We used the monthly reanalysis circulation dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric interim (ERAI) data from 1979 to 2017 (Dee et al., 2011). In addition, we obtained the monthly SST and precipitation data from the extended reconstruction of global SST (ERSSTv5) since 1854 (Smith et al., 2008) and Global Precipitation Climatology project (GPCP) version 2.3 from 1979 to 2017 (Adler et al., 2003), as well as the Climatic Research Unit (CRU) TS4.03 land precipitation from 1901 to 2017 (Harris et al., 2014), respectively. The monthly anomalies for 1979–2017 were calculated by removing the seasonal cycle and linear trend coefficient during the analysis period. The ENSO variability was characterized by a spatial average of SST anomalies over the tropical eastern Pacific Niño3 region (5∘ S–5∘ N, 150–90∘ W).

We used 40 AGCM simulations from the forced AGCM Intercomparison Projection (AMIP): 19 model runs are part of the Coupled Model Inter-comparison Project (CMIP) Phase 5 (Taylor et al., 2012) and 21 models are part of Phase 6 (Eyring et al., 2016) (i.e., AMIP5 and AMIP6; Tables S2 and S3). The AMIP simulations were forced by the observed SST and sea ice concentrations from 1979–2008 for AMIP5 and from 1979–2014 for AMIP6. The AMIP runs use the observed SST boundary forcing, which allows us to directly compare SST-forced atmospheric responses in simulations and observations. The AMIP multi-model ensemble (MME) represents the SST-forced signal, whereas a mixed signal of SST-forced variability and unforced atmospheric noise is present in the observations and individual AMIP simulations. Additionally, to examine the impact of SST forcing amplitude on the WC–HC synchronization, we analyzed a set of 40 multi-model CMIP5 historical simulations covering the industrial period from 1900–2005 (see Taylor et al., 2012 for details). Only one ensemble member (r1i1p1) was used for each model. All observations and MME data were interpolated to a regular 2.5∘×2.5∘ horizontal grid before the analyses.

We calculated the monthly mass stream function (MSF) anomalies on the three-dimensional atmospheric circulation to describe the WC and HC circulations: 1ψWC(x,z,t)=2πag∫ppsuDdp,2ψHC(y,z,t)=2πacosϕg∫pps[v]dp. Following previous work (Yu and Zwiers, 2010), the tropical zonal circulation (ψWC) is expressed as the divergent component (uD) of zonal wind averaged over the tropics (5∘ S–5∘ N) (zonal mass stream function). The tropical meridional circulation (ψHC) is the zonally averaged meridional mass stream function. Next, we conducted an empirical orthogonal function (EOF) analysis of monthly MSF anomalies to characterize the dominant modes of the tropical atmospheric mass flux variability. For fair comparison between observations and simulations, the MSF fields in every single model were projected onto the EOF pattern derived from the observations to generate principal component (PC) time series for the simulated WC and HC variability. The interannual component of variability was isolated by applying a 10-point Butterworth band-pass filter with 1.5-year (18-month) and 10-year cutoffs. The WC and HC strengths were, respectively, calculated as the maximum value of tropical mean (5∘ S–5∘ N) MSF at 500 hPa and as the maximum of zonal mean MSF at 500 hPa within the latitudinal zone of 30∘ S–30∘ N (Oort and Yienger, 1996), respectively.

To examine the phase synchronization of the large-scale circulation, we calculated the complex analytical signal (T^(t)) using the Hilbert transform. The amplitude and phase of the PC time series can be obtained from T^(t), based on a Cartesian to polar coordinate transform (e.g., Stein et al., 2014): 3α(t)=Re(T^(t))2+Im(T^(t))2andΦ(t)=ArgIm(T^(t))Re(T^(t)), where the generalized phase difference has the following expression: 4ΔΦ(t)=ΦWC(t)-ΦHC(t), where ΦWC(t) and ΦHC(t) indicate the phase of the WC and HC PC time series, respectively. If the absolute tendency of the phase difference (i.e., |d(ΔΦ(t))dt|) is close to zero, then ΦWC(t) and ΦHC(t) are synchronized (Pikovsky et al., 2000). We use the following criterion for phases synchronization: phases synchronization occurs when the absolute tendency of a smoothed (i.e., 7-month running mean) phase difference of the WC and HC shift modes is less than 0.3 degrees/month. Strictly speaking, phase synchronization can only occur in nonlinear dynamic systems.

First, we conduct an EOF analysis of the monthly MSF anomalies, obtained from atmospheric reanalysis data covering the period 1979–2017. In addition to their co-varying strength (characterized by EOF1 for WC (WC1) and EOF2 for HC (HC2) – shown in Fig. S1) that has been discussed extensively in previous studies (Ma and Li, 2008; Bayr et al., 2014; Guo and Tan, 2018; Minobe, 2004), we find that the EOF2 of the WC (WC2) and the EOF1 of the HC (HC1) are related to each other (correlation coefficient CC ∼0.49, Fig. 1a–c). Compared to the climatological circulation pattern (contours in Fig. 1a, b) of WC and HC, WC2 and HC1 describe zonal and meridional shifts occurring over the shared rising branch of the two circulations (shading in Fig. 1a, b) over the Western Pacific Warm Pool. These anomalies characterize an eastward shift of the WC and an equatorially asymmetric clockwise HC that is sometimes referred to as cross-equatorial anomalous HC (Table S1 also clearly supports the co-varying zonal and meridional changes in WC and HC variability). Due to the spatiotemporal orthogonality of EOF modes, the co-varying spatial shifts of the WC and HC are uncorrelated to the strength changes in both circulations (e.g., CC between WC2 and WC strength index ∼0.08; CC between HC1 and HC strength index ∼0.02; see Table S1).

Previous studies showed that the ENSO-related SST variability leads to the co-varying strength of WC and HC (i.e., Walker and Hadley strength modes) (e.g., Minobe, 2004; Guo and Tan, 2018). Here, we explore the relationship between ENSO and the co-varying spatial shifts of the WC and HC (Fig. 1c and e). No statistically significant linear correlation between the PCs of HC1 or WC2 and Niño3 anomalies can be found on interannual timescales (CC ∼0.06 for WC2-Niño3; CC ∼0.2 for HC1-Niño3). This indicates that the peak ENSO dynamics alone cannot explain the synchronized spatial shifts in these two circulations. This stands in sharp contrast with the peak-phase ENSO-driven co-varying strength of the cells (CC ∼0.91 for WC1–Niño3; CC ∼0.87 for HC2-Niño3; see also Fig. S1c) that has been highlighted previously. Despite the fact that there is no linear contemporaneous relationship between ENSO (Niño3 SST) and the co-varying spatial circulation shifts, there is still a pronounced statistically significant relationship between WC2 and HC1 variability (see Fig. 1d; CC ∼0.66 significant at 99 % confidence level) in a 40-member MME of SST-forced AMIP experiments. This WC2–HC1 linkage breaks down when the SST-forced MME component is subtracted from the PCs of the individual AMIP runs (i.e., PC differences between individual AMIP simulations and the MME; Fig. S2). This raises the question of what type of SST pattern is responsible for the synchronized spatial shifts of WC and HC.

This discrepancy calls for two important aspects of ENSO to be considered: one is the peak-phase ENSO signal (which occurs in boreal winter); the other are the seasonally modulated characteristics of ENSO, i.e., the combination mode between ENSO and the Indo-Pacific warm-pool SST annual cycle (C mode; with a time evolution that peaks in boreal spring) (Stuecker et al., 2013, 2015). The C mode arises from an amplitude modulation of the warm-pool annual cycle (with a frequency of 1 year-1) and the interannual ENSO signal (∼1/2–1/7 year-1 frequency). The C mode plays a crucial role in the phase transition of ENSO events as well as in bridging ENSO's impacts on the East Asian monsoon system (Stuecker et al., 2013, 2015). We emphasize that the meridionally asymmetric anomalous atmospheric C-mode circulation is mostly associated with strong El Niño events occurring in the eastern equatorial Pacific and less so for central Pacific El Niño events (McGregor et al., 2013) (e.g., CC ∼0.55 for WC2-Niño3 during boreal spring; CC ∼0.09 for WC2-Niño4). We hypothesize here that the seasonally evolving warm-pool SST anomalies after the peak ENSO phase (i.e., C mode) serve as a pacemaker linking the phase-synchronized spatial shifts in WC and HC variability. The seasonal differences in relationship between WC2 and HC1 and Niño3 indices support our hypothesis (see Fig. S3). The WC2-regressed SST anomaly pattern (bottom in Fig. 1a) also bears resemblance to the previously suggested C-mode-generated SST dipole pattern with anomalous warming in the southern Indian Ocean (SIO) and anomalous cooling in the western North Pacific (WNP) (Stuecker et al., 2015; Zhang et al., 2016). This suggests that the Walker and Hadley shift mode variability is linked via nonlinear C-mode dynamics and not well reflected by common ENSO indices (such as Niño3) that instead describe peak boreal winter ENSO variability and the associated Walker and Hadley strength modes (Fig. S1).

In the previous section, we showed that the “Walker and Hadley shift modes” are coupled to each other, and we hypothesized an important role of the seasonally modulated dynamics of ENSO. The previously applied linear correlation analysis is well suited to analyze the amplitude relationships; however, it is not sensitive to the seasonally modulated nonlinear coupling. Therefore, before focusing on the physical linkage between these shift modes, we further examine the co-varying WC–HC shifts in the framework of phase synchronization and nonlinear coupling. Phase synchronization, which requires nonlinear dynamics, is characterized by cooperative and organized oscillatory behavior between two fluctuating systems. To study this process, we first calculate the generalized phase difference between WC2 and HC1 variabilities (i.e., ΔΦt=Φ1-Φ2), using the complex analytical signal of the respective principal components WC PC2 and HC PC1 (Sect. 2.4). The analytical signal approach embeds a time series into a complex space by adding the original time series with the Hilbert transform of this time series times the imaginary number (Pikovsky et al., 2000; Stein et al., 2014; Rosenblum et al., 1998; Rosenblum, 2000; Tass et al., 1998). The phase difference between WC2 PC and HC1 PC (Fig. 2a) shows periods of near-constant phase difference. Constant phase differences, which occur more frequently than expected by randomness, are indicative of the emergence of phase synchronization between WC and HC shift modes. When the absolute tendency of the phase difference (i.e., |d(ΔΦ(t))/dt|) in our calculations is less than 0.3 degrees/month (Fig. 2a), we refer to the period as a phase-synchronized period. During these periods the phases of two signals are not drifting apart randomly but are bounded by the underlying nonlinear interactions.

We next examine the question of whether the synchronization of Walker and Hadley shift modes can in principle be driven by random atmospheric stochastic variability, or if SST-forced variability is a prerequisite. The SST-forced AMIP MME shows more frequent phase-synchronized (PSYN) months than the observations (Fig. 2a) and most CMIP5 models (Fig. S4), exhibiting the effects of both SST forcing and atmospheric noise: there are four long-lasting (greater than 6 months) PSYN periods in the observations but eight such events in the AMIP MME. The WC–HC phase synchronization is particularly prominent during the two extreme El Niño events (1982–1893 and 1997–1998) that have much longer PSYN periods (exceeding 1 year) in both observations and the AMIP MME. An interesting point is that the WC–HC phase difference shows a decadal change after 2000 in both observations and the AMIP MME. This may be a consequence of the Pacific WC intensification which can be linked to the concurrent tropical Atlantic warming and tropical eastern Pacific cooling (England et al., 2014; McGregor et al., 2014; associated with multi-decadal climate variability in both the Atlantic and Pacific) and/or zonal shifts in the dominant ENSO SST pattern (Sohn et al., 2013). Further exploration of the underlying physical mechanisms is, however, beyond the scope of this study.

To further explore the relative effects of random atmospheric noise and SST-forced variability on the WC–HC synchronization, we generate pseudo-PCs by randomly shuffling the PCs for both the observations and the AMIP MME and repeating this 10 times. A comparison of the phase difference tendencies using the original PCs (pink dots in Fig. 2b, c) and of the pseudo-PCs (sky-blue dots) reveals that during the evolution of El Niño events (Niño3 >1.5 standard deviations (SDs); denoted by gray shading), the phase synchronization (i.e., |d(ΔΦ(t))/dt|<0.3) of the original PCs is clearly distinguishable from the pseudo-PCs that have randomized phases: the frequency for phase synchronization (i.e., the ratio of the PSYN number compared to the number in the gray-shaded area) is ∼83% for the observations and 96 % for the AMIP MME, whereas the ratio for the pseudo-PCs (sky-blue dots) is only ∼33% in the observations and 39 % in the AMIP MME (Fig. 2b and c). During the evolution of La Niña events (Niño3 <-1.5 SD), the phase synchronization is indistinguishable from random variability, hinting also at an important nonlinearity in the atmospheric response to tropical Pacific SST forcing. The PSYN probability from pseudo-PCs in the case of extreme El Niño events is similar to the probability for the entire dataset (∼35 %). Consequently, this result indicates that even though the temporal correlation between all-month Niño3 SST anomalies and PC2 WC and PC1 HC is marginal, eastern equatorial Pacific SST forcing still leads to an increased probability for WC–HC phase synchronization, during the El Niño event evolution. This discrepancy can be explained by the fact that correlations emphasize amplitude relationships and are less sensitive to seasonally modulated coupling which is induced by the phase-synchronization mechanism.

Our analysis has revealed that the Walker and Hadley shift modes are more connected to the seasonally modulated dynamics of ENSO (i.e., the C mode) rather than the peak-phase ENSO amplitude signal. Figure 3a clearly shows the statistically significant co-variability between observed time series of WC–HC PCs and the C mode (which is defined here as Niño3 ×cos⁡(ωa(t)-φ), whereωa(t) is angular frequency of the annual cycle and φ is a 1-month phase shift; Stuecker et al., 2013) (CC ∼ 0.61 and 0.58 on interannual timescales). To further test the association with the C mode, we also consider an SST index representing the integrated effect of C-mode dynamics (see also discussion in Zhang et al., 2016), which is calculated from the SST gradient between the SIO (20–5∘ S, 90–120∘ E) and the WNP (0–15∘ N, 140–170∘ E) (i.e., SSTgrad; SST(SIO, WNP)), as shown by the WC2-regressed SST pattern in Fig. 1a. We can see strong seasonal characteristics in both SST indices (Niño3, C mode and SSTgrad) as well as in the shift modes (Fig. 3b–g). The common Niño3 index peaks in boreal winter (i.e., November–December–January, NDJ; blue dots) in both observations and the AMIP MME. Different from this winter-maximum El Niño variability, the SSTgrad (or C mode) variability reaches its maximum during boreal spring (i.e., February–March–April, FMA; red dots). The difference in seasonality, which is also clearly seen in Fig. S5, can explain the very low correlation coefficient between the common Niño3 index and the shift modes. Despite this insignificant correlation, during the boreal spring, warmer Niño3 anomalies tend to be associated with enhanced shift mode variability; however, the opposite is not true for cold Niño3 anomalies (i.e., La Niña). This is consistent with the previous conclusion that the WC–HC phase synchronization only occurs during extreme El Niño events but not during extreme La Niña events. This springtime seasonal preference is evident for the SSTgrad (or C mode) index, resulting in a statistically significant relationship between SSTgrad (or C mode) and WC–HC coupling in both observations and the AMIP MME (Fig. 3d and g). This again indicates the important impact of springtime SSTgrad anomalies and C-mode dynamics on the phase synchronization of WC–HC.

Our results suggest that the spring SSTgrad anomalies that occur after the El Niño winter peak phase (Stuecker et al., 2015; Zhang et al., 2016) play an important role for the phase synchronization of WC and HC shift modes. We further examine the physical mechanism for the WC–HC phase-synchronized spatial shifts by exploring the global climate patterns that occur during springtime phase-synchronized periods in WC and HC variability (Fig. 4; composite when |d(ΔΦ(t))/dt|<0.3∘/month and FMA[1] Niño3 > 1.5 SD). A key feature is that the center of low-level divergence (upper-level convergence) and drying is located over the off-equatorial WNP region, whereas the center of convergence and moistening is situated in the off-equatorial southern central Pacific (corresponding to the C-mode pattern discussed in previous studies; Stuecker et al., 2013, 2015). This equatorially asymmetric circulation pattern is considerably different from the equatorially symmetric pattern derived from the wintertime PSYN composite (see Fig. S6) and even the springtime non-PSYN composite (Fig. S7). The meridionally asymmetric WC can be linked to the HC, along with cross-equatorial northwesterly flow. A general agreement between the observation-based and AMIP MME-based patterns also reflects that the SST-forced variability acts to modulate the phase synchronization of the WC–HC shift modes.

We emphasize that the simulated ENSO SST anomaly amplitudes in coupled models of the CMIP5 are correlated with the probability of phase synchronization between the WC and HC shift modes (Fig. S4). The models exhibiting large ENSO variability can initiate strong teleconnections through the atmospheric bridge process, thus likely leading to the phase-synchronized zonal and meridional shifts of the WC and HC, respectively (see Fig. S8). An underlying cause could be the strong meridional asymmetry of the warm-pool climatological SST and zonal winds (Fig. S9) and C-mode-associated extreme shifts of the South Pacific Convergence Zone (SPCZ) shifts (McGregor et al., 2012). We further hypothesize that stronger phase synchronization of the WC–HC shift modes can generate larger global precipitation responses, regardless of the ENSO amplitude. To illustrate this, we use the individual 40 AMIP simulations that have identical ENSO SST amplitude prescribed as their boundary forcing but exhibit different strengths of WC2–HC1 phase synchronization. The strong PSYN models and weak PSYN models are thus classified as a function of their strength of WC2–HC1 phase synchronization, where this strength is measured by the (interannual) correlation coefficient between WC2 and HC1 PC variations in the individual AMIPs (see Tables S2 and S3 for chosen model groups).

By comparing the strong El Niño (i.e., 1982/1983 and 1997/1998) composite averaged for eight strong PSYN models with that averaged for eight weak PSYN models (Fig. 5), we see that the models with a strong coupling between the HC and WC shift modes generate a prominent springtime (FMA) asymmetry between WNP divergence and southern central Pacific convergence. In particular, the geographical positions of minimum low-level divergence and maximum low-level convergence exhibit a clear contrast between the strong PSYN models and weak PSYN models (see pink and cyan star symbols in Fig. 5): the NW-SE oriented pattern is predominant for the strong PSYN models, but it is less pronounced for the weak models. Accordingly, the increased precipitation anomalies in the extratropical regions (e.g., East Asia and South America) are larger for the strong PSYN models compared to the weak PSYN models (Fig. 5b and d). These differences in anomalous precipitation and circulation centers are statistically significant during boreal spring but not during boreal winter. We also emphasize that these differences in precipitation are statistically insignificant for the tropical regions, indicating that the extratropical precipitation response is not primarily a result from an enhanced tropical convective activity. Differences in model physics may generate a strengthened WC–HC synchronization (i.e., NW-SE skewed asymmetric circulation pattern changes), further intensifying the post-ENSO impact on extratropical precipitation variability. This reflects the pronounced impact of WC–HC phase-synchronized spatial shifts on extratropical precipitation variability, regardless of the ENSO amplitude.