We utilize daily mean 500 hPa geopotential height (z500; years 1979–2017) from the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim reanalysis (ERA-I; ) as well as the ECMWF and NCEP hindcasts obtained from the S2S database established by the World Weather Research Program/World Climate Research Program (WWRP/WCRP; ). The ECMWF hindcasts are composed of 11 ensemble members with hindcasts initialized four times a week (years 1995–2016). The NCEP hindcasts are composed of four ensemble members with hindcasts initialized daily (years 1999–2010). In the following analysis, the ensemble mean for both models was used, and so the different number of members between ECMWF and NCEP may contribute to differences in results between models.

We focus on December, January, and February (DJF) since MJO teleconnections are strongest during boreal winter (e.g., ), and the relationship between the MJO and QBO is strongest during these months as well (e.g., ). The annual cycle is removed from the ERA-I reanalysis by subtracting the daily climatology of z500 across 1979–2017 from the z500 field. For the hindcast models, a daily, lead-dependent climatology is subtracted from each model's z500 field. To do this, we calculate the daily climatology for each lead time independently. Since the ECMWF model is not initialized daily, two (forward- and backward-moving) 31 d running means are applied to the climatology at all lead times to reduce noise, following . These smoothed lead-dependent daily climatologies are then subtracted from the z500 field of the corresponding model to remove the annual cycle.

There is presently no definitive understanding of the impact of the El Niño–Southern Oscillation (ENSO) on the QBO–MJO relationship. Some earlier research indicates that ENSO has a limited impact on the QBO–MJO interaction (e.g., ); however, recent work on QBO–MJO teleconnections has shown a possible dependency of results on ENSO . In addition, other research suggests that the QBO affects ENSO teleconnections , which may consequently impact the MJO and its teleconnections. Thus, in an attempt to ensure our results are not somehow biased by ENSO, we use the Nino3.4 Index (https://climatedataguide.ucar.edu/climate-data; ) to remove strong ENSO winter seasons from our analysis. Specifically, when the amplitude of the NINO3.4 index for a month within DJF is greater than 1 ∘C (signifying El Niño) or less than -1 ∘C (signifying La Niña), that DJF season is excluded from the analysis. With that said, we have repeated our analysis with ENSO seasons included and find that our STRIPES conclusions remain the same. The prediction skill conclusions also remain the same during EQBO, but WQBO results appear more sensitive to ENSO (see Supplement Figs. S6–S9). The impact of ENSO on the MJO–QBO relationship and their teleconnections still remains an active area of research.

The real-time multivariate MJO (RMM) index is used to define the amplitude and phase of the MJO in the ERA-I reanalysis . This index uses empirical orthogonal function (EOF) analysis applied to anomalous outgoing longwave radiation (OLR) and 200 and 850 hPa zonal wind, near-equatorially averaged (15∘ S to 15∘ N), to determine the first two principal components (RMM1 and RMM2). A day is considered to have an active MJO when the RMM amplitude for that day (defined as (RMM12+RMM22)) is greater than 1.0. The MJO phase is then defined as tan-1(RMM2/RMM1) and largely corresponds to the longitudinal location of the convective envelope. Active MJO dates within ERA-I that correspond to initialization dates in ECMWF and NCEP are determined from this index. The RMM index is not separately calculated for each hindcast model because we do not aim to quantify the ability of the models to forecast the MJO directly (e.g., ). Rather, we use the index calculated from reanalysis to see how the hindcast models initialized on observed active MJO days ultimately forecast MJO teleconnections.

Identical to the definition of , the QBO index is calculated within ERA-I using monthly standardized zonal wind at 50 hPa, area-averaged between 10∘ S and 10∘ N. Westerly QBO (WQBO) and easterly QBO (EQBO) events are defined as when the standardized value is greater than 0.5σ or less than -0.5σ, respectively. Absolute values less than 0.5σ are considered neutral QBO (NQBO) events.

Quantification of each model's ability to represent MJO teleconnections under different QBO phases is conducted using the Sensitivities To the Remote Influence of Periodic EventS (STRIPES) index . STRIPES is an index recently developed to determine regions of extratropical sensitivity to remote periodic events such as the MJO. As used here, the STRIPES index quantifies the strength and consistency of MJO teleconnections in z500 through average phase and 0–28 d lead information at individual grid points for a variety of observed phase speeds (5–8 d per phase; ). Specifically, a composite of average z500 anomalies for each MJO phase and lead (phase–lead diagram) is created for each grid point in the Northern Hemisphere (example shown in Fig. 1a). For further intuition of the phase–lead diagram, Fig. 1b and c show composite z500 anomalies for the domain around 45∘ N and 5∘ W (marked by the white X) 12 d following phase 6 and phase 2, respectively. The value of the box in the phase–lead diagram is the same as the value plotted at the X in Fig. 1b, c. In a phase–lead diagram, MJO-induced quasi-stationary Rossby waves are apparent as slowly alternating-sign z500 anomalies with lead following a specific phase of the MJO (e.g., Fig. 1a). In addition, the MJO is a propagating phenomenon with a phase speed of approximately 5–8 d per phase. Therefore, if there is a teleconnection signal 10 d following phase 2, this signal is likely also present 5 d following phase 3 in the same region, in a composite sense. On a phase–lead diagram, this is seen as a diagonal line or “stripe” slanted at the phase speed of the MJO (Fig. 1a). Therefore, if a region is sensitive to the MJO, we expect alternating z500 anomaly stripes approximately sloped at the average phase speed of the MJO, as in Fig. 1a, which we refer to as the “stripiness”.

To calculate STRIPES, averages along the slopes in the phase–lead diagram corresponding to the MJO phase speed are calculated, and if there are alternating stripes (i.e., sensitivity to the MJO), the resulting averages concatenated together will oscillate between positive and negative z500 anomalies as a sine wave, for which the amplitude can be calculated. The amplitude of this oscillatory vector is the STRIPES index . The more sensitive the region is to MJO teleconnections, the larger the STRIPES index. Therefore, the STRIPES index allows us to regionally quantify the strength, consistency, and propagation of the MJO impact on the extratropics and thus allows us to quantify the ability of hindcast models to capture tropical–extratropical teleconnections on 1- to 4-week timescales in a single metric.

For equal comparison of STRIPES between the models and reanalysis, we calculate STRIPES for ERA-I only with dates that overlap with the hindcasts; thus, the ERA-I STRIPES figures differ for ECMWF versus NCEP dates. It should be noted that the westerly phase of the QBO has been documented to reduce the propagation speed of the MJO . However, we find that our STRIPES results are robust to changes in phase speed of ±2 d per phase. Also note that since our application focuses on extratropical sensitivity in z500, we use z500 anomalies in terms of meters instead of standard deviation for STRIPES, different from . Standardization may mute the extratropical signal due to the greater variability of z500 in the midlatitudes, which is of the most interest here. In addition, we wish to retain any differences in z500 anomaly amplitudes between the QBO phases.

STRIPES values that are statistically larger than expected by chance are determined using a bootstrapping method. The number of random days grabbed corresponds to the observed number of days for the QBO–MJO event of interest. In order to retain autocorrelation within MJO events, we keep the day of year (DOY) and phase distribution information for each MJO event and randomly sample years (with replacement). Since the ECMWF hindcast data are not initialized on the same day each year, if the DOY needed is not available for a particular year, we instead use the date of initialization closest to this DOY. From this sample, we calculate STRIPES. This is repeated 250 times for each latitude and longitude. Any STRIPES value greater than the 90th percentile of these bootstrapped values is deemed significant. When the data are subdivided by QBO phase, we begin to see the effects of sample size on the uncertainty, leading to fewer points of significance. However, when the QBO phase is not considered or, in other words, when all MJO events are included (see Fig. S1), the statistical analysis shows significance in regions of large STRIPES values. This bootstrapping analysis is only conducted on ERA-I, as these are the “observed” sensitivities and thus the regions of interest.

To quantify midlatitude prediction skill, a daily area-weighted Pearson correlation is conducted between hindcast and ERA-I anomalous z500 (anomaly correlation coefficient, ACC). The data are separated into NQBO–, EQBO– and WQBO–MJO events in each hindcast dataset, and the corresponding reanalysis data are obtained from ERA-I. The ACC between a given model day and the same day in ERA-I is calculated within a centered 60∘ wide longitude box extending from 30 to 60∘ N. Our conclusions are not affected by the latitudinal extent of the box when it is varied by ±10–30∘ N. This calculation is repeated for every initialization and subsequent lead time as well as every 5∘ longitude beginning at 0∘ E. ACCs are grouped and averaged by QBO phase to obtain average ACCs across the Northern Hemisphere at every lead for each QBO phase (see Fig. S3 for an example).

Statistically significant differences in ACCs across lead and longitude are also computed with a bootstrapping method. Specifically, all model data within DJF are shuffled and random dates are grabbed. The number of random dates corresponds to the number of observed dates for the particular QBO phase and MJO activity being tested. These dates are then found in ERA-I. The spatial correlations between the model and the observations are calculated and then averaged to get an average ACC. This is repeated for each QBO–MJO combination, and the differences between their ACCs are calculated. The above analysis is repeated 10 000 times for each longitude and lead time. Differences greater than the 90th percentile of the 10 000 bootstrapped differences are considered significantly greater from that expected by chance. In this bootstrapping analysis, we were able to repeat the calculations 10 000 times (instead of 250) because the calculation was less computationally expensive.

Figure 2a, c, and e show the STRIPES analysis of ERA-I for days within the ECMWF hindcasts, split by QBO phase. Darker shading indicates regions of greater sensitivity to the MJO for each QBO state. Regions along the North Pacific and Atlantic storm tracks as well as over North America are highlighted by STRIPES following the MJO for all phases of the QBO (Fig. 2a, c, e). This is consistent with previous research as these regions have been shown to be sensitive to MJO-excited Rossby waves through, for example, their modulation of the North Atlantic Oscillation , the Pacific North American Oscillation , and Northern Hemisphere wintertime blocking . Interestingly, the Pacific and Atlantic sectors have similar STRIPES values. One may expect higher STRIPES values over the Pacific compared to the Atlantic since the Pacific is generally known to have a strong response to the MJO. We hypothesize that the Atlantic and European sectors also have similar STRIPES values to those of the Pacific due to enhanced blocking over the Atlantic and Europe at later leads following the MJO . Since the STRIPES index accounts for all leads as well as the strength and consistency of the z500 anomalies, we therefore expect STRIPES values over the Atlantic and European sectors to be large as well.

Figure 2b, d, and f show the STRIPES analysis of the ECMWF hindcasts for the same dates. ECMWF largely captures the spatial patterns and locations sensitive to the MJO under different QBO phases (spatial correlation with ERA-I: rNQBO-MJO=0.92, rEQBO-MJO=0.93, and rWQBO-MJO=0.95), but overall the model has smaller STRIPES values than ERA-I. This is likely a result of model forecast degradation at later lead times since the calculation of STRIPES utilizes z500 forecasts out to 28 d lead time.

An examination of the NCEP hindcasts shows that it also generally captures regions sensitive to the MJO under varying phases of the QBO (Fig. 3b, d, f; spatial correlation with ERA-I: rNQBO-MJO=0.96, rEQBO-MJO=0.95, and rWQBO-MJO=0.93) and is also weaker than the corresponding ERA-I analysis (Fig. 3a, c, e). The ERA-I STRIPES analysis for NCEP hindcasts largely has the same features as the ERA-I analysis for ECMWF hindcasts, but with larger values due to differences in sample size and dates of initialization between NCEP and ECMWF. From this STRIPES comparison (Figs. 2 and 3), we conclude that the ECMWF and NCEP hindcast models generally capture Northern Hemisphere regions sensitive to the MJO as highlighted by large spatial correlations between each model and ERA-I.

Recent research has shown that during EQBO, the MJO amplitude is larger and the convective envelope propagates more slowly compared to MJO activity during WQBO . If direct impacts on the MJO (e.g., through changes in upper tropospheric tropical static stability) lead to changes in MJO teleconnection sensitivity across the Northern Hemisphere, we might expect EQBO–MJO events to have larger midlatitude sensitivity to the MJO compared to WQBO–MJO. Instead, we find that Northern Hemisphere sensitivity to the MJO is significantly reduced during EQBO–MJO events compared to WQBO–MJO events (compare Figs. 2c, e and 3c, e; significance of difference not shown). We explored this further and found that this difference can largely be explained by the tendency of WQBO to have larger magnitude z500 anomalies compared to EQBO, not more distinct stripes. This is likely due to the larger sample size during EQBO (Table S1 in the Supplement) leading to reduced noise in the average. Therefore, when the amplitude differences between the z500 anomalies are accounted for through normalization, the difference in Northern Hemispheric sensitivity to the MJO between QBO phases is greatly reduced (Fig. S3).