBM, and their indices The PDO is de ned by the rst empirical orthogonal function (EOF) mode of sea surface temperature (SST) anomalies in the North Paci c basin (poleward of 20°N) (Mantua and Hare 2002)  . In the previous model version, there were no vegetation dynamics or carbon cycle, and there was a large radiation energy imbalance. In the NESMv3, the atmospheric model was coupled with the land surface model, which contains the dynamic vegetation scheme and carbon exchange. In addition, the resolution of the atmospheric model, and ocean and sea ice model were increased with an upgraded physical parameterization associated with convective processes (Cao et al. 2018). The NESMv3 has been used to conduct sub-seasonal to decadal climate prediction, simulate the past and future projection of climate, and explore possible mechanisms and processes responsible for climate variability (Yang et al. 2020a).
To examine the respective roles of PDO and IOBM, we conducted two pacemaker experiments with four ensemble members in each experiment. First, we nudged the monthly observed SST with a 3-day nudging timescale in the Paci c Ocean (120°E-280°E, 70°S-70°N) only for 1948 to 2013 in NESMv3. Note that the initial conditions in each ensemble member are obtained from the Coupled Model Intercomparison Project Phase 6 (CMIP6) pre-industrial run (Yang et al. 2020b). The other was the same as the rst one except that the monthly observed SST was nudged in the Indian Ocean (40°E-110°E, 90°S-20°N) only for 1948-2013 in NESMv3. The atmosphere and ocean in the region outside the Paci c Ocean and the Indian Ocean are freely coupled in NESMv3, respectively. Therefore, the PDO and IOBM act as a pacemaker in each experiment, which help to identify the role of PDO and the IOBM in the PDO-IOBM relationship. The observational dataset used to nudge the observed SST was obtained from the averaged of HadISST and the ERSST v4. These two datasets were linearly combined and then interpolated to t the model grid. While the resolution between the HadISST and ERSST v4 datasets is not the same, the PDO and IOBM indices calculated in each SST dataset are almost identical ( gure not shown). To obtain more accurate SST elds, we used the average of two different observation datasets. All of the other external forcings (e.g., aerosols, greenhouse gases, etc.) varied historically.

A non-stationary relationship between PDO and IOBM
We rst 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 Paci c to the central North Paci c, and the warm SST anomaly along the western coast of North America wraps the cold anomaly in a horseshoe shape in the Paci c 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 Paci c and Indian Ocean basins when the phases of PDO and IOBM are positive (Figs. 1a,b). The pattern correlation coe cient 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 uctuate on low-frequency time scales and they are nearly in-phase relationship. The simultaneous correlation coe cient between the monthly PDO and IOBM indices for 1900-2018 is 0.36, which is statistically signi cant at a 95% con dence level. In addition, the correlation coe cient between the 11-year running mean time series is 0.55, which is also statistically signi cant at a 95% con dence level. While the correlation coe cient 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.  Fig. 1). It is evident that the 31-year running correlations between the PDO and the IOBM indices uctuate (Fig. 2c). Note that we remove the linear trend to eliminate the anthropogenic warming trend in every 31-year window and obtain the statistical signi cance 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 signi cantly 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 signi cant above a 95% con dence level. In contrast, the We nd 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 ( . 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 nd 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 nonstationary 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.

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 ( gure not shown).  (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 Paci c and a triangular structure of anomalous cool SST is not as well shaped in the Paci c 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 Paci c (Fig. 6a). Reduced precipitation in the western-to-central tropical Paci c 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 Paci c 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 Paci c 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 Paci c. In particular, the precipitation amount is reduced in the far western tropical Paci c as well as the Maritime Continent and it increases over the Indian Ocean basin. In addition, it is slightly increased in the central tropical Paci c. 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 ux in the North Indian Ocean (0°N-20°N, 30°E-120°E) is 0.95 w/m 2 , the average in the South Indian Ocean (20°S-0°N, 30°E-120°E) is -0.02 w/m 2 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 Paci c, plays an important role in causing the weakening of PDO-IOBM relationship.

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 Paci c Ocean (120°E-280°E, 70°S-70°N) only for 1948 to 2013 in NESMv3, which is referred to as Paci c_Exp. In the other experiment, we do the same as for the Paci c_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.  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 Paci c_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 Paci c_Exp. This result indicates that the weakening of PDO-IOBM is primarily due to the difference in the SST forcing in the Paci c Ocean because the Indian Ocean SST is largely explained by the forcing of the Paci c Ocean SST in the Paci c_Exp. To further support this notion, we also calculate the 31-yr running correlation coe cient between the PDO and the IOBM indices in each four ensemble member of the Paci c_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 Paci c 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 Paci c_Exp.  (Figs. 5b,d, and Figs. 9a,b). In contrast to the Paci c_Exp, however, the composited SSTs in the Paci c 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 Paci c Ocean basin (Figs. 5b,d, and Figs. 9a,b). This result indicates that the Paci c Ocean SST in both −PDO_ALL and −PDO_76 − 06 is not forced by the Indian Ocean SST in the observations, because the Paci c Ocean SST is largely in uenced 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 Paci c_Exp (Fig. 9c), which supports the theory that the low-frequency uctuations of the PDO-IOBM relationship is not due to the Indian Ocean SST forcing.

Summary And Discussion
In this study, we examined the non-stationary relationship of PDO-IOBM. The relationship between the two variabilities uctuates on the low-frequency time scale (i.e., one cycle in analyzed period). A long-term simulation of climate model and its large ensemble simulations indicated that the non-stationary relationship of PDO-IOBM is intrinsic in a climate system and it could be at least partly due to internal climate variability. In the observation, we found that, while the PDO and the IOBM indices were signi cantly, positively correlated in most periods, there were some periods when its relationship was weak (i.e., . By comparing the SST structures in the Paci c and Indian Ocean basins during positive and negative phases of PDO for 1976 to 2006 and for the entire period, respectively, we found that a weakening of the relationship between the PDO and IOBM for 1976 to 2006 was primarily due to the negative phase of PDO. We further analyzed the structure of tropical convection as well as the atmospheric circulation at the upper level in −PDO_76 − 06 and −PDO_ALL. We found that there are structural differences in precipitation between −PDO_76 − 06 and −PDO_ALL, which were closely associated with those of the upper level divergence/convergence. This result emphasized the importance of the tropical convection structure in the two ocean basins. To test this argument, we analyzed two pacemaker experiments in which the monthly observed SST in the Paci c Ocean (120°E-280°E, 70°S-70°N) for 1948 to 2013 was only used in NESMv3 (i.e., Paci c_Exp), and the other was the same as Pac c_Exp except that the monthly observed SST was only prescribed in the Indian Ocean (40°E-110°E, 90°S-20°N) for 1948-2013 (i.e., Indian_Exp). We obtained a similar result in the Paci c_Exp including a non-stationary relationship of PDO-IOBM compared with the results of the reanalysis. In contrast, the Indian_Exp failed to simulate such a low frequency uctuation of the PDO-IOBM relationship as well as the SST structures. This result indicated that the non-stationary relationship of PDO-IOBM was primarily due to the change in the SST forcing in the Paci c. Although we did not examine the details on the role of the Atlantic Ocean in the current study, we compared the Atlantic Multi-decadal Oscillation (AMO) index with the relationship of PDO-IOBM (Fig. 10). The AMO index is de ned as the SST anomalies averaged in the Atlantic Ocean basin (0°-60°N, 280°E-360°E) (En eld et al. 2001; Zhang et al. 2018b). The correlation coe cient between the AMO and the PDO-IOBM relationship with a 31-year window is 0.19, which is not statistically signi cant. However, there may exist a lagged relationship between the AMO and PDO-IOBM relationship (Fig. 10b). While a minimum of the AMO index is observed in the late-1970s, that of the PDO-IOBM relationship is observed in the late 1980s. This implies that the AMO may play a role to change the PDO-IOBM relationship with a lagged time, which is necessary to examine more details. Figure 1 The spatial structures of the regressed SST anomalies against the monthly PDO index (a) and the IOBM index (b) from 1900 to 2018. (c), (d) display the time series of the monthly PDO and IOBM indices, respectively, from 1900 to 2018. The green lines in (c), (d) denote the 11-year running mean time series of each index. Shading in Fig. 1a,b represents the region where the statistical signi cance is at a 95% con dence level  The SST spatial structure of the regressed SST anomalies against the (a)PDO and (b)IOBM index during DJF based on a long term period (1,100 years) of simulation in a CESM. Shading in Fig. 4a,b represents the region where the statistical signi cance is at a 95% con dence level.       Figure 8b is the same as Fig. 7a except for the zonally (30-E-120 E) averaged omega in (-) PDO_76-06 (shading). Dots in Fig. 7a indicate the statistical signi cance at a 90% con dence level. Solid (dashed) lines in Fig. 7b denote the climatological (1948-2018) descending (ascending) motion. The units are watt/m2 in Fig. 7a and Pascal/s in Fig. 7b. It should be noted that we multiplied 103 by the original value