The gridded precipitation datasets used in this study are the 1∘ resolution Global Precipitation Climatology Project (GPCP) v2.3 dataset and the Global Precipitation Climatology Centre (GPCC) dataset version 6 at 0.5∘ resolution – in both cases available as monthly means. GPCP is a merged product of satellite and land rain-gauge observations and provides coverage over land and ocean, whereas GPCC uses a large network of surface station data going back to the early 1900s and has a higher horizontal resolution but does not provide data over oceanic regions . The HadSST 4.0 dataset is used for SSTs (1930–2021) . Zonal winds at the 70 hPa level from the Freie Universität Berlin (FUB) radiosonde dataset and from a long reconstruction (1930–2021 in this study) from sea-level pressure data (; hereafter B07) are also used to diagnose the QBO (see Sect. ).

For the other diagnostics, including zonal wind, vertical velocity and convective precipitation, we use the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 Reanalyses downloaded at the 0.75∘×0.75∘ resolution. Monthly mean data were used for all observational datasets. The GPCP and ERA5 datasets span the 1979–2021 period, whereas the period 1953–2019 is used for GPCC.

The MOHC submitted three simulations for the piControl experiment of CMIP6 using two models: HadGEM3 GC3.1 at N96 and N216 horizontal resolutions (hereafter referred to as GC3 N96-pi and GC3 N216-pi) and UKESM1 at N96 horizontal resolution (hereafter referred to as UKESM N96-pi). The HadGEM3 model is the core physical climate model, and UKESM1 is an earth system model extension, with additional treatment of aspects of, for example, land surface, ocean and sea-ice processes, as well as improved chemical processes . The N in N96 refers to the maximum number of zonal 2 grid-point waves that can be represented by the model at that resolution, so the N96 and N216 atmospheric resolutions at the mid-latitudes are 1.875∘×1.25∘ and 0.83∘×0.56∘, respectively, whereas their oceanic resolutions using the NEMO model are 1∘ (ORCA1) and 0.25∘ (ORCA025) , respectively.

The three simulations (GC3 N216-pi, UKESM N96-pi and GC3 N96-pi) used in this study are 500 years long and have the same experimental design with only one ensemble member. The simulations were run with constant year-1850 external forcing; further details about the MOHC piControl experiments can be found in and about the UKESM1 model in . The majority of diagnostics are shown for the GC3 N216-pi simulation, and comparisons with the other two simulations are noted where appropriate.

The equatorial climate of GC3 N216-pi captures tropical dynamical processes including mean and extreme precipitation reasonably well as this configuration is amongst the best compared to other CMIP5/CMIP6 models, e.g. in tropical extreme precipitation and the annual cycle of equatorial Atlantic SSTs and low-level winds . However, notable biases of the MOHC models include the southward bias of the Atlantic ITCZ linked to the dry Amazon bias and a wet bias over the East Pacific ITCZ .

Furthermore, the MOHC models have improved their representation of ENSO characteristics; e.g. finds that HadGEM3 configurations represent the pattern, seasonal cycle, amplitude and life cycle of ENSO better than the CMIP6 multi-model mean. These results agree with other studies that indicate the GC3 N216-pi configuration reasonably simulates the seasonal phase-locking and the spectral power of ENSO .

In the stratosphere, this and previous configurations of the model reasonably simulate the QBO . The model QBO is driven by both resolved and parameterised non-orographic gravity waves and is tied to total precipitation sources in the tropics . However, the atmosphere model configuration used in this study underestimates the amplitude of the QBO in the lower stratosphere (60–90 hPa), with the maximum bias found at 70 hPa of 5 ms-1, and the power spectrum of QBO periods shows more power at longer periods (32–36 months) than observations .

The index used to characterise the QBO for ERA5, the FUB and the simulations is the monthly mean zonal-mean zonal winds at 70 hPa averaged between 5∘ S and 5∘ N, which is well suited to diagnose impacts in the tropical tropopause region . The QBO phase is defined using a threshold of 2 ms-1 , so the transition months when the QBO winds fall within the range ±2 ms-1 are excluded. The reconstruction from B07 uses the 90 hPa winds and a threshold of ±2 ms-1. The amplitude and descent rates of the QBO are calculated using the deseasonalised zonal-mean zonal wind averaged over the stated latitudes between 10 and 70 hPa. The amplitude (A) of the QBO is defined using the first and second principal components (PCs) following an empirical orthogonal function (EOF) decomposition of the 10–70 hPa wind time series as A=PC12+PC22. The descent rates are calculated following for descending westerly and easterly phases individually by finding the level of the zero wind line (u=0) for each month computing the height difference between consecutive months. These definitions of the amplitude and descent rates were chosen to evaluate the influence of ENSO on the whole profile of the QBO and not just one single level.

The EN3.4 SST index is used to characterise ENSO by area-averaging the box within 5∘ S–5∘ N and 190–240∘ E. A 5-month running mean of the index is calculated and a threshold of ±0.5 K used to define positive (EN) and negative (LN) events. ENSO-neutral (NN) months are defined where the magnitude of the EN3.4 index is smaller than ±0.5 K. For the Indian Ocean Dipole (IOD), an index to characterise the zonal gradient in convective precipitation in the Indian Ocean (convective IOD Index) was defined as the difference of the deseasonalised area-averaged convective precipitation between the western (50–70∘ E) and eastern (80–100∘ E) equatorial (10∘ S–10∘ N) Indian Ocean, which is in a similar region as the standard SST IOD index . This index was computed using the convective precipitation from the models and ERA5, and IOD events were defined using a 1 standard deviation threshold.

Composite analysis is the primary technique used in the study. Annual-mean and seasonal-mean composites were derived by computing weighted averages to account for differences in the number of samples from each month and avoid a possible seasonal effect due to QBO or ENSO phase-locking, so all months contribute equally to a seasonal- or annual-mean composite. The length of the experiments is such that the number of total El Niño and La Niña months for GC3 N216-pi were 1700 and 1600, respectively, whereas 2400 months were classified as QBOW and 1800 as QBOE. Moreover, EN months found under QBOW were 626 compared to 392 under QBOE for the simulation, whereas in the observed 1979–2020 period using HadSST SSTs and the ERA5 QBO index, 65 QBOW–EN months and 45 QBOE–EN months were diagnosed. The ratio of QBOW–EN and QBOE–EN months to the total number of available months is slightly lower in the models (0.10 and 0.06, respectively) compared to ERA5 1979–2020 (0.11 and 0.08, respectively) because in the models fewer months satisfy our threshold for each QBO phase at 70 hPa due to the low-amplitude bias of the QBO in the lower stratosphere in GCMs .

In addition to composite analysis, multi-linear regression analysis is also employed to explore the impact of one or more of the indices. Previous studies have shown that the regression can separate candidate mechanisms or indices , for example, by removing the influence of ENSO. Details of the regression analysis technique are provided in Appendix .

The statistical significance of the observed composite differences is estimated using a randomised resampling (“bootstrapping with replacement”) method that generates a distribution of differences constructed from randomly sampling the observed period.

The significance level is then interpreted as QBO W–E differences that are outside of the 95 % confidence level of the distribution of randomly generated differences. The significance in the simulations is estimated using Welch's two-sided t test, but other bootstrap methods were tested without significantly changing the results.

QBO composite differences in annual mean precipitation (QBOW minus QBOE) are shown in Fig.  for the GPCP observational dataset and the three model simulations. In the observations, the QBO signals are largest and statistically significant in the tropical Pacific, equatorial Atlantic and Indian oceans, in good agreement with previous analyses . The three simulations show positive differences of up to 1.2 mmd-1 in the equatorial Central Pacific and the Indian Ocean and negative differences of up to 0.6 mmd-1 in the off-equatorial North Pacific. In the tropical Atlantic, however, there is a weak but significant signal in two of the simulations, but this signal is absent in the case of GC3 N96-pi. Note that precipitation in this region is affected by the biased southward position of the Atlantic ITCZ in the model which is more pronounced in December–January–February (DJF) .

The precipitation signal associated with the QBO is strongly dependent on the seasonal cycle in the model. Figure  shows a comparison of the GPCP dataset and GC3 N216-pi for individual seasons (see Fig. S1 in the Supplement for the other models). The positive equatorial Pacific signal in the GPCP dataset, which resembles an El Niño anomaly , is particularly strong and statistically significant in DJF (Fig. a). In GC3 N216-pi, the QBO signal in the Pacific is significant in all seasons but is generally weaker than observations likely due to the greater number of years in the simulation.

In the Atlantic, the QBO signal over the ITCZ region is more evident in the individual seasons. In DJF, the model response becomes negative in the southern equatorial Atlantic, whereas in March–April–May (MAM) the response is characterised by a dipole that resembles a northward shift of the Atlantic ITCZ. In addition, all models indicate that the Caribbean Sea is wetter in June–July–August (JJA) during QBOW than in QBOE (see Figs.  and S1). In the Indian Ocean, all models show relatively large and significant differences in September–October–November (SON; Fig. e and f), characterised by a dipole of wet anomalies to the west and dry anomalies to the east. The dipole anomalies suggest a possible QBO influence on the IOD, which is characterised by a zonal gradient of SSTs and convective activity in the Indian Ocean that is specially prominent in SON . This possibility is explored further in Sect.  below.

In summary, the observed (1979–2020) composite analyses show a zonally asymmetric QBO signal primarily in the ITCZ regions over the oceans, consistent with previous studies . The results in the simulations show several regions where there is a significant precipitation difference associated with the QBO phase. The significant response to the QBO in these long simulations (500 years) suggests that the analysis of the modelled QBO signals may help us to understand the mechanisms that give rise to the QBO signals at the surface. However, the QBO signals in the models show strong similarities to well-known response patterns for ENSO and the IOD. Before further investigating the QBO surface impacts, these tropical interactions are investigated in the following sections.

The tropical SSTs and the EN3.4 index differences for each QBO phase are investigated in this section to understand the precipitation patterns found in Figs.  and . The SST response (QBO W–E) closely follows the precipitation patterns for observations and models (Figs. , S2 and S3), with warmer SSTs found in regions with increased precipitation. In DJF, warmer SSTs in the equatorial Pacific and western Indian oceans are observed for QBOW compared to QBOE. In particular, the pattern in the HadSST dataset since 1979 resembles an East Pacific (or “standard”) El Niño, whereas the simulated anomalies in DJF (see also Fig. S3) are weaker and resemble a Central Pacific El Niño .

Previous studies have noted that the QBO–ENSO relationship in observations has changed since 1979. Figure  confirms that the Pacific SST response to the QBO has changed over different decades, with an anti-correlation relationship in 1960–1980 and a positive relationship emerging from 1985 to present. In the period prior to the radiosonde era (1930–1960) the relationship was also positive, according to the B07 QBO index.

The model simulations also exhibit decadal variability in the QBO–ENSO relationship (Fig. e). Even though the QBO–ENSO relationship is mostly positive, some 30–50-year periods exhibit a negative relationship. The link between the variability in the QBO–ENSO relationship in the model and the Atlantic Multidecadal Variability or the Pacific Decadal Oscillation indices was investigated (not shown), and no significant relationship was found. The observed multidecadal changes to the QBO–ENSO relationship (Fig. 3) means that the precipitation response (Figs. 1 and 2) would likely be different if a longer record of precipitation was available. While our analysis of the observed record is affected by statistical uncertainty e.g., this is likely not the case in the pre-industrial control simulations given their length and constant external forcing. This result further highlights the advantage of using these model experiments to understand QBO tropical teleconnections, including ENSO relationships, in the remainder of this paper.

As an initial investigation of the possibility of aliasing between the QBO and ENSO signals, Fig. a and b show the DJF QBOW minus QBOE composite differences of total precipitation from the GC3 N216-pi simulation using all years (as in Fig. ) compared with using only those years identified as “ENSO-neutral”. Although the sample size is substantially reduced in the latter (see figure for the number of months in each QBO composite), the sample size is still large. The response patterns are similar in each plot, e.g. the drier patch north of the Equator over the eastern Pacific or the wet anomaly over Madagascar. This result suggests that there is a QBO signal that is unlikely to be the result of a sampling bias that favours one particular phase of ENSO.

An alternative approach to investigate the possibility of aliasing of the QBO and ENSO signals is to use a multi-linear regression technique (see Sect. 2) in which the signal is analysed for both QBO and ENSO simultaneously. Here, we switch to analysing convective precipitation to better investigate the possible influence of the QBO on deep tropical convection.

Figure a and b show results from a simple linear regression analysis of the monthly averaged time series of GC3 N216-pi total precipitation in which only the 70 hPa QBO index was employed. Figure a includes all available years, while Fig. b includes only ENSO-neutral years. The results are very similar to the annual-mean composite differences in total precipitation (Fig. ), with increased convective precipitation over the equatorial Pacific when the zonal winds at 70 hPa are positive.

Figure c and d show the ENSO and QBO signals when the EN3.4 index is included, as well as the QBO index. The ENSO response is clearly evident, highly statistically significant and compares well with the well-known patterns obtained from observations. The amplitude of the ENSO signal is also much larger than the QBO signal. Nevertheless, the QBO signal remains intact, and all of the main features are still significant (Fig. c). For example, the positive regression coefficients that suggest a northward shift of the Atlantic ITCZ and the wetter Caribbean Sea and western Indian Ocean in the simple regression model are still found in the multivariate regression analysis. A similar analysis of tropical SSTs (Fig. S4) shows a QBO signal in SSTs that is separate from the effect of ENSO and agrees with the results of the composite analysis (Fig. ).

These results suggest that the modelled QBO signal in total precipitation does not arise due to a simple aliasing of the signal with ENSO. However, the multi-linear regression technique assumes that the QBO and ENSO indices are linearly independent and that their responses add together linearly. The similarity of the two responses suggests that this is probably not the case and there may be substantial non-linear interaction between the two phenomena e.g.. Nevertheless, the QBO signal remains even when only ENSO-neutral years are included in the analysis, suggesting that the QBO has a real influence on the surface precipitation.

To further explore the interaction of the QBO and ENSO, we first investigate whether aspects of the QBO are influenced by ENSO events. This relationship could be a real possibility since the intrinsic mechanism of the QBO involves tropical waves that are generated within the troposphere. found in a GCM that under El Niño conditions tropospheric wave activity increases and accelerates the downward propagation speed of the QBO westerly phase. However, the analysis by shows that only models with relatively high horizontal resolution can reproduce the observed ENSO effects on the QBO amplitude, although with weaker impacts than observed, while several models, including the MOHC UM, show no impact of ENSO on the QBO.

For that reason, we analyse several characteristics of the QBO and their dependence on the ENSO phase, namely the descent rate and the amplitude of the QBO (see Sect.  for details of how these metrics are defined). The results are summarised in Fig.  for the ERA5 reanalysis dataset (41 years; 1979–2020) and for the GC3 N216-pi simulation (500 years). In ERA5, the well-known faster descent rates during the westerly phase than in the easterly phase are evident and agree well with studies of longer datasets such as the Berlin radiosonde data . Also, the ERA5 QBO descent rates and the amplitude both depend on the phase of ENSO. A higher amplitude and slower descent rates are observed during La Niña phases and weaker amplitudes and faster descent rates during El Niño, in agreement with .

In the model, the descent rates are also faster for the westerly than the easterly QBO phase, as observed, but the relationship between the QBO characteristics and ENSO is less clear. Neither the amplitudes nor descent rates of the QBO are significantly different between EN and LN phases, according to Welch's t test. Interestingly, the only significant difference in the model is that descending westerlies are slower in ENSO-neutral months compared to EN or LN conditions, perhaps suggesting that characteristics of tropical wave activity may be different in ENSO phases compared with neutral years e.g.. The model results therefore suggest that there is little influence of ENSO on the descent rate and amplitude of the QBO in the GC3 N216-pi simulation; this result was also found for the lower-resolution simulations (not shown). In addition, no evidence was found that strong warm ENSO events change the phase of the QBO in this model, in contrast to the findings of . This finding of a null influence of ENSO on the QBO agrees well with the results of , who examined these relationships in an older version of the HadGEM model.

The reverse possibility, i.e. that the QBO may somehow influence ENSO, is now examined, first, by estimating whether the frequency of ENSO events significantly depends on the QBO phase. Table  documents the frequency of ENSO events in each QBO phase from observations/reanalysis and the three model simulations. A higher frequency of EN events during QBOW and of LN during QBOE has been observed from 1979 to 2020 , but the opposite is diagnosed if the period is extended to 1953–2020, in agreement with previous sections and studies . Probability density functions (PDFs) were constructed, first, for the observations by bootstrapping with replacement to account for observational uncertainty and for the model data using 39-year samples to match the length of the ERA5 period. In addition to Welch's t test, a Kolmogorov–Smirnov (KS) test was used to evaluate if the PDFs of an event frequency (e.g. EN) were significantly different for each phase of the QBO.

The results show significant differences, according to both KS and Welch tests, for each ENSO phase in the three model simulations. EN events are more frequent under QBOW conditions than under QBOE in both observations and model datasets. LN events are equally frequent in both QBO phases in the HadSST dataset, but in GC3 N216-pi they are more frequent under QBOE than under QBOW. Note that the frequencies of LN and EN under neutral QBO conditions in the model were ±0.26 month per month in both cases.

Figure a and b show the EN3.4 index amplitude and interannual standard deviation as a function of each month from the HadSST dataset and the GC3 N216-pi simulation, separated for each phase of the QBO. From this we can examine, for example, whether any QBOW minus QBOE differences in ENSO characteristics arise primarily from one QBO phase or the other (i.e. a non-linear response) or whether both phases contribute equally to the response difference.

In the observed period of 1979–2021, the EN3.4 SST is negative from December to April under QBOE. These results are consistent with the analysis of ENSO frequency in Table , which shows more frequent La Niña events under QBOE and El Niño events under QBOW. In the model, the mean EN3.4 index is frequently positive under QBOW and also negative from December to April under QBOE. In both cases, the strength and sign of the differences varies seasonally; for example, the only month where the EN3.4 index is statistically different is April.

The previous sections have demonstrated that the mean QBO response is affected by an uneven frequency of ENSO events in each QBO phase. In addition, evidence was found of non-linear ENSO impacts associated with the QBO or, in other words, that the QBO response can also be a function of ENSO. This non-linearity can be observed in Fig.  where the QBO composite differences in convective precipitation in MAM are shown using all years, ENSO-neutral years, and EN or LN years. While the broad nature of the QBO signal remains similar, the details differ depending on the phase of ENSO (Fig. c and d). For example, the Atlantic and Pacific ITCZ responses are opposite during LN compared to neutral and EN years. The total equatorial Atlantic response is then a result of the combination of EN and neutral years which is dampened or obscured by the LN years.

Another prominent feature of the composite of all years is the off-equatorial West Pacific positive response which is only observed for neutral years. This result suggests that some ENSO impacts, e.g. over the Atlantic basin, are different depending on the QBO phase. In GC3 N216-pi, this effect is more readily observed during MAM, but similar results are found for the other two models in DJF (Figs. S6 and S7). The implication of these results would be that, in some cases, regression analysis may not be the right approach because the QBO surface impacts may be non-linear.

In the previous sections, the precipitation and SST analyses also show suggestive evidence of a relationship between the QBO and the Indian Ocean, in both the observations and the model. The link between the QBO and the IOD event frequency have been analysed in the same way as for the ENSO index and a significant relationship is confirmed (Table  and Fig. c and d). The IOD event frequency is also markedly different depending on the QBO phase, with positive events more frequently observed in the westerly phase of the QBO and negative events found more frequently under QBOE, both for ERA5 and the model simulations (Table ). The monthly mean values in Fig. c and d for the model indicate a more frequently positive IOD index under QBOW and a negative index for QBOE, and these differences are statistically significant in September and October. The GC3 N96-pi and UKESM N96-pi results are very similar (Fig. S5), and the differences are also significant in SON.

This section demonstrates statistically robust links between the IOD and ENSO, as well as the QBO. These phenomena (ENSO and the IOD) are intertwined by pan-tropical teleconnections through zonal circulations , and they interact with monsoons and the ITCZ. For that reason, the following section explores more closely the links between the QBO and features of the circulation in the tropics.

This section investigates the QBO impacts on the ITCZ, monsoons and the Walker circulation. The previous sections demonstrated a robust link in the simulations between ENSO and the QBO, and for that reason, this section presents results of when the influence of ENSO has been removed by using ENSO-neutral (NN) composites. Model biases in the representation of the migration and dynamics of the ITCZ, measured by zonally averaged convective precipitation in the Pacific and Atlantic sectors (Fig. a and b), are highly relevant since these biases may modify any physical mechanisms of the QBO over convection. These biases can be characterised by a southward shift of the simulated Atlantic ITCZ in DJF and MAM and a wider extent of the Central Pacific ITCZ compared to ERA5 leading to a “double ITCZ” in the Pacific during boreal winter . Note that the magnitude of the biases is almost as large as the climatological values during boreal winter.

The monthly mean QBO W–E zonal-mean convective precipitation differences in the Pacific and Atlantic ITCZ regions during NN conditions (Fig. ) show that the ITCZ impacts are seasonally dependent. While there are no clear differences in the Atlantic sector for ERA5 in any month, in GC3 N216-pi there is a significant northward shift of the ITCZ from April to June, which is likely associated with the warm SST anomalies found in this season in the northern tropical Atlantic (Fig. ).

The differences in the Pacific sector for ERA5 show a very noisy and mixed result. However, in GC3 N216-pi, a southward shift of the ITCZ is observed from February to July, maximised in the MAM season. Very similar results for the Atlantic and Pacific sectors were observed for the other two simulations (Fig. S8). Note that these results are for ENSO-neutral conditions, and for all years the link between QBO and ENSO is evident (Fig. S9).

Observational and modelling evidence has documented links between the QBO and monsoon regions. However, the results in the previous sections (Fig. ) show little-to-no robust effects of the QBO on precipitation over land in the simulations. The precipitation response over land is examined more closely by analysing regions that fit the concept of the global monsoon. For this purpose, a monsoon region is defined as a region in which over 55 % of the total annual rainfall is observed or simulated in the respective summer season, and the summer–winter precipitation difference is higher than 2 mmd-1 . After defining these regions, the QBO W–E differences, during ENSO-neutral only, are computed for June–September (JJAS) and December–March (DJFM) for Northern Hemisphere and Southern Hemisphere monsoons, respectively, for GPCC (1953–2020) and GC3 N216-pi.

Figure  shows that precipitation response over monsoon regions is relatively weak in GPCC and GC3 N216-pi. In the South American and Indian monsoon regions, for example, both positive and negative significant differences are observed, indicating no region-wide coherent impact. This lack of spatial coherency suggests that regional dynamics are likely important. In GC3 N216-pi, in the South American monsoon region, the QBO W–E differences indicate a significantly wetter region in South America, where the South Atlantic Convergence Zone is located . Similarly, wetter conditions over southern Mexico and Central America (the Midsummer Drought region) are observed during QBOW compared to QBOE in GPCC and, albeit much weaker, in GC3 N216-pi.

The climatological biases in the representation of the monsoon dynamics by this and other climate models e.g. in South America; could mean that the impacts seen in Fig.  are model-dependent and that our analysis of the lower-resolution simulations (Fig. S10) indicates that some of these impacts are also resolution-dependent. This reinforces the notion that the mean representation of the dynamical features of each monsoon by a model configuration is important for any subsequent response to the QBO. Nevertheless, this analysis shows that in the model the QBO impacts on land convection are weaker than on oceanic convection, suggesting that SST feedbacks may be important for the QBO response in the model.

A number of studies have suggested a link between the QBO and the Walker circulation that could explain the zonally asymmetric nature of the QBO surface impacts in the tropics e.g.. Therefore, the relationship between the Walker circulation and the QBO is examined to evaluate this hypothesis through the use of the zonal streamfunction , defined as 1ψ=2πag∫0puDdp, where ψ is the zonal streamfunction, uD is the divergence part of the zonal wind, a is the Earth's radius, p is the pressure coordinate, and g is the gravitational acceleration. The divergent component of the zonal wind (uD) is computed by solving the Poisson equation for the velocity potential using the python package windspharm that employs spherical geometry. The streamfunction is calculated by first averaging over the equatorial band of 10∘ S–10∘ N and integrating from the top level of each dataset to the surface.

QBOW minus QBOE composite differences in DJF show that the streamfunction in the eastern Pacific (220–260∘ E) is significantly weaker during QBOE than during QBOW in ERA5 and GC3 N216-pi (Fig. ). In the model, these streamfunction differences are significant even low in the troposphere. The zonal wind at upper levels (300–100 hPa) is also weaker in QBOW compared to QBOE at 200∘ E in both model and reanalysis. In GC3 N216-pi, the negative ψ difference is accompanied by descending motion anomalies in the 170–220∘ E region, whereas anomalous ascent is observed in the Maritime Continent and Indian Ocean. The differences in the other simulations agree with the results of GC3 N216-pi (not shown).

In boreal fall (Fig. ), the differences are also significant and can be linked to the relationships found between the IOD and the QBO. Specifically, significant positive differences (W–E) in the streamfunction are found in the eastern Indian Ocean and Maritime Continent and negative differences in the eastern Pacific. In GC3 N216-pi, vertical velocity anomalies indicate stronger ascent in the western Indian Ocean and in the Maritime Continent, whereas weaker ascent anomalies are found in the eastern Indian Ocean. These results agree with positive IOD indices found in QBOW and a mean negative index during QBOE.

The rightmost panels in Figs.  and , in which only ENSO-neutral months are considered, suggest that this relationship between the QBO and the Walker circulation occurs regardless of ENSO events for GC3 N216-pi. However, some QBO–ENSO superposition can be seen from the plots; e.g. in ERA5, removing ENSO events changes the sign of the response. This effect is likely due to the small sample size in the observational record when only neutral months are considered. The weakening of the Walker circulation under QBOW compared to QBOE is also seen in the other model configurations (Figs. S11 and S12). These results highlight links between the large-scale overturning circulation and local precipitation found in previous studies and in early sections of this paper.