Influence of the Quasi‐Biennial Oscillation on tropical convection and its teleconnection to the midlatitudes in boreal winter

Recently, a connection between the quasi‐biennial oscillation (QBO) and the Madden–Julian oscillation (MJO) was found in observations. The boreal winter seasonal mean amplitude of the daily MJO is anticorrelated with the QBO winds measured at 50 hPa. We investigate whether this relationship is captured in reforecasts of past winters in a seasonal prediction system, and find the ensemble mean response does not show this association, with essentially zero correlation. By repeated subsampling of the ensemble reforecast data, we also show that the observed correlation is very unlikely to arise merely as the result of sampling in the relatively short observational record. Instead, we conclude that the reforecasts genuinely cannot capture the observed QBO–MJO seasonal relationship. We also consider the boreal winter seasonal mean response of tropical convection to the QBO and its influence on the subtropics. We find that the reforecasts are able to capture the stationary pattern found in the observed outgoing long‐wave radiation (OLR) over the tropical west Pacific in response to the QBO. We also find that the associated upper tropospheric divergence in observations interacts with the west Pacific subtropical jet to produce atmospheric Rossby wave patterns that propagate across the midlatitude Pacific Ocean. These extratropical waves have the potential to interfere with the climatological waves in midlatitudes, modifying the strength of the midlatitude annular mode through interactions with the extratropical stratosphere. However, the observed influence on wavenumber 1 is not captured by the reforecasts, suggesting a weak extratropical influence and a partial explanation for the weaker‐than‐observed QBO teleconnection to the Arctic Oscillation and North Atlantic Oscillation.

and a mean period of approximately 28 months.This slow atmospheric variation in the equatorial stratosphere may provide a source of long-range prediction of midlatitude weather (Scaife et al., 2014).For example, the observed influence of the QBO on the stratospheric polar vortex (SPV; Holton & Tan, 1980, 1982), referred to as the Holton-Tan effect (HTE), links the direction of the QBO zonal winds at 50 hPa with the strength of the SPV in winter.Easterly QBO winds are associated with a weaker polar vortex, and westerly QBO winds with a stronger polar vortex (e.g., Anstey et al., 2021).The strength of the SPV has an inverse relationship with the probability of a sudden stratospheric warming (Scherhag, 1952) occurring during winter (Anstey et al., 2021), which can have a downward influence on midlatitude weather regimes (Baldwin & Dunkerton, 2001).Another related example is the influence of the HTE on the Arctic oscillation (AO; Thompson & Wallace, 1998).The response of the AO to the QBO is stronger when the QBO wind direction is vertically coherent (Andrews et al., 2019), resulting in a more positive AO for deep QBO-westerly (QBOW) minus deep QBO-easterly (QBOE) conditions.
The vertical influence of the QBO on modes of equatorial tropospheric variability such as the Madden-Julian oscillation (MJO) (Madden & Julian, 1994) is an emerging topic of interest.The MJO is a major mode of organised convective variability in the tropical troposphere.It is characterised by eastward-propagating pulses of large-scale organised deep convection and rainfall that typically strengthen in the Indian Ocean before passing over the Maritime Continent into the western equatorial Pacific before subsequently weakening (Zhang, 2005).The pulses have a period of between 30 and 60 days.The MJO is traditionally categorised into eight phases, following Wheeler and Hendon (2004;WH04), representing the eastward propagation of the region of deep convection.Teleconnections from specific phases of the MJO convection have an influence on the midlatitude atmospheric circulation, such as the North Atlantic oscillation (NAO; Hurrell et al., 2003), via tropospheric wavetrains (Cassou, 2008;Hood et al., 2020;Lin & Brunet, 2009;Roundy, 2022) and modulation of the SPV (Garfinkel et al., 2012;Lee et al., 2019).
The influence of the QBO on the MJO is believed to involve the anomalously warm and cool zones associated with QBO's downward propagation toward the tropopause over time (Collimore et al., 2003;Giorgetta et al., 1999;Liess & Geller, 2012;Martin, Son, et al., 2021;Son et al., 2017;Yamazaki et al., 2020) although the mechanism is still uncertain.Under QBOE conditions at 50 hPa, an anomalously cool zone lies above the tropical tropopause.This reduces the static stability in the upper troposphere/lower stratosphere (UTLS) region which may enhance deep tropospheric convection (Giorgetta et al., 1999;Gray et al., 1992).Conversely, for QBOW conditions at 50 hPa, the warm zone above the tropical tropopause leads to a more stable UTLS region with the opposite influence on tropospheric convection.This interaction between the QBO and deep tropical convection is the leading mechanism proposed to explain the significant correlation between the phase of the QBO at 50 hPa and the seasonal mean amplitude of the daily MJO in boreal winter (Son et al., 2017).The interaction between the observed seasonal mean QBO and the seasonal mean MJO amplitude appears to be an emerging relationship that has only become significant since the 1980s (Klotzbach et al., 2019;Sakaeda et al., 2020).Attempts to capture this seasonal mean interaction in climate models have hitherto not been successful (Lee & Klingaman, 2018;Martin, Orbe, et al., 2021;Nishimoto & Yoden, 2017), even when the simulated lower equatorial stratosphere is nudged toward observations (Martin, Orbe, et al., 2021).
In addition to changes in the amplitude of MJO variability, seasonal mean shifts in the tropics in response to QBO phase have also been examined.The observed boreal winter seasonal mean OLR response to the QBO shows a stationary OLR anomaly in the tropical west Pacific in the vicinity of the warm pool, where the tropical tropopause is at its highest (Yamazaki et al., 2020).Collimore et al. (2003) found that QBOE conditions promoted deeper convection in the tropics, suggesting a possible link with the mean-meridional circulation associated with the QBO.Liess and Geller (2012) found that the QBOE phase is linked to increased convective cloud cover over regions in the tropical west Pacific.More recently, Yamazaki et al. (2020) looked at the difference in OLR for QBOE and QBOW conditions in late autumn and early winter.They found that these teleconnections projected onto the climatological stationary waves in the northern hemisphere, specifically zonal wavenumbers 1 and 2. In that study, the QBOE convection results in a significant enhancement of wavenumber 1, enhancing the amplitude of vertically propagating planetary waves in the midlatitudes, leading to a weakened SPV.These seasonal teleconnections will likely have a contribution from the transitory and time-varying subseasonal MJO teleconnections which are known to be modulated by the easterly and westerly phases of the QBO (Cassou, 2008;Garfinkel et al., 2012;Hood et al., 2020;Lee et al., 2019;Lin & Brunet, 2009;Roundy, 2022).
The ability of models to capture QBO teleconnections could be beneficial for seasonal forecasts especially as models are capable of predicting the QBO out to interannual timescales (Pohlmann et al., 2013;Scaife et al., 2014).Nevertheless, correctly quantifying teleconnections is hampered by the short observational record, which limits the available sample size.Modelling studies can typically offer larger samples and are therefore useful for assessing the robustness of these observed influences.
In this study, we focus on the QBO's downward influence on the tropical troposphere and subsequent teleconnections to the midlatitudes generated by these tropical changes.We investigate whether the Met Office seasonal forecast system GS5 (MacLachlan et al., 2015), is able to capture the observed correlation between the winter QBO index and the seasonal mean MJO amplitude.We then investigate whether GS5 is able to reproduce the seasonal OLR signal in the tropical west Pacific (TWP) in response to the QBO phase at 50 hPa.Furthermore, we go on to consider the simulation of extratropical teleconnections linked to QBO-related tropical anomalies.If these observed tropical connections and associated teleconnections to the northern midlatitudes can be replicated by seasonal forecast systems such as GS5, it may prove to be a source of skill in seasonal forecasts.

DATA AND METHODS
We use monthly-mean European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5) data (Hersbach et al., 2020) to represent observations, in particular, zonal (u) and meridional (v) winds, and geopotential height (Z).Monthly-mean OLR data are taken from the National Oceanic and Atmospheric Administration (NOAA) (Liebmann & Smith, 1996) on a 2.5-degree latitude/longitude grid.All other fields used in this study, both ERA5 and GS5, are regridded onto the same grid.The GS5 reforecast datasets, also known as hindcasts, form part of the Met Office seasonal forecast production system (MacLachlan et al., 2015).The daily QBO-MJO analysis in this paper uses a 30-member hindcast dataset, with initialisation dates of 25 October, 1 November, and 9 November for each year from 1993 to 2015.The seasonal QBO-OLR tropical deep convection analysis uses a more recent 21-member hindcast dataset with the same October/November start dates, but extended to include the winter of 2016/17.Both sets of hindcasts use the same model version hence the interpretation of our results is not affected.
The QBO indices for ERA5 and the GS5 hindcasts are calculated using zonal mean zonal wind at 50 hPa, averaged across the latitude band 10 • S-10 • N. We define the QBO phase as easterly when the QBO index is below −5 m⋅s −1 , and westerly when it is above 5 m⋅s −1 .The number of QBOE and QBOW winters in ERA5 is 14 and 12, respectively.A comparison of the December-January-February (DJF) QBOE − W index at 50 hPa, −21 m⋅s −1 for ERA5 and −19 m⋅s −1 for GS5, indicates that the amplitude of the QBO wind variability matches that in observations to within 10%.The wind shear zone at 70 hPa, which is dynamically associated with the specified QBO index (50 hPa), has a QBOE − W temperature response of −2.8 K for ERA5.Unfortunately, this level was not output by the GS5 experiments.We find, however, that the QBOE − W temperature differences at 100 hPa are similar: −0.55 K for ERA5 and −0.50 K for GS5.
The preprocessing of the hindcast u-winds and OLR fields, prior to calculating the MJO indices, consists of three key steps: deseasonalising, removing the influence of El Niño-Southern Oscillation (ENSO), and detrending.Deseasonalising is performed by calculating the daily climatology for each lead time across the hindcast dataset and removing this daily climatology from each hindcast.This is performed for each of the three start dates separately, producing an anomaly dataset with the seasonal progression removed.Removal of the ENSO signal is achieved by linear regression of the fields with the Niño3.4index.This relies on the linearity of the ENSO influence, which may not be a good assumption for strong ENSO events, such as occurred in the winters of 1982/83, 1997/98, and 2015/16 (Toniazzo & Scaife, 2006).Consequently, these winters are excluded from the analysis.The linear regression approach may not capture the influence of the varying structure of ENSO events on the structure and propagation characteristics of the MJO.Further, detrending is applied separately for each lead time in the hindcasts on a gridpoint basis.The reanalysis u-winds and OLR fields are preprocessed in the same manner.
For the calculation of the MJO, the modified OLR, u850 (u wind at 850 hPa), and u200 (u wind at 200 hPa) fields are averaged between the latitudes of 15 • S and 15 • N for each hindcast, and then normalised by the variance calculated across all hindcasts.These fields are concatenated and then projected against the WH04 multivariate EOF1 (empirical orthogonal function 1) and EOF2, resulting in two real-time multivariate MJO timeseries, RMM1 and RMM2.These orthogonal timeseries can be plotted to produce an MJO phase space diagram (WH04; their figure 7).The location of each point on this diagram indicates both the MJO phase and MJO amplitude.The MJO amplitudes are normalised using the standard deviation calculated across the entire hindcast dataset.The reanalysis MJO is calculated in the same manner.
The fields used for the QBO-OLR analysis, that is, the monthly-mean OLR, Z200 (geopotential height at 200 hPa), u200, and v200 (v wind at 200 hPa), are preprocessed in a similar manner to the QBO-MJO preprocessing, that is, deseasonalising, removing the influence of ENSO, and detrending, but using winter-mean ensemble-mean data.
The QBO is highly predictable on seasonal timescales (apart from on rare occasions when a zonal-wind reversal occurs in the lower stratosphere within a zone of opposite phase [Osprey et al., 2016;Newman et al., 2016]).Therefore, we ensure that the same winters are analysed for ERA5 and GS5 over the hindcast period by selecting GS5 QBOE and QBOW winters using the QBO phase in reanalysis.The Rossby wave source (RWS) fields at 200 hPa are calculated using the windspharm python package (Dawson, 2016).

QBO-MJO TELECONNECTION
We first examine the relationship between the QBO and the MJO amplitude.For GS5, the evolution of the OLR field as a function of MJO phase (Figure 1a) demonstrates a good model reproduction of the observed MJO (WH04, their figure 8; Son et al., 2017, their figure 2).The magnitude of the OLR response agrees with the previous GloSea5 MJO analysis of Yang et al. (2021) and the GloSea4 MJO analysis of Arribas et al. (2011), and is slightly weaker by approximately a third than the MJO in ERA5 calculated using the same method.The response of the MJO to the QBO, calculated as the difference between composites of QBOE and QBOW (Figure 1b) does not reveal an MJO-like progression, however.The relationship between the seasonal mean QBO at 50 hPa and the seasonal mean MJO amplitude for GS5 has a non-significant correlation of r = −0.06.In reanalysis, for the period 1980-2020 the correlation between the seasonal mean QBO at 50 hPa and the seasonal mean MJO amplitude is calculated as r = −0.48,and, for the Son et al. ( 2017) period 1980-2013, r = −0.52,which is comparable to their r = −0.57.This suggests that GS5 ensemble means are unable to reproduce the significant QBO-MJO relationship found in the reanalysis.
The observationally-based relationship is the result of analysing a record of only 40 years, and therefore contains limited samples of QBOE and QBOW years.As a result, there is a possibility that despite its apparent strength it could be attributable to aliasing from finite sampling.To test this, we extract subsamples of the GS5 hindcasts to quantitatively assess the distribution of possible correlation values, assuming that the amplitude of noise in the hindcasts is realistic.We randomly sample winters from individual hindcasts to produce 1000 trials, each with the same number (40) of winters as in the reanalysis period.For each trial the DJF correlation between the QBO phase and the seasonal mean MJO amplitude is calculated.The spread of correlations (Figure 1c) confirms that both positive and negative correlations are possible as a result of sampling but the reanalysis value of r = −0.48lies on the very lowest margin of the distribution and is significantly different at the 0.1% level using a one-tailed test.The observed correlation is therefore unlikely to occur by random sampling of the variability in the hindcast ensemble and we conclude that this is likely to be a genuine error in the seasonal hindcasts.
This lack of connection between the QBO phase and MJO amplitude in GS5 might be due to errors in the equatorial lower stratospheric temperature and wind structure associated with the QBOE − W at 50 hPa.This possibility was tested in an equivalent seasonal hindcast (not shown) by nudging the u, v, and T (temperature) fields in the middle-to-lower equatorial stratosphere (down to ∼70 hPa) towards ERA-Interim (Dee et al., 2011) values.In this nudged experiment the QBOE − W u-winds at 50 hPa, for example, are within approximately 99% of the reanalysis value.Despite the lower stratospheric temperature and winds being nudged closely towards observed values, the QBO-MJO relationship was still not evident, consistent with the experiments by Martin, Orbe, et al. (2021).The link between the amplitude of the MJO and the QBO index at 50 hPa therefore appears not to be captured by our seasonal forecast model and is also not easily attributable to an error in the representation of the QBO wind and temperature structure given the evidence of the nudged experiment.

QUASI-BIENNIAL OSCILLATION MEAN WINTER TELECONNECTION
Examination of the winter-mean QBOE − W response in OLR, Figure 1b, suggests a largely consistent negative OLR region in the tropical west Pacific across most MJO phases in boreal winter, most clearly seen in MJO phases 1-3 and 6-7.Given that we see this consistent regional response rather than a propagating MJO-like response, we now consider the seasonal mean OLR response to the QBO without stratification by MJO phase.The ERA5 response to QBOE − W (Figure 2a) exhibits a number of potentially significant regions of OLR response across the globe, but the largest and most coherent signal appears to be the negative OLR response in the TWP with a horseshoe pattern of significant positive OLR across northern Australasia, Indonesia and the Philippines.
In this case, the hindcast response to QBOE − W (Figure 2b) reproduces the same pattern and highlights a similar region, with significant negative OLR in the west Pacific, surrounded by a horseshoe pattern of significant positive OLR.While similar to observations, we note this pattern is shifted westwards by about 15 • in longitude.This westward shift is reminiscent of the overestimate of penetration of ENSO precipitation anomalies in the west Pacific in GS5 (MacLachlan et al., 2015), suggesting the presence of a more general westward bias in TWP convection that might also exert an influence on the QBOE − W response.The hindcasts analysed here (starting around 1 November), an equivalent set of GS5 hindcasts starting one month earlier (not shown) and the nudged runs (not shown), are able to capture the same, statistically significant DJF  response, which indicates a robust dynamical response in the model.The negative OLR anomaly is associated with increased deep convection in the TWP, and results in colocated upper tropospheric divergence at 200 hPa (not shown).Anomalous upper tropospheric flow from the tropics to subtropics interacts with the west Pacific subtropical jet to create RWS regions (Figure 3a,b).In reanalysis, the strongest significant positive RWS region lies south of Japan and forms part of a positive-negative-positive zonal 'tripole' pattern across the Pacific towards the dateline (Figure 3a).For the GS5 hindcasts, the 'tripole' response pattern is shifted westward, with the first significant positive RWS node located over East China (Figure 3b).The lack of the positive RWS south of Japan together with a weaker pattern will likely lead to the model having a different midlatitude response from observations.
A comparison of the geopotential height response at 200 hPa (Z200; Figure 3c,d) shows that the northern hemispheric-scale wave pattern response differs between ERA5 and GS5.In reanalysis there is a wavetrain that appears to originate over eastern Asia which extends across the Pacific.It has a northwest to southeast phase tilt from the mid-Pacific towards North America, suggesting wave propagation polewards and eastwards away from the Pacific RWS regions.Upon reaching the midlatitudes the zonal wavenumber 1 appears to dominate.In GS5, there is also evidence of Rossby wave propagation away from the Pacific RWS regions, although the pattern is shifted westwards compared to reanalysis and is considerably weaker.Given the different locations of the RWSs, the negative/positive Z200 anomaly over North America in reanalysis is potentially equivalent to the negative/positive regions in the north Pacific/Alaska in GS5 (Figure 3c,d), again indicating a westward shift in the model response.This westward shift and the differing extent of the eastward propagation of Rossby waves may, in part, be influenced by the climatological upper tropospheric westerly zonal winds in the midlatitude Pacific (not shown) which are slightly weaker in GS5 than in reanalysis (Henderson et al., 2017;Hoskins & Ambrizzi, 1993).
We next consider the relationship between the QBOE − W wavenumber 1 response and the climatological wavenumber 1 in the northern midlatitudes due to its potential impact on the SPV.When the climatological wavenumber 1 is enhanced, it increases the wave momentum flux that propagates into the winter stratosphere (Ineson & Scaife, 2009;Taguchi & Hartmann, 2005).Deposition of momentum into the stratospheric polar westerly jet acts to weaken the polar vortex, the strength of which has an influence on both the AO and the NAO (Manzini et al., 2006;Smith & Kushner, 2012).
The ERA5 Z200 wavenumber 1 response to QBOE − W, Figure 3e, constructively interferes with the northern hemisphere midlatitude climatological wavenumber 1, with an approximate magnitude of 10% of the climatological amplitude.This result agrees with Yamazaki et al. (2020) who found a similar constructive interference response in November using the ERA-Interim dataset.However, due to the shift in the modelled pattern, the GS5 wavenumber 1 pattern in the northern midlatitudes (Figure 3f) is out of phase with the climatological wavenumber 1.These results suggest that the QBO in reanalysis indirectly enhances the vertically propagating wave momentum flux from the midlatitude troposphere, but this does not occur in the hindcast simulations.The ERA5 midlatitude wavenumber 2 response (not shown) destructively interferes with the climatological wavenumber 2. For GS5, the midlatitude wavenumber 2 (not shown) exhibits an eastward shift to the climatological wavenumber 2 and lies in approximate quadrature.This is comparable to the eastward shift in Yamazaki et al. (2020).
It is clear that the GS5 response differs from reanalysis in terms of upper tropospheric circulation pattern (Figure 3c,d) and midlatitude wavenumber 1 response (Figure 3e,f), potentially as a result of differences in the pattern of RWSs.To address this possibility, we subsample the GS5 hindcast members which have a similar pattern of RWSs to those derived from observations.We make QBO composite differences (QBOE − W) of the RWS field for 500 randomly selected GS5 subsets of the same size as the reanalysis dataset.For each trial, we project the RWS composite difference against the ERA5 RWS composite difference in the region 130 • E-180 • E, 25 • N-38 • N (indicated by the black rectangle in Figure 3a).This encompasses the positive and negative RWSs south of Japan.The 10 trials with the highest total point-wise product are selected as the best matches.These, by construction, have mean RWS patterns similar to reanalysis in the region used for projection.The Z200 and OLR mean fields for the average of these 10 matches are shown in Figure 4a,b.The negative Z200 response east of Japan (Figure 4a) is similar to that in reanalysis (Figure 3c), which provides confidence in the model response to the strong RWS south of Japan.However, the downstream response in GS5 still diverges markedly from reanalysis across the north Pacific.This indicates that even when GS5 matches the RWSs in the selected region, it is still unable to reproduce the observed response.It is possible, therefore, that additional factors outside of the selected area may be important to generate this pattern.The composite OLR anomaly (Figure 4b) shows a negative pattern in the TWP which is more consistent with the estimate of the QBO response in the full GS5 ensemble (Figure 2b) than for ERA5 (Figure 2a) despite the runs being selected to match the ERA5 RWS QBO difference pattern.
Given this failure to replicate the northern hemispheric wave response to the observed RWS pattern, we test whether the observed response is nevertheless linked to negative OLR in the TWP through wider patterns of RWS than considered in the analysis in Figure 4a.Since a TWP OLR pattern exists in QBOE − W composites regardless of the extratropical response, we construct a set of 500 trials sampled without consideration of the sign of the QBO anomaly to identify trials that match the Z200 wave pattern over the north Pacific and North America.For each trial we calculate the area-averages in each of the four boxes highlighted in Figure 4c which are located over the positive and negative nodes of interest in the observed Z200 pattern (Figure 3c).We create an index by subtracting the sum of the area means of the negative nodes from the sum of area means of the positive nodes.The composite Z200 anomaly for the 10 trials with the highest index values (Figure 4c) resembles, by construction, the north Pacific to North America pattern in observations (Figure 3c).The composite OLR mean (Figure 4d) does not show a dipole OLR response in the TWP, instead, the dipolar pattern is weak and shifted substantially eastward.This again indicates that the model does not capture the observed link between the Z200 pattern and the negative OLR in the TWP.
Given that the model Z200 response is shifted westwards compared to observations, we can redefine the four boxes (Figure 4e) using the model-derived pattern (Figure 3d) and repeat the analysis performed for Figure 4c.The composite Z200 anomaly (Figure 4e) is similar to that in Figure 3d by construction.On this occasion the negative OLR anomaly is found in the TWP (Figure 4f), implying a link to the model Z200 pattern.This demonstrates that in the model, TWP OLR anomalies like those identified in the QBO composites typically favour teleconnection patterns on trajectories that are more confined to the Pacific sector when compared to reanalysis.
The distributions of index values for all trials based on the matching of observed and model-derived patterns are shown in Figure 5.The 1979-2020 QBOE − W composite value (Figure 5, black line) of the observed pattern index lies above the central 88% of the model distribution of that index (blue shading).This indicates that the model rarely produces composites of this pattern with this magnitude, suggesting that the observed QBO response is not simply a result of aliasing of internal noise in the midlatitude circulation.Nevertheless, this may not be the case if we assume, as suggested by the results above, that there is an error in the model's pattern of response.To test this we compare the observed QBOE − W composite amplitude with the trials conditioned on the model's apparent QBO response pattern (pink shading).In fact, we find that this also suggests that the amplitude in the observed QBO composite is highly unusual, implying that even allowing for pattern differences, the observed QBO response is unlikely to be a result of sampling.

DISCUSSION AND CONCLUSIONS
Our analysis of the MJO in GS5 confirms the results of previous analyses (Arribas et al., 2011;Yang et al., 2021) that our seasonal forecast system is able to internally generate a convincing MJO across all phases (Figure 1a) in boreal winter.However, unlike the relationship found in the observational reanalysis, there appears to be essentially no connection between the boreal winter QBO phase and MJO amplitude.Additional hindcast experiments in which the lower equatorial stratosphere was relaxed towards observations confirmed that despite improved QBO wind and temperature profiles, the seasonal mean amplitude of the MJO is unresponsive to QBO signals in the UTLS region.We also examined the distribution (Figure 1c) of QBO-MJO correlations in random GS5 trials with the same number of winters as in observations.The observed negative correlation has a lower value than 99% of the trials.Assuming the simulations contain realistic noise, this shows a genuine error in the seasonal forecast system examined here.These results are consistent with other model studies which investigated the winter seasonal-mean QBO-MJO relationship (Lee & Klingaman, 2018;Martin, Orbe, et al., 2021) even when the model is relaxed towards the observed QBO (Martin, Orbe, et al., 2021).However, we also note that the observed QBO-MJO correlation is suggested to be significant only since the early 1980s (Klotzbach et al., 2019;Sakaeda et al., 2020) so it is still possible that this may only be an apparent relationship that emerges from a limited number of observational samples.
While we do not reproduce a QBO effect on the MJO, we do show a significant QBO-related TWP winter-mean negative OLR response, independent of the MJO.Yamazaki et al. (2020) found a similar response in early winter.The tropical tropopause is highest over this region, making the interaction between upper tropospheric static stability and the cold zone at ∼70 hPa associated with the QBOE phase, and conversely the warm zone associated with the QBOW phase, more likely.The decreased UTLS stability associated with the QBOE cool anomaly at 70 hPa may result in deeper convection and hence lower OLR values compared to QBOW conditions (Martin, Son, et al., 2021).Compared to observations, the model OLR response pattern is shifted westward.
The observed negative OLR anomaly in the TWP captured by GS5 is linked with stronger upper tropospheric divergence and meridional outflow that interacts with vorticity gradients at the north Pacific subtropical jet, producing RWSs.These, as for the OLR, are shifted westward in GS5.The Z200 responses in ERA5 and GS5, although not significant in the west-mid-Pacific (Figure 3c,d), are consistent with the location of the RWS regions, with clear Rossby wave propagation towards the midlatitudes.The positions of the Z200 anomalies associated with the Rossby waves are shifted westwards in the model compared to reanalysis; for example, the positive region over Hudson Bay in observations is positioned over Alaska in the model.
Although there is evidence of a systematic westward shift in the ensemble mean atmospheric circulation response, we can find QBOE − W conditioned hindcast composites that contain the observed RWS pattern in the subtropical west Pacific.However, even in these cases the associated Z200 midlatitude wave train response (Figure 4a) is not consistent with the observed Z200 response.By considering the chain of influence in the opposite direction, that is, starting from the observed Z200 pattern, we can find hindcast composites (not conditioned by QBO) that capture the observed Z200 wave pattern (Figure 4c,d).Despite this, the associated TWP OLR anomaly is inconsistent with that seen as the response to QBOE − W. This suggests that wave patterns such as those associated with the QBO in observations are not produced by similar OLR patterns in the model (compare Figures 2a  and 4d).This demonstrates that the model is unable to convincingly capture the observed relationship between the TWP OLR and midlatitude wave response.Examination of the distribution (Figure 5) of amplitudes of trial Z200 composites also shows that the magnitude of the observed QBO relationship with midlatitude circulation is unlikely to be the result of aliasing of internal noise.
The differing positions of the ensemble mean and reanalysis Z200 circulation anomalies affect how the midlatitude wavenumber 1 interacts with the climatological wavenumber 1.The constructive interference seen using reanalysis fields is not captured in GS5, that is, the observed deepening of the Aleutian Low for QBOE − W is absent from the model.As a result, we do not expect QBO-related modulation of vertically propagating wave momentum flux from the troposphere into the midlatitude stratosphere in the prediction system which implies a weaker SPV response.The failure of the prediction system to replicate the enhancement of wavenumber 1 may offer a possible explanation of the weak QBO boreal winter teleconnection to the SPV, and consequently may contribute towards a weak teleconnection to the AO and NAO in current models.

1
Reproduction of the Madden-Julian oscillation (MJO) and the absence of a link with the quasi-biennial oscillation (QBO) in seasonal hindcasts in December-January-February (DJF).Daily outgoing long-wave radiation (OLR) response in GS5 (a) composited by MJO phase; (b) difference field for QBOE minus QBOW phases composited by MJO phase.(c) Histogram showing correlations between the QBO at 50 hPa and the MJO amplitude for 1000 trials in GS5.The dashed vertical line indicates the observed correlation value.Panels (a) and (b) are composed of MJO days with an amplitude above 1.0 standard deviation.The number of days used in each panel is indicated in brackets.
Quasi-biennial oscillation (QBO)-induced Rossby waves.Boreal winter mean Rossby wave sources (top row), geopotential height anomaly from zonal mean (middle row), and zonal wavenumber 1 (bottom row) at 200 hPa for QBOE − W. Columns show ERA5 (winters 1980-2020), and GS5 (winters 1993-2017).Significance at the two-sided 90% level is indicated by stippling.The contours in panels e and f represent wavenumber 1 climatology for ERA5 and GS5, respectively.Contours are six times the colour scale values, that is, 0 m, 30 m, 60 m, 90 m, etc … Strong ENSO winters (1982/3, 1997/8, 2015/6) have been excluded from this analysis.The Rossby wave source (RWS) region bounded by a black box in panel (a) is used for RWS analysis.

F
Magnitude of observed midlatitude Z200 pattern index is unlikely to be replicated by hindcast trials.Histogram showing pattern index distribution in hindcast trials for the observed Z200 pattern (blue) and the ensemble mean Z200 pattern (pink; mean value represented by the red vertical line).The observed value is represented by the black vertical line.