Role of equatorial planetary and gravity waves in the 2015–16 quasi-biennial oscillation disruption

In February 2016, the descent of the westerly phase of the quasi-biennial oscillation (QBO) was unprecedentedly disrupted by the development of easterly winds. Previous studies have shown that extratropical Rossby waves propagating into the deep Tropics were the major cause of the 2015–16 QBO disruption. However, a large portion of the negative momentum forcing associated with the disruption still stems from equatorial planetary and small-scale gravity waves, which calls for 10 detailed analyses by separating each wave mode compared with climatological QBO cases. Here, the contributions of resolved equatorial planetary waves [Kelvin, Rossby, mixed-Rossby gravity (MRG), and inertia-gravity (IG) waves] and small-scale convective gravity waves (CGWs) obtained from an offline CGW parameterization to the 2015–16 QBO disruption are investigated using MERRA-2 global reanalysis data from October 2015 to February 2016. In October and November 2015, anomalously strong negative forcing by MRG and IG waves weakened the QBO jet at 0°–5°S near 40 hPa, leading to Rossby 15 wave breaking at the QBO jet core in the southern hemisphere. From December 2015 to January 2016, exceptionally strong Rossby waves propagating horizontally (vertically) continuously decelerated the southern (northern) flank of the jet. In February 2016, when the westward CGW momentum flux at the source level was much stronger than its climatology, CGWs began to exert considerable negative forcing at 40–50 hPa near the equator, in addition to the Rossby waves. The enhancement of the negative wave forcing in the Tropics stems mostly from strong wave activity in the troposphere associated with increased 20 convective activity and the strong westerlies (or weaker easterlies) in the troposphere, except that the MRG wave forcing is more likely associated with increased barotropic instability in the lower stratosphere.

In Eq. (1), ̂ is the modified Coriolis parameter defined by ̂= − 1 ( cos ) ⁄ ⁄ ( ̅ cos ) where is the Coriolis parameter, and ̅ * and ̅ * are the residual meridional and vertical velocities defined by ̅ * = ̅ − 0 −1 ( 0 ′ ′ ̅ ⁄ ) and ̅ * = 125 cpd are defined as high-frequency eastward ( ) and westward ( ) waves, respectively, which approximately represent eastward and westward IG waves, respectively. This separation method in the troposphere enables us to identify the source 155 location of the anomalously strong waves observed in the stratosphere.

Offline CGW parameterization
We apply the offline CGW parameterization using MERRA-2 data focusing on small-scale waves ( ℎ < 100 km and < 40 km, where is the vertical wavelength), which is similar to the work of Kang et al. (2017Kang et al. ( , 2018 using NCEP Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) data. The offline CGW parameterization calculates GW momentum flux 160 induced by convective heating rate at the source level (cloud top) as a function of phase velocity; the GW momentum flux and drag from the cloud top to the stratosphere are calculated based on columnar wave propagation by using Lindzen's saturation theory (Lindzen, 1981). The parameterization requires convective heating rate and convective cloud-top and -bottom heights in addition to standard variables such as wind, temperature, and geopotential height as input data. MERRA-2 provides only cloud-top height without convective heating rate, so we tried to extract convection-induced heating rate from the MERRA-2 165 output field DTDTMST; this field contains all process that contributes to latent heating by moist convection, not exclusively by cumulus convection (Bosilovich et al., 2016). To reconcile this limitation, we select cases that satisfy several criteria to represent clouds which can generate convective GWs. First, we only considered DTDTMST profiles in which columnmaximum height is higher than 850 hPa. Second, we estimated the convective cloud-top and -bottom heights as the locations where DTDTMST falls to 20% and 5%, respectively, from its maximum. Here, the convective cloud top should not exceed 170 cloud-top height provided by MERRA-2. Although the percentage of 20% seems large, we decided to use the value considering the large tail in the upper part of the DTDTMST profile (Fig. S1). Note that the cloud-top height is provided by MERRA-2, but we chose instead to estimate it from the DTDTMST profile because the cloud-top heights in MERRA-2 are sometimes too high due to stratiform clouds, such as anvil clouds, which do not represent the top height of the convection properly. Third, when (i) the convective cloud top height is lower than 700 hPa, (ii) the convective cloud bottom height is higher than 7 km, or 175 (iii) the convective cloud depth is shallower than 1 km, the profiles are eliminated. The DTDTMST profiles selected using the aforementioned procedure will be referred to as convective heating profiles hereafter; they are generally similar to the convection-induced heating profiles estimated from satellite observations (GPM Science Team, 2017;Lang and Tao, 2018) ( Fig. S1). Note that the magnitude of the CGW momentum flux is constrained by the observed GW momentum flux from SPBs in the tropical region (Jewtoukoff et al., 2013). Because spatio-temporal variations in convective activity and background 180 flows are considered in the parameterization, it is valuable to investigate the variations in the magnitude and the spectral shape of the CGW momentum flux during the QBO disruption.
https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License. Figure 1 shows zonal-mean zonal wind in a latitude-height cross section from October 2015 to February 2016, monthly climatology from October to February, and the zonal-mean zonal wind profile averaged over 5°N-5°S during the disruption, compared with its monthly climatology. In October 2015, WQBO is very deep compared to the climatology. The WQBO starts to split into two maxima as early as November 2015, and the westerly wind becomes anomalously weak at 40-50 hPa by more than 1 , where is the standard deviation of the zonal-mean zonal wind, in December 2015. In January 2016, the zonal wind 190 at 40 hPa continuously decelerates, and then changes into easterly in February. From January 2016, the zonal wind at the altitude above 30 hPa exhibits a strong westerly wind greater than the climatology by more than 1 , indicating that the WQBO is anomalously deep. In the upper troposphere (100-150 hPa), easterly anomalies are shown in November 2015, but from January 2016, westerly anomalies appear. Figure 2 shows latitude-height cross sections of the EPF and EPD for each type of wave in February 2016. Note that the 195 parameterized CGW momentum flux ( 0 ′ ′ ) is multiplied by (− cos ) to display the vertical EPF vectors of CGWs, and each of the wave forcings and vectors in Fig. 2 is scaled differently in order to mainly focus on their morphology. The EPD more negative than climatology by more than 1 is stippled, which represents anomalously strong negative wave forcing. The parameterized CGWs (P-CGWs in Fig. 2a) generally exert a positive or negative drag on the zonal wind in regions of positive or negative wind shear, respectively, with the strongest negative forcing at 7-20 hPa between 5°N and 10°S. The negative 200 CGW forcing at 40-50 hPa between 10°N and 10°S is anomalously strong. In 20°N-5°S, westward-propagating P-CGWs are dominant, which can be inferred from the direction of vertical EPF vectors. Kelvin waves (Fig. 2b) exert positive wave forcing in the positive shear zone, strengthening the bottom side of the westerly jet. Therefore, Kelvin waves may help to maintain two westerly jets (5-30 hPa and 50-80 hPa) with a developing easterly jet in between. MRG waves ( Fig. 2c) show anomalously strong negative forcing at 50-80 hPa, 30-40 hPa, and 15-20 hPa, concentrated at the equator. They seem to be generated in 205 the altitude range (60-90 hPa and 30-40 hPa) in which the EPD has positive values at 5°-10°N/S. As will be shown later, the effect of the MRG waves is to flatten the meridional profile of the westerly jet, possibly making the jet more sensitive to erosion by other waves, such as Rossby waves. IG waves (Fig. 2d) near the equator (10°N-10°S) exhibit a negative forcing from 70 hPa to 5 hPa with a maximum forcing at 8-20 hPa, while the anomalously strong negative IG wave forcing is mainly located at 50-70 hPa and 8-20 hPa. The negative Rossby wave forcing (Fig. 2e) is anomalously stronger than the climatology 210 at 30-50 hPa between 20°N and 25°S, which is attributed to the waves that propagate from the NH extratropics. The same figure during the whole QBO disruption period from October 2015 to February 2016 is shown in Fig. S2 in the online supplemental material. Figure 3 shows time-height cross sections of the zonal wind, zonal wind tendency, vertical advection [the second term on the right-hand side of Eq. (1)], required wave forcing, and forcing due to each type of wave averaged over 5°N-5°S from July 2015 to June 2016; and their monthly climatology from July to June. The required wave forcing term (REQ) is calculated as a residual by subtracting the advection terms from the zonal wind tendency in the TEM equation. In Fig. 3a, both the zonalmean zonal wind during the disruption and the climatology propagate downward with time, but the WQBO is much deeper during the disruption than in the climatology. This feature is clearly seen in the difference plot of the zonal-mean zonal wind ( Fig. 3b), showing a strong westerly anomaly in the upper stratosphere. The westerly wind decelerates at 40 hPa from October 220 2015, changes into easterly in February 2016, and starts to propagate downward as an easterly QBO phase afterward. The deceleration of the westerly wind at 40 hPa is also revealed in the zonal-wind tendency (Fig. 3a), as the negative wind tendency at 40 hPa becomes anomalously strong in October 2015.

General characteristics of zonal wind and equatorial waves 185
To investigate whether vertical advection contributes to the anomalous zonal wind tendency near 40 hPa, the vertical advection term (ADVz) in the TEM equation is shown in Fig. 3d. Climatologically, the sign of the equatorial wave forcing is 225 the same as that of the vertical wind shear. Therefore, positive ̅ * makes the sign of ADVz opposite to that of the vertical wind shear (Eq. 1), acting to oppose zonal wind tendency (Dunkerton, 1991). From November to December 2015 at 40 hPa, however, ADVz has the same negative sign as the zonal wind tendency because both ̅ * and vertical wind shear are positive (not shown), while the wave forcing is negative regardless of the positive wind shear. Therefore, ADVz acts to accelerate the easterly development by 17% and 2% of the zonal-wind tendency, respectively, with values of -0.3 and -0.1 m s -1 mon -1 in November 230 and December 2015, respectively. This implies that ADVz also contributes to the QBO disruption in the early stages. Kelvin wave forcing (Fig. 3g) during the disruption is much greater than the climatology near the altitude of 30 and 60 hPa due to the positive wind shear. The wave forcing could be stronger because of the strong vertical wave flux propagating from the troposphere, which is identified by the enhanced vertical EPF for the Kelvin waves at 70 hPa (Fig. S3). The positive forcing near 30 and 60 hPa from January to March 2016 accelerates the upper and lower jets, respectively, thereby the upper and lower 240 parts of the QBO jet are not dissipated totally, maintaining the separated jet during the disruption (Fig. 2). Acceleration in the upper and lower parts of the separated QBO jet is also shown by the momentum forcing by P-CGWs (Fig. 3f). The contribution of CGWs to the enhanced jet in the current study may explain why the westerly winds simulated by Watanabe et al. (2018) are relatively weak compared to those in MERRA-2 near 20 hPa and 70 hPa, without non-orographic GW parameterization.
MRG wave forcing (Fig. 3h) is generally stronger during the disruption than in the climatology. In addition, there is a 245 sudden increase in the negative MRG forcing at 40 hPa from October to November 2015, which is similar to the pattern seen in REQ at this time and location. This suggests that the MRG waves influence the early stage of the QBO disruption by slowing down the QBO jet. IG waves (Fig. 3i) exert a strong negative forcing in November 2015 contributing to the enhancement of https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License.
negative REQ near 40 hPa, together with the MRG wave forcing. Rossby wave forcing (Fig. 3j) near 40 hPa is stronger than the climatology consistently from November 2015 to March 2016, which is considered as a major cause of the QBO disruption. 250 To summarize, in October 2015, the negative forcing by MRG waves is anomalously strong compared to the climatology at 40 hPa between 5°N and 5°S, and becomes stronger in November 2015 together with IG waves when the Rossby waves start to break at the southern hemispheric (SH) part of the QBO (see Fig. 5). Therefore, MRG and IG wave forcing may precondition the zonal mean flow near the QBO jet core to be easily disrupted by the Rossby waves. From December 2015 to February 2016, the Rossby wave forcing is dominant among the equatorial waves, while the negative CGW forcing contributes 255 significantly to the disruption in February 2016 when negative vertical wind shear appears near 40 hPa. Figure S4 is the same figure with Fig. 3 but using ERA-I data. We found that the time evolution of each wave forcing in ERA-I is similar to that in MERRA-2, although the magnitudes of the REQ and wave forcing (vertical advection) in ERA-I is generally stronger (weaker) than that in MERRA-2. Figure 4 shows the time series of zonal wind, zonal wind tendency, and wave forcing by each type of wave from July 2015 to June 2016 at 40 hPa. The monthly averaged momentum forcing by each type of wave and its contribution to the total negative wave forcing (percentage) are given in Table 1 contributions of 39% and 41%, respectively, while Rossby wave forcing is -0.22 m s -1 mon -1 , with a relatively small contribution of 20% (Fig. 4b). In November 2015, negative wave forcing by Rossby, MRG, and IG waves increase with contributions of 45%, 27%, and 28%, respectively, which are 2.4, 2.5, and 1.6 times stronger than the climatology, respectively.

Quantitative contributions of the equatorial waves 260
Afterward, Rossby waves mainly provide negative forcing which induces easterly accelerations in December 2015 and January 2016, with the contributions of 70% and 91% of the total negative forcing, respectively. They are 3.2 and 4.3 times larger than 270 the climatology, respectively. In February 2016, Rossby waves, parameterized CGWs, MRG waves, and IG waves at 40 hPa contribute to the total negative wave forcing by 61%, 20%, 12%, and 7%, respectively. The CGWs dominate the negative forcing with a percentage of 60% in March 2016. When the average is taken over 5°-10°S, however, Rossby waves dominate from October 2015 (Fig. S5). This implies that the Rossby wave forcing was strong enough to decelerate the edge of the QBO jet (5°-10°S), while it presumably extends to the jet core (0°-5°S; reported by Coy et al. (2017). This implies that the negative momentum forcing by CGWs is stronger than that by GWs from a fixed source during the disruption.  (Table 1). The strong vertical EPD in the stratosphere (40 hPa) does not necessarily indicate the wave propagation from the equatorial region. Hence, the origination of the vertical Rossby wave forcing will be analyzed in the following subsection. 295

Contributions of Rossby waves and MRG waves
In this subsection, we focus on the Rossby and MRG waves and their sources. Figure 5 shows the evolution of the EPF and EPD for the Rossby waves (left), and their meridional (middle) and vertical (right) components, separately, from November 2015 to February 2016. The vertical profiles of meridional EPF (EPF-y) at 10°N and 10°S are included, and meridional distribution of the vertical EPF (EPF-z) at 70 hPa are plotted at the bottom of each month in red lines. In the vertical 300 profiles and meridional distribution plots, climatological monthly means are included with black lines with ±1 values indicated in gray shading. In November 2015 (Fig. 5a), the Rossby waves start to break at the southern flank of the QBO westerly jet near 50 hPa, which is anomalously strong compared to the climatology. They most likely propagate from the NH, given that EPF-y at 10°N is directed southward with a magnitude greater than the climatology by more than 1 . The EPF-y at 10°S is directed northward at the altitude below 70 hPa, and it is slightly stronger than the climatology; however, this EPF 305 hardly propagates into the QBO jet. In December 2015 (Fig. 5b), anomalously strong negative EPD near 40 hPa in the SH extends northward to 10°N, with the strong EPF-y at 10°N propagating toward SH. The negative EPD in the SH part of the QBO jet at 40 hPa is mainly explained by its meridional component, which presumably originates from the EPF-y at 10°N between 70 and 30 hPa. On the other hand, the negative EPD in the NH part of the QBO jet at 40 hPa is mainly explained by its vertical component considering the anomalously strong vertical EPD there. The strong vertical EPD seems to originate from 310 the EPF-z at 70 hPa between 0° and 15°N. In January 2016 (Fig. 5c) when the Rossby wave forcing is the strongest, the overall feature is similar to December 2015 although with somewhat different aspects: (i) negative EPD at 40 hPa exhibits a significant https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License. peak in 0°-5°S, (ii) EPF-y at 10°N has an additional peak at 40 hPa, and the (iii) EPF-z at 70 hPa in the SH becomes much stronger than the climatology. In February 2016 (Fig. 5d), the anomalously strong negative EPD is more concentrated at 40 hPa with a larger contribution from the meridional EPD at 0°-25°N, while the vertical EPF at 70 hPa is less pronounced 315 compared to January. To sum up, the Rossby wave forcing and the associated wave flux are anomalously strong from November 2015 to February 2016, and both the meridional and vertical components are significantly stronger than the climatology. The meridional EPD, most likely caused by waves propagating southward at 10°N, largely contributes to the deceleration of the QBO jet in the SH. The vertical EPD, presumably caused by waves propagating vertically at 70 hPa between 0° and 15°N, largely contributes to the deceleration of the QBO jet in the NH. 320 To investigate whether the anomalously strong EPF-z at 70 hPa in Fig. 5 originates in the equatorial region, Fig. 6 shows the EPF and EPD for the waves, which are westward-propagating low-frequency waves, in the troposphere and for the Rossby waves in the lower stratosphere. Here, we focus on January and February 2016 when EPF-z is strong and moderate, respectively. Note that the EPF in Fig. 6 is the same as in Fig. 2, except that it is divided by air density for better visualization.
In January 2016 (Fig. 6a), there are three potential source regions of the Rossby waves: (i) 5°N-10°S at 120-400 hPa 325 (equatorial source), (ii) 15°-25°S at 200-350 hPa (SH source), and (iii) 20°-25°N and 250-450 hPa (NH source), considering that the positive EPD region is a source region of the westward-propagating waves. First, from the equatorial source, wave activity propagates upward and northward up to ~120 hPa. There, it seems to merge with the wave activity from the NH sources, while part of it propagates upward to the NH stratosphere near 0°-15°N. Second, some of the waves from the SH source propagate to the SH stratosphere after depositing a large amount of negative momentum between 100 and 70 hPa, and 330 others propagate to the NH stratosphere. Third, the wave activity from the NH source does not seem to propagate upward. In addition to the three source regions, there might be other source regions at the midlatitude, so the propagation from the midlatitudes in both hemispheres also needs to be considered. It is shown that the wave activity from the NH (SH) midlatitude propagates into the equatorial stratosphere at the altitude range above 100 hPa (200 hPa). The behaviour in February 2016 shows a similar pattern to that in January 2016, except for an additional positive EPD region at [15][16][17][18][19][20][21][22][23][24][25] In summary, the strong EPF-z for Rossby waves at 70 hPa is attributed to both the equatorially generated waves and the waves propagating from the NH and the SH. panel. In Fig. 7, we will focus on the altitude near 40 hPa, where the wave forcing is directly related to the QBO disruption, although strong negative wave forcing also exists in the upper stratosphere. In October 2015 (Fig. 7a), all the wave forcing is similar to the climatology except for the MRG waves (Fig. S2); the negative MRG wave forcing is stronger than the climatology by more than 1 at 50 hPa in 0°-5°S (indicated by the magenta dots). Given the dominant upward propagation in the lower to middle stratosphere, the MRG waves exerting negative forcing near 50 hPa in 0°-5°S seem to propagate from 60-80 hPa and 5°-10°S where the positive EPD exists. While the increase in the meridional EPF at 5°-10°S near 70 hPa is somewhat unclear in the EPF-y at 10°S, it is clear in the EPF-y at 7°S and 5°S showing a noticeable increase toward the equator compared to the climatology (not shown). The increase in the vertical EPF at 60-80 hPa is evident in the EPF-z at 70 hPa, which is greater than the climatology by more than 1 in 10°S-0°. It is worthwhile to note that there exists positive EPD over 5°-10°N at 70 hPa as well, implying that 5°-10°N and 60-80 hPa might be another source region for MRG wave generation. 350 However, the increases in the EPF-z at 70 hPa and EPF-y at 5°-10°N are less significant compared to the climatology. In November 2015 (Fig. 7b), a pattern similar to that in October 2015 appears, but with an increase in the magnitude of the negative EPD at 40-60 hPa within 5°N/S and the EPF-y at 10°S in 50-80 hPa. The strong EPD at 0°-10°S and 40-60 hPa originates most likely from the strong EPF-y at 10°S in 60-80 hPa and EPF-z at 70 hPa in 5°-15°S. In December 2015 (Fig.   7c) and February 2016 (Fig. 7d), strong negative EPD, equatorward EPF-y at 10°S, and upward EPF-z at 70 hPa are still 355 evident.
According to this analysis, we conclude that MRG waves decelerate the QBO jet core at the onset of the QBO disruption, given that the negative zonal wind tendency from October to November 2015 is partly attributed to the anomalously strong MRG wave forcing. The positive EPD at 60-80 hPa between 5°S and 15°S by MRG is much greater than the climatology both for the meridional and vertical components.
where Ω is the Earth's rotation and is the buoyancy frequency. The negative regions of ̅ suggest a possibility of baroclinic instability, because the positive and negative ̅ values in a neighboring region satisfy the necessary condition for the instability (Gill, 1982). This suggests that baroclinic instability at the boxed region is a possible source for generating the anomalously strong MRG waves. The MRG waves generated by the baroclinic instability in the narrow westerly jets accelerate the zonal wind off the equator and decelerate the zonal wind near the equator, reducing the curvature and thus the instability, which indicates that the MRG waves respond to the QBO wind system (Garcia and Richter, 2019). However, as the deceleration of the jet core is important in the QBO disruption, such behavior may play an important role in preconditioning the background wind. It should 385 be noted that the baroclinic instability does not seem to be an exclusive source of the MRG waves because there exist precedent WQBO cases having considerable negative ̅ without significant enhancement in the wave generation (e.g., 2010, 1987, and 1982). Therefore, further studies on the source of the MRG waves should be done in the future. It is also interesting that ̅ shows large negative values at the upper stratosphere (~5 hPa) where the zonal wind curvature is large in association with strong westerly jet (Hamilton, 1984). Nevertheless, it is unlikely that the MRG waves generated at 5 hPa affects the QBO 390 disruption as the upward propagating MRG waves (i.e., vertical EPF >0) are dominant in the stratosphere, and the strong easterlies between 5 to 10 hPa inhibit the propagation of the MRG waves.
We found in the previous figures (Figs. 5 and 6) that the increased Rossby wave forcing in the stratosphere partly originates from the equatorial troposphere. Therefore, in Fig. 9, we examine the zonal-mean precipitation in the equatorial troposphere to identify convective activity using MERRA-2 data. Overall, the zonal-mean precipitation from November 2015 395 to February 2016 is stronger than the climatology in 5°N-5°S. It is greater than the climatology by more than 1 from November to December 2015 (Figs. 9a-b). In February 2016 (Fig. 9d), the precipitation is much stronger than the climatology between 5°N and 10°S by more than 3 . The maximum precipitation is slightly shifted southward in December-January-February (DJF), following the location of the inter-tropical convergence zone (ITCZ).
We further check whether the precipitation spectrum related to each equatorial wave type is enhanced during the 400 disruption. Figure 10 illustrates the power spectrum of the precipitation data of MERRA-2 divided by background spectrum averaged over 10°N-10°S for both the symmetric and anti-symmetric components. The background spectrum is obtained by applying 1-2-1 smoothing to the base-10 logarithm of the raw spectrum (separately for the symmetric and antisymmetric spectrum) in wavenumber and frequency 40 and 10 times, respectively, and applying based-10 exponential again to the smoothed spectrum (Chao et al., 2009). If the raw spectrum divided by the background spectrum is greater than 1.4, it is 405 considered statistically significant at the 95% level for 41 degrees of freedom (i.e., corresponding to the number of the latitude grid cells from 10°N to 10°S) (Wheeler and Kiladis, 1999).
The area where the precipitation spectrum is greater than the climatology by more than 1 , which is denoted by a stippled pattern, widens from November 2015 to February 2016, indicating that not only the mean value but also the variability of the convection significantly increases during the disruption. The spectra related to Rossby waves in the symmetric spectrum ( = -10-0, = 0-0.15 cpd) are statistically significant throughout the period, suggesting that the convective activity in the troposphere is the probable source for Rossby waves. However, the waves in the low-frequency spectra have less possibility to propagate upward into the stratosphere due to their slow vertical-group velocity (Yang et al., 2011). In November 2015 (Fig.   10a) and December 2015 (Fig. 10b), the spectra related to MRG waves in the anti-symmetric component ( = -9 and = 0.12; = -5 and = 0.28) are statistically significant and their amplitude is stronger than the climatology by more than 1 . However, 415 they are less likely to be the primary source of the anomalously negative MRG wave forcing in the stratosphere, given that the EPF-z for MRG waves greater than the climatology only appears at altitude above 70 hPa (Fig. 7). It is also interesting that the peaks related to Kelvin waves ( = 0-10 and = 0-0.25) are increasing from November 2015 (Fig. 10a) to February 2016 ( Fig. 10d), consistent with the increasing EPF-z at 70 hPa (see Fig. S3) and the resultant EPD (Fig. 2) during the disruption.
To validate the realism of the MERRA-2 precipitation data, we additionally calculate the space-time spectra of 420 precipitation provided by TRMM in Fig. S6. The key features are present in TRMM, but its amplitude is larger than that of MERRA-2, possibly attributed to the finer resolution. Note that TRMM data are available in a shorter period (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016) than the MERRA-2 data , so only five years are included as WQBO climatology in Fig. S6. As in the MERRA-2 data, there exists significant increase in the precipitation of TRMM during January and February 2016 (Fig. S6) compared to the climatology. 425 Figure 11 shows EPF vectors and EPD for the IG waves, together with the meridional distribution of EPF-z at 70 hPa, from November 2015 to February 2016. In this figure, the vertical cross section of EPF-y is not shown because EPF-z dominates the total EPF. EPF-z here is the net EPF of eastward and westward IG waves, so the positive EPF-z indicates stronger westward EPF than the eastward one, given the dominant upward propagation in the stratosphere. Anomalously strong 430 negative wave forcing exists at 10-20 hPa near the equator throughout the period. In November 2015 (Fig. 11a), negative wave forcing is anomalously strong at 40-80 hPa near the equator (0°-5°S), influencing the deceleration and the downward shift of the WQBO jet core in the following months. The strong negative forcing is likely attributable to the strong vertical EPF at 70 hPa, which is greater than the climatology by more than 1 . In December 2015 (Fig. 11b) and January 2016 (Fig. 11c)  propagating waves when the phase-speed is larger (smaller) than the zonal wind at the source level. The double-sided arrows represent the zonal wind range between the source level (140 hPa) and 70 hPa in each month, indicating the phase-speed range 450 of the critical-level filtering. In November 2015 (Fig. 13a), the zonal wind at the source level is near zero, so the precipitation spectrum has a similar amplitude between the eastward and westward waves. However, the eastward waves are almost filtered out due to the positive vertical wind shear between 140 and 70 hPa (see Fig. 1). This feature is different from the climatology, which has stronger westward waves than eastward waves at the source level. As most of the pronounced westward waves are filtered out due to the negative vertical wind shear (see Fig. 1), the remaining spectrum at 70 hPa in November 2015 has more 455 westward waves than the climatology. In December 2015 (Fig. 13b), the wave characteristics at the source level during the disruption agree well with the climatology-that is, stronger westward waves than eastward waves and a similar magnitude of westerly winds at the source level. However, both a larger magnitude of the precipitation spectrum and the narrower criticallevel filtering range for the westward waves result in stronger westward momentum flux at 70 hPa during the disruption than the climatology. From January 2016 (Fig. 13c) simulation. They explained that larger westward forcing is due to the strong westward EPF in the UTLS, which is attributed 470 to the enhanced convective activity with -10 < < 10 m s -1 (where is the phase speed) and less critical-level filtering of the IG waves during El Niño than during La Niña. This is consistent with our result, implying that the enhanced wave source (i.e., convection) and the propagation conditions favorable for westward IG waves in the current study are presumably associated with the strong El Niño condition.

Contribution of inertia-gravity waves
https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License. Figure 14 illustrates the zonal-mean zonal CGWD overlaid with zonal-mean zonal wind profile and the source-level CGW momentum flux averaged over 5°N-5°S in February 2016, when CGWD started to contribute to the QBO disruption, along with the climatology. Negative CGWD appears where the vertical wind shear is negative, with a maximum magnitude of -1.9 m s -1 mon -1 at 47 hPa. Once a negative vertical wind shear develops, CGWs begin to exert negative forcing on the zonal wind, making the vertical wind shear stronger, which in turn leads to a greater negative CGWD. It is noticeable that the source-level 480 CGW spectrum reveals much stronger momentum flux than the climatology and the difference from the climatology is larger for the westward momentum flux than the eastward momentum flux, resulting in a faster and more irreversible easterly development at 40 hPa. In addition to the source spectrum, the apparent positive wind shear in the upper troposphere during February 2016 enhances the propagation of westward waves into the stratosphere in comparison to the negative wind shear in the climatology. 485

Contribution of parameterized CGWs 475
We would like to answer the following two questions: (1) Why is the source-level CGW momentum flux stronger in February 2016 than in the climatology? (2) Why is the increased amount of westward momentum flux larger than that of eastward momentum flux? Figure 15 illustrates the convective source spectrum and the wave-filtering and resonance factor (WFRF) spectrum, which are two important factors constituting source-level CGW momentum flux spectrum in the parameterization by Kang et al. (2017). The magnitude of convective source spectrum is proportional to the square of the 490 convective heating rate, having a peak where the phase speed equals to the moving speed of convection ( ℎ ). WFRF includes two main effects: (i) critical-level filtering within the convective forcing region and (ii) the amplification of the response due to the matching of the vertical wavelength of the GW and the vertical configuration of convective heating. As the convective heating is deeper, WFRF integrated over all phase speeds becomes larger and its peak is shifted to the higher phase speed (Song and Chun, 2005). The magnitude of the convective source spectrum (Fig. 15a) is much stronger than the climatology 495 and WFRF (Fig. 15b) shows a stronger magnitude throughout all phase speeds, both of which lead to the exceptionally strong momentum flux of CGWs. Stronger magnitude of WFRF is due to a higher static stability and deeper convection that are possibly triggered by El Niño, in which there is a warm troposphere and cool stratosphere (Domeisen et al., 2019;Kawatani et al., 2019;Richter et al., 2020). The zonal wind at the cloud top (white line) exhibits a weaker easterly compared to the climatology (gray line): zonal winds at the cloud top averaged over 5°N-5°S are -3.4 and -4.4 m s -1 for the disruption and the 500 climatology, respectively. On the other hand, the difference in ℎ (gray line) is negligible. Thus, the westerly wind anomaly at the cloud top is responsible for the westward CGWs that are increased more than the eastward CGWs at the source level during the disruption.

Summary and Conclusion
In this study, we have investigated the contribution of each equatorial planetary wave mode and parameterized 505 convectively-excited gravity waves, CGWs, to the 2015-16 QBO disruption by utilizing the equatorial wave separation method https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License.
of Kim and Chun (2015) and the offline CGW parameterization by Kang et al. (2017) using MERRA-2 model-level data. The main results, represented in schematic form in Fig. 16, are as follows: • From October to November 2015, anomalously strong negative forcing by MRG waves mainly decelerated the QBO jet at 0°-5°S near 40-50 hPa. From November 2015, IG wave forcing became anomalously strong at the altitudes 510 below 50 hPa, when the Rossby waves propagating from the NH began to break at the southern flank of the westerly jet (0°-10°S) at 30-60 hPa. The anomalous MRG waves were possibly generated by the increased frequency of barotropic instability in the lower stratosphere. IG wave forcing was attributed to (i) stronger convection in the equatorial troposphere, (ii) stronger westerly (or weaker easterly) winds leading to an enhanced westward momentum flux at the source level, and (iii) the reduced critical-level filtering of the westward waves arising from 515 weaker negative wind shear in the UTLS compared to the climatology.

•
From December 2015, Rossby-wave breaking extends from the SH to the equator. The deceleration of the QBO jet in the NH was mainly induced by the vertically propagating Rossby waves penetrating into the stratosphere. They likely originated in the NH and SH extratropics as well as in the tropics, generated by the convection in the equatorial troposphere. The deceleration of the QBO jet in the SH is mainly induced by Rossby waves propagating laterally 520 from the NH extratropics. In January 2016, Rossby wave forcing was the strongest among all equatorial waves.

•
In February 2016, the QBO jet at 40 hPa was continuously decelerated by the Rossby waves, propagating both vertically and latitudinally. At the same time, the estimation of the CGW forcing suggests that CGWs provided negative forcing on the QBO jet at 40-50 hPa near the equator, contributing to 20% of the total negative wave forcing.
The enhancement in the negative CGWD is partly explained by excessively strong westward momentum flux at the 525 source level, which was attributed to the westerly wind anomaly at the source level and the reduced critical-level filtering of the westward waves in the upper troposphere.

•
Meanwhile, the Kelvin waves and CGWs helped confine the development of the easterlies to the region near 40 hPa by strengthening the westerly jets near 20-30 hPa and 60-80 hPa from January 2016.
In previous studies, laterally propagating Rossby waves from the midlatitudes have been considered as the primary cause 530 of the QBO disruption, although Lin et al. (2019) emphasized the role of local equatorial wave forcing in preconditioning the Rossby wave breaking. In the present study, we found that anomalously strong negative MRG and IG wave forcing in the early stage of the QBO disruption played a significant role in preconditioning the QBO jet core. Figure 17 shows scatter plots demonstrating how the wave flux or wave forcing was anomalously strong compared to the climatology. The negative EPDs for the MRG and IG waves in 2015 were the strongest among those in other WQBO cases (Fig. 17a), where the EPDs for the 535 MRG waves and IG waves are averaged for October-November and November-December, respectively. We also found that Rossby waves propagating upward from the equatorial troposphere significantly contribute to the QBO jet in the NH, which helped to interrupt the westerly jet along with the equatorward propagating Rossby waves. Both the meridional and vertical EPF of the Rossby waves propagating into the equatorial stratosphere averaged for January-February in 2016 were stronger https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License. than those in any other years of WQBO phases (Fig. 17b). The contribution of the parameterized CGWs to the QBO disruption, 540 which had been considered small, was found to be substantial when a physically based CGW parameterization was used; the negative CGWD in February 2016 was the largest among CGWD values in February with WQBO phases at 30-50 hPa (Fig.   17c). The strongest CGWD at 30-50 hPa is not surprising given that 2016 is the only year when the negative vertical wind shear occurs near 40 hPa due to sudden easterly development. However, it is surprising that the westward CGW momentum flux at the source level in February 2016 was much stronger than in any of the February with WQBO phases (Fig. 16c). This 545 suggests that the variability of the GWs according to the convective activity leads to an enhancement in the negative CGWD at 40 hPa.
The current results are based on the MERRA-2 data, and some uncertainties might be included in association with reanalysis data. Therefore, we checked whether the behavior of the equatorial waves in MERRA-2 also appears in ERA-I during the QBO disruption period (Fig. S3). The equatorial wave forcing in ERA-I showed similar time evolution to that in 550 MERRA-2, despite somewhat larger wave forcing in ERA-I. In addition, the tropical precipitation in MERRA-2, which increased during the QBO disruption, was found to be evident in the observed precipitation (TRMM; Fig. S6). One additional point to mention about the uncertainties in our results is on the cloud top and bottom heights used for the CGW parameterization.
Although we tried to make vertical profiles of the convective heating rate comparable to those estimated from the satellite observations (Sect. 2.4), CGW momentum flux spectrum is very sensitive to the cloud-top and -bottom heights (Song and 555 Chun, 2005;Kang et al., 2017) that are derived from the threshold percentage of the convective heating profiles. Considering the importance of cloud-top and -bottom heights, their realistic estimation needs to be further investigated in the future.
Although not discussed in the results section, a QBO westerly phase that does not rapidly propagate downward and maintains westerly winds throughout a deep layer might provide a favorable condition for the QBO disruption. Hitchcock et al. (2018) mentioned that westerly QBO should be deep enough to develop easterly winds away from the top and bottom shear 560 regions of the jet. In addition, Osprey et al. (2016) reported enhanced tropical upwelling during the disruption. In our analysis, it is found that not only the mean upwelling ( ̅ * ) in the whole stratosphere was strengthened but also upwelling in the upper stratosphere was stronger than the climatology (c.f. strong positive ADVz at the top of the QBO in Fig. 3), which made a deep and stalled QBO jet susceptible to the continuous deceleration by wave forcing. Therefore, it would be interesting to investigate the vertical upwelling and its importance during the disruption period. 565 In this study, we found that the 2015-16 QBO disruption occurred when the following conditions were met: (i) negative equatorial wave (MRG, IG) forcing in the early stages and (ii) strong vertical and horizontal components of Rossby waves with strong small-scale CGWs in the later stages. The enhancement in the convective activity as well as anomalous wind profile, possibly attributed to a strong El Niño, leads to anomalously strong negative equatorial wave forcing. However, it is still puzzling why the equatorial wave activity in 2015/16 is stronger than those in other El Niño periods, which requires further 570 investigation. Because more frequent occurrences of the QBO disruption are expected in a warmer climate (Osprey et al., 2016; https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License. Hirota et al., 2018), understanding the 2015-16 QBO disruption would eventually lead to an improvement of the long-range forecast in the future.
Data availability. The MERRA-2 data were provided by the Global Modeling and Assimilation Office at NASA Goddard 575 Space Flight Center through the NASA GES DISC online archive (available online at https://gmao.gsfc.nasa.gov/reanalysis/).
The ERA-I data were obtained from the ECMWF data server (available online at http://apps.ecmwf.int/datasets/).
Author contributions. HYC and MJK designed the study and MJK carried it out. MJK prepared the manuscript with contribution from HYC and RRG. All co-authors interpreted the results and reviewed and edited the paper. Table 1. Momentum forcing at 40 hPa by each wave (m s -1 mon -1 ) and its percentage to the total negative wave forcing (parenthesis) averaged over 5°N-5°S from October 2015 to March 2016 and for the climatology. The percentage is calculated when a wave forcing is negative during the QBO disruption.

2015-16
Oct 2015   Positive (negative) zonal winds are plotted with solid (dashed) lines with a contour interval of 2 m s -1 , and thick contour lines denote a zero zonal wind speed. The magenta stippled pattern represents a region where the EPD is algebraically smaller (more negative) than the climatology by more than its standard deviation. The arrow on the upper right corner denotes the reference 760 vector.
https://doi.org/10.5194/acp-2020-791 Preprint. Discussion started: 17 August 2020 c Author(s) 2020. CC BY 4.0 License.   (negative) zonal winds are plotted with solid (dashed) lines with a contour interval of 2 m s -1 , and thick contour lines denote a zero zonal wind speed. The magenta stippled pattern represents a region where the EPD is smaller than the climatology by more than its standard deviation. Here, EPF and EPD are multiplied by 8 and 4, respectively. is considered a statistically significant spectrum at 95% level. The blue-stippled pattern denotes a spectrum where the power is stronger than the climatology by more than its standard deviation. Thick solid lines denote theoretical dispersion lines of each equatorial waves for the equivalent depth of = 8, 40, 240 m, although only = 8 m line is shown for IG waves.