Captured QBO‐MJO Connection in a Subseasonal Prediction System

The quasi‐biennial oscillation (QBO) impacts the Madden‐Julian Oscillation (MJO) activity with a stronger MJO in QBO easterly (QBOE) than QBO westerly (QBOW) winters. However, this relationship is poorly represented in the current generation climate models. For the first time, this paper applies a stratospheric zonal‐mean nudging in a subseasonal prediction system to capture it. Two strong MJO cases in a QBO‐neutral winter are investigated. The QBO temperature and zonal wind anomalies are added separately as well as together to the stratosphere using nudging in MJO case hindcast. Only by nudging the QBO temperature anomalies while leaving the zonal wind free, can the prediction system capture the observed QBO‐MJO connection. The tropopause instability is found positively correlated to the MJO amplitude, but it cannot fully explain the captured connection. The free‐evolving zonal wind anomalies in the stratosphere due to the nudged QBO temperature are crucial for the captured connection.

One of the factors limiting our understanding of the mechanism is that current general circulation models (GCMs) fail to reproduce the observed QBO-MJO connection in their simulations (Kim et al., 2020;Lim & Son, 2020). Previous studies have attempted to reproduce the QBO-MJO connection in models by artificially imposing QBOE and QBOW anomalies. Martin et al. (2019) and Back et al. (2020) found that the Weather Research and Forecasting Model, a regional atmospheric model, can capture the QBO's influence on MJO. They attribute it to the tropopause instability mechanism. However, Martin, Orbe et al. (2021) found that the QBO-MJO connection is still missing in a GCM simulation with a realistically nudged QBO wind field. One possible reason is the imposing of prescribed wind shear as a forcing that interferes with the interaction between the QBO and MJO. Therefore, it is necessary to investigate whether the QBO-MJO connection will be captured in a global model where the observed QBO variation is appropriately introduced with the zonal wind shear allowed for such interaction. This paper identifies a new modeling framework that can capture this relationship and provide new insights into the mechanisms responsible for the QBO-MJO relationship.
Subseasonal-to-seasonal (S2S) prediction systems better represent the QBO-MJO connection than uninitialized GCM simulations Kim et al., 2019;Lim et al., 2019;Marshall et al., 2017;Martin et al., 2020;Martin, Son, et al., 2021;Wang et al., 2019). S2S prediction systems are initialized with the observed MJO that makes the MJO structure more realistic than the uninitialized GCM simulations. Although some previous studies demonstrate that the MJO amplitude differences from the initial conditions are trivial for the QBO-MJO connection in S2S prediction systems (e.g., Marshall et al., 2017), the QBO-MJO connection in many S2S prediction systems is highly dependent on the initial MJO phase (Kim et al., 2019;Martin et al., 2020;Wang et al., 2019). Martin et al. (2020) also demonstrate that the predicted MJO is dominated by the initial tropospheric conditions rather than the initial stratospheric conditions. It is still an open question whether the initialized predictions are simply maintaining the different MJO amplitude from their initialization in different QBO phases (Martin, Son, et al., 2021). Therefore, a question arises whether S2S prediction systems are able to capture the QBO-MJO relationship when the initial differences in MJO amplitude are removed.
In this study, we carry out MJO case hindcasts using a subseasonal Earth system prediction system based on a fully coupled global model, to address the following questions. (a) Is this subseasonal forecast system capable of producing the QBO-MJO connection with the QBO influences excluded from the tropospheric initial conditions? (b) If yes, is the tropopause instability theory, the most popular proposed QBO-MJO mechanism, responsible for capturing of the QBO-MJO connection?

Methods
Two strong MJO cases, A and B, are selected for this study based on the observed Real-time Multivariate MJO (RMM) index from the boreal winter season of 2000-2001, one QBO-neutral (QBON) boreal winter with the seasonal-averaged equatorial zonal-mean u50 anomaly of 2.05 m/s (details of the selection are described in Supporting Information S1). Initialized subseasonal hindcasts for these cases are carried out using the CESM2 subseasonal prediction system (Richter et al. (2022), described in Supporting Information S1) with a 21-member ensemble. The selected MJO cases are reasonably well predicted in the standard CESM2 hindcasts (referred as PreCtrl hereafter, Figure S1 in Supporting Information S1).
Both MJO cases are selected from a QBON winter which ensures that their initial conditions are least influenced by the QBO. This is crucial for our experiment as it guarantees any differences in the predicted MJO behaviors among different QBO phases are entirely from the stratospheric QBO signals through nudging as described below.
The QBO anomalies are introduced by applying a zonal-mean nudging. The PreCtrl outputs are used as reference QBON states. The composited DJF QBO temperature anomalies from the era-interim reanalysis (Dee et al., 2011) are added to the reference PreCtrl states and the sum is used as the nudging target for QBOT_FreeU experiment. Similarly, the composited QBO zonal wind anomalies are added and nudged for the QBOU_FreeT experiment, and both QBO temperature and zonal wind anomalies for the QBOUT experiment. Each experiment includes the QBOE run, the QBOW run, the super QBOE (sQBOE) as well as super QBOW (sQBOW) runs with doubled QBO

Writing -original draft: Kai Huang
Writing -review & editing: Jadwiga H. Richter, Kathleen V. Pegion anomalies added for nudging, and a Ctrl run nudged to the reference QBON states. The Ctrl run is conducted to investigate the effects of nudging. The nudging is done in the zonal mean only and in the stratosphere with a linear transition from full to zero nudging from 100 to 150 hPa. Results show that the zonal-mean nudging has minimal impact on the predicted MJO (see the detailed discussions in Supporting Information S1). In summary, for each MJO case, there is one PreCtrl experiment without nudging, one QBOT_FreeU experiment, one QBOU_FreeT experiment, and one QBOUT experiment. For each nudged experiment, there are Ctrl (QBON), QBOE, QBOW, sQBOE, and sQBOW runs as listed in Table S1 in Supporting Information S1. Details regarding the prediction system and the nudging strategy employed in this study can be found in Supporting Information S1.
The vertical sections of zonal-mean temperature and zonal wind differences between QBO phases for the three experiments of case A are displayed in Figure 1. Either by nudging temperature or zonal wind only, the corresponding QBO anomalies for the other variable are evident such as the zonal wind anomalies in the QBOT_FreeU experiment. However, the wind anomalies in the QBOT_FreeU experiment are not centered over the equator but around 10° in both hemispheres. The zonal wind anomalies at 50 hPa (u50) in the QBOT_FreeeU experiment is overlapped with the meridional gradient for the nudged temperature anomalies at 75 hPa level (T75) as presented in Figure S3 in Supporting Information S1. Therefore, the off-equatorial zonal wind shear in the QBOT_FreeU experiment ( Figure 1c) is thought to be a result of the thermal wind balance to the nudged stratospheric zonal mean QBO temperature anomalies (see details in Supporting Information S1). Although the equatorial temperature and zonal wind anomalies are found in all three experiments, the differences are in which variable is allowed to evolve freely and which is constrained by nudging. We also notice that in the QBOT_FreeU experiment, the differences in zonal-mean zonal wind between QBOE and QBOW phases are less than half of that in the observations, especially in the lower stratosphere around 50 hPa ( Figure 1c). Only in the sQBO runs where the doubled QBO temperature anomalies are added and nudged is the magnitude of the zonal wind shear consistent with observations.

The Unique QBO-MJO Connection in QBOT_FreeU Experiment
The predicted MJO cases in these initialized hindcasts are investigated, specifically for their magnitude and how far eastward they propagate between runs with varied QBO phases. We focus on the RMM index, Real-time OLR MJO Index (ROMI; Kiladis et al., 2014) as well as the OLR and u200 anomalies to describe the differences in the predicted MJO. Considering there are 21 ensemble members for each MJO hindcast, confidence intervals of the differences are calculated using a method designed for small sample sizes. The confidence interval for a population with sample size of n which is 21 here, standard deviation as σ, and mean as is defined as ± ( ∕ √ ) , where t is the t value calculated from a t-distribution with (n−1) as its degree of freedom.
The QBO-MJO connection is captured by the subseasonal prediction system when the stratospheric zonal mean temperature is nudged, but the zonal wind is allowed to evolve freely (QBOT_FreeU; Figure 2). For both cases, after week 2, when the active MJO convection is over the central-western Pacific, the RMM and ROMI indices in different QBO phases start to deviate from each other. The sQBOE runs for both show the larger RMM and ROMI amplitude than the Ctrl run, while the sQBOW runs are weaker (Figure 2a-2d). The amplitude of QBOE and QBOW runs are in between with relatively stronger MJO in QBOE runs and weaker MJO in QBOW runs (Figures S2a-S2d in Supporting Information S1).
The predicted MJO cases also propagate farther eastward into the central-western Pacific in sQBOE than in sQBOW runs (Figures 2e and 2m). For case A, the active convection of the MJO stops its eastward propagation over the western Pacific in sQBOW runs (Figure 2c). In QBOE runs, it maintains a robust eastward propagation to the dateline (Figure 2d) with a stronger amplitude over the MC (Figure 2e). Similar differences in the propagating features for case B are evident (Figures 2k-2m). The zonal wind at 200 hPa (u200) also shows large differences between sQBOE and sQBOW runs for case A (Figures 2f-2h) with a divergent field nearly stalling over the MC after day 14 in sQBOW runs but a robust eastward propagating divergent field in sQBOE runs. For case B, the differences in u200 are less obvious (Figures 2n-2p). Differences between QBOE and QBOW runs in both cases show similar patterns as sQBO runs, but the amplitude is smaller ( Figure S2 in Supporting Information S1). For case A, the further eastward propagation of MJO convection is still found, but it occurs later around day 28. For case B, the OLR decrease pattern is less organized. Similar to OLR, the u200 differences between QBOE and QBOW runs for the two cases are also smaller compared with sQBO runs.
As we are using the CESM2 subseasonal prediction system, a global model, to carry out our experiment, we are able to assess the MJO amplitude comprehensively. Three metrics are used here such as the OLR anomalies averaged over the central-western Pacific, the RMM amplitude, and the ROMI amplitude ( Figure 3). Since the latter two indices require the global OLR and zonal wind variables in the tropical belt, they are not available for MJO simulations using regional models such as in Martin et al. (2019) and Back et al. (2020).
The stronger negative OLR anomalies over the central-western Pacific in QBOE runs than in QBOW runs, as well as in sQBOE runs than in sQBOW runs are evident in all three sets of experiments. However, only the QBOT_ FreeU experiment shows a significantly increased MJO amplitude during sQBOE versus sQBOW, measured by the RMM and ROMI index, and it is consistent with the observed relationship. This indicates that although the convection over the central-western Pacific gets amplified in QBOE/sQBOE runs for QBOU_FreeT and QBOUT experiments, it is not associated with the predicted MJO mode.
To directly assess the convection signals associated with the MJO in the QBOT_FreeU experiment, we reconstruct the OLR anomalies based on the EOFs and the PCs of the ROMI index. The reconstructed ROMI OLR is therefore only related to the MJO mode. The Hovmöller diagrams of the ROMI OLR are shown in Figure  S3 in Supporting Information S1. The amplifications of the MJO for both active and suppressed convection in QBOE and sQBOE runs are clearly shown here. The amplification of the MJO convection begins around day 20 in QBOE runs and starts earlier around day 10 in sQBOE runs. For both cases A and B, the differences are only significant when the sQBOE and sQBOW anomalies are imposed in the QBOT_FreeU experiment, indicating the potential physics linking MJO to QBO in the CESM2 subseasonal prediction system might be weak. As presented in Figures 1b and 1c, three sets of experiments could all simulate the changes in wind shear and temperature profiles around the UTLS caused by the QBO. The main differences are which is a fixed forcing through nudging and which is allowed to evolve freely. Comparing the results between the QBOT_FreeU experiment with the other two experiments (Figure 3), we conclude that the free-evolving zonal-mean zonal wind in the QBOT_FreeU experiment as a result of the nudged zonal-mean QBO temperature anomalies is crucial for the captured QBO-MJO connection.

The Tropopause Instability Theory
Tropopause instability theory is one of the most accepted mechanisms for the QBO-MJO connection as the correlation between the tropopause instability and MJO amplitude is demonstrated in observations (Hendon & Abhik, 2018;Huang & Pegion, 2022) and in model simulations (Back et al., 2020;Martin et al., 2019). However, the QBO-MJO connection is missing in GCM simulation even when the tropopause instability changes caused by QBO are realistically simulated (Martin, Orbe, et al., 2021). Now that we have demonstrated a modeling framework that can represent the QBO-MJO relationship, we use it to investigate whether the tropopause instability is the mechanism for this relationship.
There are two schools of thought on the tropopause instability theory. One hypothesis is that the zonal-mean cooling over the zonal-mean heating around the tropopause directly induced by the QBO is important . This is referred to as the zonal-mean tropopause instability. The other tropopause instability theory focuses on the cooling-over-heating structure induced by the propagating MJO convection which is related to the Kelvin waves propagating from the MJO convection top around UTLS. It is tuned by the QBO and becomes stronger in QBOE than in QBOW phases (Back et al., 2020;Hendon & Abhik, 2018;Huang & Pegion, 2022;Lim & Son, 2022). This is referred to as MJO tropopause instability.
The zonal-mean tropopause instability alone is not enough to fully explain the QBO-MJO connection in the QBOT_FreeU experiment because the zonal-mean tropopause instability tuned by QBO is reproduced in all  (Figure 1b), but only the QBOT_FreeU experiment captures the QBO-MJO connection (Figure 3). This conclusion does not change when the zonal-mean tropopause instability is investigated during weeks 3 and 4 ( Figure S6 in Supporting Information S1) for case A and during weeks 2 and 3 for case B ( Figure S9 in Supporting Information S1) when the predicted MJO amplitude shows distinct differences in runs of the QBOT_FreeU experiment (see detailed discussions in Supporting Information S1). As demonstrated by Klotzbach et al. (2019), the QBO-related tropopause instability maxima occur over the warm pool, and its sufficient changes passing a threshold in different QBO phases are required to generate the observed QBO-MJO connection. The changes of tropopause instability over the warm pool in three sets of experiments (Figures S7 and S10 in Supporting Information S1) are also investigated in Supporting Information S1. Again, the warm-pool tropopause instability is sufficiently reduced in the sQBOE runs for all three sets of experiments, but only the QBOT_FreeU experiment captures the QBO-MJO connection. Therefore, the warm-pool tropopause instability changes are also not enough to explain the captured QBO-MJO connection.
The MJO tropopause instability theory is a potential mechanism for the QBO-MJO connection in the QBOT_ FreeU experiment. To investigate it, the equatorial (15°S−5°N) circulation and temperature vertical sections are composited for the ROMI phase 6/7 days of each ensemble member for all runs ( Figure S4 in Supporting Information S1) since the predicted MJO convection shows largest differences when it is over the central-western Pacific ( Figure S3 in Supporting Information S1). The zonal means are subtracted before the composites in order to exclude the differences coming from the zonal-mean temperature profiles (Figure 1b). Therefore, the temperature anomalies with zonal means subtracted only include the zonally asymmetric signals which are associated with the MJO convection, allowing us to investigate the MJO tropopause instability. The composites are also conducted with a reference longitude (0°) where the equatorial ROMI OLR is the lowest. The eastward-tilted wave-like temperature disturbances are evident in the UTLS which propagate eastward and upward from the MJO convection top into the middle-higher stratosphere ( Figure S4 in Supporting Information S1). These waves are amplified in QBOE/sQBOE runs but suppressed in QBOW/sQBOW runs, consistent with the conclusion by Lim and Son (2022) that the QBO wind shear may affect the amplitude and vertical propagation of the UTLS Kelvin wave induced by the MJO convection, thus influencing the MJO tropopause instability. Note such behaviors are also evident in the QBOU_FreeT and QBOUT experiments ( Figures S5 and S6 in Supporting Information S1, respectively). The distributions of the composited MJO tropopause stability measured by the zonally asymmetric temperature difference between 100 and 200 hPa as well as the MJO amplitude measured by ROMI OLR are given in Figure 4. For each set of experiments, there are 105 data points (21 ensemble members for 5 QBO phases). The positive correlation between the MJO amplitude and the tropopause instability is found in three sets of experiments. Although the correlation is lower for QBOU_FreeT and QBOUT experiments, they are all significant. The relationship between the MJO amplitude and MJO tropopause stability does not change much among the three sets of experiments for both cases. However, only the QBOT_FreeU experiment can capture the QBO-MJO connection ( Figure 3). Therefore, this result strongly suggests that the changed MJO tropopause instability is only correlated with MJO amplitude, and it alone is not enough to be the causality of the QBO-MJO connection.

Discussions and Outlooks
The questions proposed near the end of Section 1 are now answered. (a) The CESM2 subseasonal ensemble prediction system can capture the QBO-MJO connection even with the QBO influences ruled out from the initial conditions. (b) Although the tropopause instability is correlated with the MJO amplitude, the changed tropopause instability alone cannot fully explain the captured QBO-MJO connection in this study. However, the tropopause instability theory cannot be denied by this study as this theory does not eliminate the possible roles of the associated altering zonal wind or other factors such as the changed high cloud cover in the QBO-MJO connection (e.g., Son et al., 2017). There are also some limitations of this study. The free-evolving stratospheric zonal wind shears in the QBOT_FreeU experiment are unrealistically shifted to be off-equatorial (Figure 1d). The QBO zonal wind shear and QBO temperature anomalies are not completely independent from each other in this study. Future experiments better separating the QBO temperature from its zonal wind anomalies are needed to quantify the contribution of tropopause instability changes in QBO-MJO connection.
The reproduction of QBO-MJO connection by the CESM2 subseasonal prediction system demonstrates that at least part of the QBO-MJO connection mechanism is represented by the model physics, which is also supported 10.1029/2022GL102648 8 of 10 by the nudged MJO case simulations using Specified Chemistry version of the Whole Atmosphere Community Climate Model (WACCM, part of CESM1) in Sena et al. (2022). It is intuitive to ask why it is not captured by the uninitialized simulations with current generation GCMs such as CESM2-WACCM (Kim et al., 2020). Possible reasons are (a) the MJO structure in the MJO case hindcast experiment in this study may be more realistic than those in the uninitialized simulations due to the memory of the observed MJO structure in the initial conditions; (b) QBO within the lower stratosphere is insufficiently represented in the uninitialized simulations by current generation GCMs such as CESM2-WACCM (Toms et al., 2020) or even missing in some GCM uninitialized simulations like CESM2, while the QBO signals with a comparable magnitude is induced into the prediction system through nudging in this study; (c) the QBO-MJO mechanism included in the model physics is too weak and to make it work, it requires both strong MJO as we selected strong MJO cases from observations and strong QBO by doubling the QBO anomalies to mimic the super QBO conditions and capture the significant QBO-MJO connection in this study.
The nudging strategy used in this study to capture the QBO-MJO connection, nudging zonal-mean temperature only, also provides a new perspective to understand its mechanism, especially as the changed tropopause instability . Scatter plots of the phase 6/7 Madden-Julian Oscillation (MJO) tropopause stability (zonal-asymmetric differences between T100 and T200, X-axis) and Real-time OLR MJO Index (ROMI) OLR (Y-axis) averaged over 15°S to 5°N, and 10°E to 10°W of the reference longitude for each ensemble member in each run of different quasi-biennial oscillation (QBO) phases for cases A and B. The correlation coefficient between ROMI OLR and MJO tropopause stability as well as its p value are given in the bottom right of each panel.
is found not able to fully explain the reproduced QBO-MJO connection here (Section 4). The free-evolving zonal-mean wind is also crucial. This indicates that the QBO-MJO connection works in a way that requires the wave mean-flow interactions. Therefore, by nudging zonal mean zonal wind in the model, such interactions are disrupted. This might be one of the reasons why the QBO-MJO connection is missing in GCMs with a stratospheric nudging of QBO wind components (Martin, Orbe, et al., 2021), along with other possible reasons such as the biased QBO or MJO structure in GCMs (Martin, Son, et al., 2021).
Future studies on the QBO-MJO connection in the uninitialized GCM simulations are also necessary due to the possible case dependency in this study. However, they are limited by the quality of the simulation of the QBO in global models which tends to be too weak in the lower stratosphere ) and by the model biases in MJO. We attempted to include more MJO cases in this study but found that the simulations of other strong MJO events in the QBON winters in the CESM2 subseasonal prediction system were not realistic enough in the standard hindcasts, especially regarding the eastward propagation of MJO-related convection.