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Southwestward propagating quasi-biweekly oscillations over the South-West Indian Ocean during boreal winter

An analysis of outgoing longwave radiation (OLR) over the South-West Indian Ocean (SWIO) yields regular, poleward propagating, large-scale, convectively coupled systems of alternating cyclonic and anticyclonic circulation with a quasibiweekly period during boreal winter. Composites from 10 years (2000/01 – 2009/10) of OLR and reanalysis data show wellformed rotational gyres that can be tracked from near the equator to almost 35◦S appearing slightly west of Sumatra and going towards Madagascar, i.e., with mean southwest propagation. The gyres show a marked northwest-southeast tilt, giving rise to 5 a northeast-southwest oriented wavetrain. The scale of the gyres is about 30◦–35◦, their period is 18–20 days and they have a westward phase speed of approximately 4 ms−1. The group velocity of these wave packets is near-zero. Velocity fields with OLR indicate that maxima of moist convective activity lie in the northeast sector of the gyres (in the Southern Hemisphere), likely a result of both convergence and the poleward rotational advection of moist air. Wavetrains comprising the quasi biweekly oscillation (QBWO) are born near the equator with a barotropic profile; a first baroclinic form emerges as they move 10 southward and couple with moisture. In their decaying stage, convective activity decreases and the systems regain an equivalent barotropic structure. A vorticity budget reveals that the β effect plays a leading role in the propagation of the QBWO, though moist coupling (via stretching) is important in reducing the speed of propagation of this mode. Further, these two terms with horizontal advection account for much of the observed vorticity tendency. Finally, apart from their contribution to intraseasonal variability, moist convection and strong circulation anomalies in the QBWO lows (cyclonic gyres with negative OLR anoma15 lies) — especially in combination with the vorticity of the background flow during the boreal winter season — are shown to provide favourable conditions for the genesis of tropical cyclones (TCs). In particular, depressions are spawned within QBWO lows, some of which mature into TCs that affect Madagascar, other SWIO islands and the coast of southeast Africa.

The most detailed work on sub-monthly intraseasonal variability till date over this broad geographical region in boreal winter was done by Yasunari (2013, 2014). These authors used Japanese reanalysis (JRA25-JCDAS) data to examine variability in a broad 6-30 day window. They found wavetrains oriented in a northeast-southwest direction from Sumatra towards Madagascar, with a wavelength of 3000-5000 km, and westward-southwestward phase propagation. These were interpreted as combinations of ER and mixed Rossby-gravity (MRG) gyres, propagating in a favorable background of monsoon westerlies. But, effects of coupling with moisture have not been investigated, nor was a time period range of quasi-biweekly 95 activity (without smaller timescale synoptic influence) considered in isolation. Moreover, the propagation and dynamical ingredients required for the formation of the QBWO in this region have not been clearly identified, nor has the influence of this mode on TCs been elucidated.
In this paper, we aim to fill some of these gaps; after a description of the data and methods used in the study (Section 2), we proceed with a detailed documentation of the characteristic features of the QBWO in the SWIO (Section 3), including its 100 spatial and temporal scales, propagation, horizontal and vertical structure and evolution. Our analysis is based on composites generated from ten years of daily reanalysis data. With the characterisation in hand, we then proceed to a vorticity balance (Section 4) to examine the features involved in the maintenance and propagation of this mode. We then consider the influence of the QBWO on tropical depressions and TCs (Section 5); in particular, a detailed case study of the 2008-09 winter season is presented to show the evolution of the QBWO wavetrain and the concomitant birth and development of depressions, which 105 eventually mature into TCs in the convective environment of the quasi-biweekly system. Finally, in Section 6, a summary and discussion of our results concludes the paper.

Data and Methodology
Daily mean products from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project serve as the main data set for this study (Kalnay et al., 1996). Specifically, we have used 110 10 years of horizontal winds and vertical velocity data at 12 pressure levels (1000 to 100 hPa) that spans December to March (DJFM) from 2000/2001-2009/2010 and has a horizontal resolution of 2.5 • . This data is used to calculate the derived fields presented in this paper. Some fields, such as relative vorticity and various terms of the vorticity budget are computed using Windspharm package (Dawson, 2016). Daily outgoing longwave radiation (OLR) data from the National Oceanic and Atmospheric Administration (NOAA) satellites serves as a proxy for moist tropical convection (Liebmann and Smith, 1996). 115 4-times daily precipitable water (PW) data is used from ERA-Interim reanalysis (Dee et al., 2011), from which daily average is calculated. Both, PW and OLR have a spatial resolution of 2.5 • . In addition, wind (at 850 hPa) and OLR data at 0000UTC of specific days are taken from hourly wind data of ERA5 (Hersbach et al., 2020), and 8-times daily OLR of the Kalpana satellite (Mahakur et al., 2013) respectively, to examine specific events associated with TCs, these data are at a much finer spatial resolution of 0.25 • . Precipitation data is from the Tropical Rainfall Measuring Mission (TRMM), specifically the product 120 3B42 is used at a daily resolution (Huffman et al., 2007). This data also has a spatial resolution of 0.25 • . Finally, to examine 1999), 12-24 day (Chen and Chen, 1995) and 6-30 day Yasunari, 2013, 2014) in particular studies. Here, we use a lower limit of 14 day to exclude synoptic scale signals, and the upper limit of 30 day is used instead of widely used 20 day as previous studies have shown that there can be systems of QBWO scale which have a slightly larger period than 20 days (Molinari et al., 2007). It turns out that the dominant period around the two-week scale is actually near 20 day in the SWIO, hence, for the upper threshold, the use of 30 day (instead of the widely used 20 day cutoff) seems appropriate, as it doesn't 130 exclude signals which might have periodicity slightly larger than 20 days. We note that significant power associated with MJO is well above 30 day, so we don't run into the risk of including MJO signals while using a 14-30 day band window.
To extract 14-30 day variability, a Lanczos band-pass filtering method is used (Duchon, 1979). Further, to highlight the QBWO, the annual cycle of the time series in question is removed by subtracting the mean and the first three Fourier harmonics before filtering is done. To check robustness, we varied the filtering band and it produces essentially identical results up to a 10-35 day 135 range, so our result is not sensitive to the width of the filter as long as it satisfactorily isolates QBWO signal from the variability of other tropical modes. To describe the structure and evolution of the QBWO, we have constructed composites of OLR and low-level (850 hPa) circulation from the filtered data. Members for the composites satisfy the following three criteria: 1) In the chosen box (52.5 • -60 • E, 10 • -17.5 • S; Figure 1) -a region of high 14-30 day variability (in terms of standard deviation) of OLR anomaly -there should be complete and distinct phase cycle of averaged 14-30 day OLR anomaly, i.e., a distinct 140 maximum should monotonically decrease to a distinct minimum and then again monotonically increase to a distinct maximum.
2) The negative anomaly of box-averaged OLR on Day 0 (which is the day when the box-averaged OLR is locally minimum) must be less than −1 standard deviation; and similarly the previous and subsequent maxima of positive anomalies of boxaveraged OLR must be more than 1 standard deviation.
3) The identified minima should be outside the first and last 16 days of the season. This condition is used as we leave 16 days before and after the minima based on the filter to ensure that there 145 is room for a complete cycle within the season (DJFM). These criteria help us to identify strong convectively coupled systems and result in 19 members from 2000/01-2009/10 in the composite. We also varied the base region a bit to check whether the results depend strongly on the particular box chosen. Indeed, as long as the base box remains inside the region of high filtered OLR standard deviation, the composite structure is not affected. Further, the composite vertical structure and vorticity budget of these systems are also analyzed to understand the evolution of the QBWO and its propagation. A detailed description of 150 these analysis methods are given in the respective sections.

Boreal Winter Quasi-biweekly Activity
The winter season 14-30 day variability of organized moist convection in terms of the standard deviation of filtered OLR is shown in Figure 1, along with mean background PW. Quite clearly, in the SWIO, the quasi-biweekly part of intraseasonal activity is contained within regions of high PW (Sukhatme, 2013). Further, the north-east to south-west(NE-SW) tilt of moist 155 convective activity in the SWIO appears to follow that of PW and suggests that this could be a pathway for the propagation of quasi-biweekly intraseasonal systems in this region.
This possible southward propagation is exemplified in Hovmoller diagrams of OLR and rainfall anomalies presented in Figure   2. The winters chosen are 2001-02 (first panel from above), 2006-07 (second panel from above) and 2008-09 (third panel from above), though this type of movement is seen in almost every year. Examining the OLR anomalies (contours in Figure   160 2), propagation begins near the equator and extends up to about 35 • S, with some degree of variability. Further, wavepackets in the form of alternating highs and lows in the filtered OLR anomaly are visible in each of these cases -specifically, from Day 70 to 115 in 2001-02, Day 80 to 120 in 2006-07 and Day 40-120 in 2008-09. From these diagrams, one can note that these systems are slightly more probable in the second half of the season, i.e., late winter. This is also by and large true of other winters in the 10-year data we have examined. The phase speed of these disturbances is negative indicating southward 165 movement but some wavepackets suggest a small positive or northward group velocity (for example, in 2008-09 from Day 60 to 90). We will return to quantification of these issues when we construct composites of the southward moving systems. It should be kept in mind that we have shown specific years in Figure 2, but in fact, cohesive southward propagating events are observed in almost every winter season. The colors in Figure 2 show rainfall anomalies, and negative OLR contours contain positive (blue) precipitation anomalies, or enhanced rainfall. In most cases, precipitation anomalies are large near the equator, 170 though in some cases (for example, 2001-002, Days 100-110) large deviations of rainfall from the mean state are observed as far as 35 • S, i.e., well into the subtropical SWIO. Note that, even during the winter, we observe some instances of northward propagation (for example, between Days 15 and 40 in 2006-07), albeit weaker, in this intraseasonal window (Srinivasan and Smith, 1996). Though the movement of such systems is restricted from the equator to about 10 • N.

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Composites of the southward moving intraseasonal systems, constructed using the techniques outlined in the Data and Methodology section, are presented in Figure 3. On Day −9, northeast of Madagascar, we see a well-developed anomalous anticyclonic circulation coupled with positive OLR anomalies (red color in Figure 3) indicating a lack of moist convection. Meanwhile, near the equator, we see an emerging low with anomalous westerlies between 50 • -90 • E and scattered negative OLR anomalies.
North of the equator too, we see a hint of a cyclonic circulation, with anomalous westerlies hugging the equator between simi-180 lar longitudes, and negative OLR anomalies (though weaker in magnitude than the Southern Hemisphere counterpart). By Day −6, the newly formed cyclonic vortex near the equator becomes more prominent, gets a little tilted and a small area of strong anomalous convection is seen in its northeast sector. North of the equator, the weak cyclonic anomaly has almost vanished but  (or, wavenumber 5-6). These lower tropospheric horizontal features that we have catalogued here are similar to that of boreal summer QBWO (Chen and Sui, 2010;Wang and Chen, 2017), and apart from a larger spatial scale, they also have a striking resemblance with n = 1 ER waves (Molinari et al., 2007). In fact, the QBWO over WNP has been interpreted as a modified ER wave (Chen and Sui, 2010). Our composite structure is also quite similar to that of the observed ER waves (Wheeler et al., 2000), except for the striking asymmetry about the equator and somewhat larger poleward movement. A distinguishing feature 215 of the QBWO over SWIO is that the strongest convection -or, most negative OLR anomaly -is located in the northeast sector of the cyclonic circulation. This negative OLR anomaly is likely due to both convergence between the gyres as well as horizontal rotational poleward advection of moist air out of the equatorial region. This too is reminiscent of observations of ER waves (Wheeler et al., 2000;Molinari et al., 2007) and has been noted in recent idealized moist shallow water simulations (Suhas and Sukhatme, 2020).

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To estimate the period and speed of propagation of the QBWO, we now construct time-latitude and time-longitude Hovmöller diagrams. Specifically, two panels in Figure 4 show the time-latitude diagrams of filtered OLR and zonal wind anomalies averaged over 40 • -70 • E, both depicting a southward phase speed of approximately 1.4 • /day. Similarly, the two panels in Figure 5 show the longitude-time diagrams of filtered OLR and meridional wind anomalies averaged over 5 • -25 • S. The OLR anomalies show that from Day −8 to 4 or so, there is a westward speed of approximately 3 • /day, but after that, this movement 225 ceases. This is in accord with the composite which suggests that from Day 3 to Day 6, southward propagation dominates over the westward motion. Consistent with this, the meridional wind anomalies averaged over the same area also show a westward speed of about 3 • /day or 4 m s −1 . The group velocity that can be estimated from 4 and 5 is quite clearly close to zero. The wavelength that can be estimated here also matches with our estimation discussed above. The time period from both these figures is also consistent, i.e., close to 18-20 days. Closer to the equator, Figure 6 shows the longitude-time diagram of filtered 230 zonal wind anomalies averaged over 0 • -10 • S. Here, the movement captured is slightly faster, in fact, westward propagation of approximately 3.3 • /day is evident. The wavelength also appears to be slightly larger than what can be seen from Figure   5. The apparent disagreement between the westward phase speeds and wavelengths from zonal and meridional winds of the same system seems paradoxical. But, in fact, this is quite similar to the properties of ER waves noted in different parts of the tropics (Molinari et al., 2007), and the difference is attributed to the changes in the background flows in equatorial and 235 off-equatorial regions. As seen in Figure 7, the low-level background winds have a cyclonic shear with westerly flow near the equator between 50 • E to almost 90 • E, and an easterly further poleward, creating a patch of strong cyclonic vorticity, with a monsoon trough-like character.
In all, our composites are quite similar to Northern Hemisphere counterparts such as those from the SCS or the WNP (Chen and Sui, 2010;Wang and Chen, 2017), where QBWOs are asymmetric about the equator, i.e., mostly confined in one hemisphere 240 (the summer hemisphere) and usually understood as modified ER waves. Indeed, ER waves observed by Molinari et al. (2007) also have a similar hemispheric asymmetry. As suggested in these studies, this shift from the theoretical symmetric structure (Matsuno, 1966), is likely due to the prevalent background flow. Further, in the boreal winter, PW is concentrated in the Southern Hemisphere which points to the possibility of moist coupling and growth south of the equator. The wavelength (around 6500-7500 km) and time-period (18-20 days) in our observations are comparable to the range of estimates for convectively coupled ER waves (Numaguti, 1995;Wheeler et al., 2000;Janicot et al., 2010). Kiladis and Wheeler (1995) also observed ER waves with similar wavelengths, but slightly smaller time-periods and faster phase speeds, though this might be an artefact of focusing on circulation features rather than strongly convectively coupled cases (Wheeler and Kiladis, 1999). These scales also match with observations of the westward propagating QBWO (Chatterjee and Goswami, 2004;Kikuchi and Wang, 2009;Chen and Sui, 2010). In fact, the observed wavelength and time-period lie well within the designated region for convectively 250 coupled ER waves (Wheeler and Kiladis, 1999;Wheeler et al., 2000;Roundy and Frank, 2004a). Naturally, the phase speed is also comparable to that of observed westward propagation of convectively coupled ER waves (Numaguti, 1995;Wheeler and Kiladis, 1999;Wheeler et al., 2000;Bessafi and Wheeler, 2006;Kiladis et al., 2009;Janicot et al., 2010) as well as westward propagating QBWOs (Chatterjee and Goswami, 2004;Chen and Sui, 2010). Quite remarkably, the length and time scales, as well as phase velocity observed here match with that of westward propagating equatorial modes in an idealized moist shallow 255 water system (Sukhatme, 2014). The movement of wave packets ( Figure 2) suggests a near-zero group velocity which also agrees with observations of ER waves (Wheeler and Kiladis, 1999;Wheeler et al., 2000;Molinari et al., 2007) and the boreal summer QBWO (Chen and Sui, 2010;Wang and Chen, 2017). For an equivalent depth range of 12-50 m (Wheeler and Kiladis, 1999), the theoretical n = 1 ER wave with a typical wavelength of 6000 km and a westward phase speed of 4-5.5 m s −1 and group velocity of 0.8-2.6 m s −1 , with no background flow. Here, the estimated phase velocity is in close agreement with 260 theory, though the group velocity is somewhat smaller. Of course, the QBWO in SWIO is subjected to a complex background flow with horizontal and vertical shear, and we don't expect the theoretical phase and group velocity estimates to exactly match real-world observations. Thus, much like its boreal summer counterparts, the properties and horizontal structure of the boreal winter QBWO bear a close relation with ER waves in the SWIO region. Indeed, observed ER waves in the SWIO (for example, Figure 13 in Bessafi and Wheeler, 2006) bear a close resemblance to our composite.

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Notably, these results are somewhat different than those presented by Fukutomi and Yasunari (2013) in their study of submonthly scale intraseasonal activity in the SWIO. They found meridionally elongated cyclonic and anti-cyclonic vortices and documented continuous northeast-southwest propagation, whereas we observe an initial southwest movement of zonally elongated gyres followed by predominantly southward propagation. Further, unlike our analysis, they found wavetrains to cross the equator. Though the estimated phase speed in their study is close to ours, they noted an eastward group velocity of 8 m s −1 , 270 which we clearly do not observe in our composite. These differences may be an artefact of using different temporal windows, as their analysis likely included both mixed Rossby-gravity and ER signals.

Vertical Structure
With a description of horizontal composites, we now examine the vertical structure of QBWO using data on 12 pressure levels that range from 1000 to 100 hPa. Specifically, vertical cross-sections of relative vorticity and vertical wind associated with 275 QBWO along the track line in Figure 3, from Day −9 to Day 6, are shown in Figure 8. A well-developed train of positive and negative vorticity anomalies can be seen on all days. Specifically, if we follow the negative vorticity anomaly in the lower troposphere, we can observe its evolution in time and space. On Day −9, when the negative anomaly centre in the lower troposphere is near 10 • S, the system has a barotropic structure, i.e., contours of the negative vorticity anomaly reach straight up to about 100 hPa from the surface, though, the anomaly extends slightly towards the southwest in the upper troposphere near 280 200 hPa. One can note, at this stage, the negative vorticity lobe is not associated with convection. By Day −6, this anomaly has barely moved but it has intensified, particularly up to about 400 hPa,and the barotropic shape (no change of sign of perturbation up to 100 hPa) remains, though we can see a more prominent southwest extension of the negative anomaly at the upper levels from about 300 hPa. By Day −3, the negative anomaly at lower levels has moved southwestward and expanded, and the system is no longer barotropic in structure. In fact, the anomaly extends up to 400 hPa and then changes the sign. This negative anomaly 285 tilts towards the southwest from about 400 hPa and resembles a first baroclinic mode. At this stage, the cyclonic vortex at the lower level is associated with strong convection as can be deduced from the OLR anomalies on Day −3 in Figure 3.
By Day 0, the system moves further southwestward, the negative vorticity anomaly strengthens in the lower and the middle troposphere and maintains its tilt and baroclinic structure. Now by Day 3, the lower troposphere negative anomaly centre continues its propagation and the area it covers expands up to 35 • S, which is the southernmost point of the track in Figure 3.  The panels in Figure 8 are arranged such that the snapshots in the upper and lower rows are 9 days apart; clearly, we see similar structures in the rows but of opposite signs, which is expected after approximately half-period of the QBWO. So, the 295 positive vorticity anomaly (red in Figure 8) goes through a similar life cycle as described in the previous two paragraphs for the negative anomaly. To summarize, the QBWO starts with an almost barotropic structure near the equator when it is not strongly coupled with moist convection. In its mature stage, when coupled with convection, it strengthens, changes progressively from an equivalent barotropic to a first baroclinic profile and tilts towards the southwest. Towards the end, convection dies down, the system becomes weak and comes back to a barotropic structure. These observations are in line with findings on ER waves 300 in different parts of the global tropics (Wheeler et al., 2000;Yang et al., 2007;Kiladis et al., 2009), where it is seen that convectively uncoupled/weakly coupled waves have a near barotropic structure, and convectively coupled waves have a more baroclinic structure.

Vorticity budget of the QBWO
We now analyse the propagation and dynamics of the QBWO by constructing a budget of the vorticity anomalies of the system.
The relevant equation reads (Wang and Chen, 2017), where, ζ = ( ∂v ∂x − ∂u ∂y ) and D = ( ∂u ∂x + ∂v ∂y ) are the relative vorticity and divergence, respectively. V = ui + vj is the horizontal wind, ∇ h = i( ∂ ∂x ) + j( ∂ ∂y ) is the horizontal gradient operator, f is Coriolis parameter and ω is the vertical velocity in pressure co-ordinates. Here, prime denotes a 14-30 day anomaly. T is given by [( ∂ω ∂y )( ∂u ∂p ) − ( ∂ω ∂x )( ∂v ∂p )] , which is the anomaly of the tilting term, [−(ζ + f )D] represents the anomaly of the stretching term, ∂ζ ∂t is the local tendency of the vorticity anomaly, 320 (−V.∇ h ζ) and (−ω ∂ζ ∂p ) represent anomalies of the horizontal and vertical advection of relative vorticity, respectively, and (−v ∂f ∂y ) is the anomaly due to the β effect. The last term, R , is the residual, which includes contributions from all processes not expressed explicitly in Equation 1.
We compute composite means of individual terms in this budget, i.e., we first compute the terms for each day, and then take the mean over all the cases included in the composite. For Figure 9, we adopt an Eulerian view and spatially average the The budget in Figure 9 shows that in the positive QBWO convection phase (associated with above-average convection, near Day 0 in the figure), relative vorticity anomalies (contours) are negative below 300 hPa and positive above that level. The negative QBWO phase (associated with below average convection) shows the opposite pattern. At these lower levels, negative vorticity anomalies begin to develop on Day −5, attain a maximum by Day −2 and decay by approximately Day 3 which is 335 in agreement with the lower level circulation described in Figure 3. After that, the cycle begins again and positive vorticity anomalies start to develop. The tilting and vertical advection terms (Figure 9 lower panel) are small (one order smaller than other terms) at the lower levels and large at upper levels. So, to understand the lower level vorticity dynamics, these two terms can be safely ignored.
The stretching term (Figure 9, third from left in the upper panel) is high in magnitude in the convective phase at both upper 340 and lower levels, of course with opposite signs. This is intuitive as this term is expected to be strongly influenced by local divergence. At lower levels, stretching is mostly concentrated below 850 hPa (as convergence is strongest near the surface), and is almost in phase with vorticity anomalies with a slight lag. This lag is consistent with the observation that convection peaks behind or northeast of the cyclonic circulation. Further, like the vorticity anomalies, stretching has the same sign up to 300 hPa. Essentially, the stretching term acts to maintain the low level vorticity anomalies after it reach a peak. We observe that 345 this tendency of the stretching term is somewhat negated by the horizontal advection vorticity anomaly (Figure 9, first from the left in the upper panel), i.e., advection helps in suppressing the low-level negative anomalies after it reach a peak. The β effect term (Figure 9, second from the left in the upper panel) leads the vorticity anomalies by about a quarter of a cycle, and also shows a similar tilt at upper levels (above 300 hPa). Hence, β contributes to the sign change of vorticity anomalies in the next cycle and is the most likely candidate responsible for its propagation. In all, the view presented by Figure 9, which is an 350 Eulerian one, where, by averaging over a specified box, we see the vorticity anomalies as it pass by a fixed observer, and its successive crests and troughs are led by those of the β effect term. Further, the vorticity anomalies are fed and damped at lower levels by the stretching and horizontal advection terms, respectively. Whereas, at upper levels, the terms that mostly cancel each other are the vertical advection and titling, with the former and latter responsible for decay and growth, respectively.
To understand the dynamics at the lower levels in more detail and from a spatial perspective, we present the composite mean of 355 various terms averaged over 850 to 600 hPa to represent the lower level circulation (Figures 10-12). Note that, at near-surface levels the residual term can be quite large in reanalysis (Boos et al., 2015). In fact, Boos et al. (2015) found that the influence  of this term lessens by about 700 hPa, guided by that observation, we average over 850 hPa to 600 hPa values to represent the lower level circulation. Further, as seen in Figure 9, the major terms of the equation have little vertical variation in these pressure levels.

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In Figure 10, on Day −3, we see the Eulerian tendency of relative vorticity of the QBWO has a minimum to the southwest of the cyclonic vortex centre at 850 hPa (marked by a black dot), and maxima in the northeast of the centre. This is consistent with the fact that the cyclonic vortex is moving to the southwest. The only individual term that matches this pattern, that is, has a dipole structure with a minimum in the southwest and maximum in the northeast is the β term, though its extent is much larger spatially than the vorticity tendency. The horizontal advection term is not as strong and has more of a fine scale structure. The 365 stretching term has strong maximum southeast of Madagascar, and a weaker minimum to the northeast. This strong positive stretching term is likely a direct effect of the divergence associated with the anticyclonic circulation that is situated in the same location (Figure 3). The combination of the β and the stretching captures the Eulerian vorticity tendency to some extent, especially to the southwest of the vorticity centre. In fact,the stretching southeast of Madagascar limits the extent of the β by cancelling it out in that region. When we add the horizontal advection term with the aforementioned combination, in spite of 370 some mismatch due to the neglected smaller terms and the residual, the sum is a reasonable approximation to the Eulerian vorticity tendency pattern.
For Day 0 (Figure 11), we see a similar pattern. Now, the vortex centre and associated dipole pattern of the vorticity tendency shift southwest as compared to Day −3. Once again, only the β term has a similar dipole pattern as the vorticity tendency.
In this occasion, the stretching term is strongly negative to the north and east of the vorticity centre, i.e. , to the eastern side 375 of Madagascar. This is expected as convergence and convection are strongest in that region. This limits the southward extent of the positive β term on the eastern side of the centre, and helps the vorticity tendency take the observed shape. Horizontal advection is again comparatively scattered through the domain. The combination of the β,the stretching and the horizontal advection do not approximate the vorticity tendency as well as on Day −3. Though, the rough pattern is captured, with the NE-SW oriented dipole structure about the vortex centre.
its inclusion with β and stretching helps to capture the overall vorticity tendency pattern.
Overall, from Figures 10-12, we see that the most important factors in defining the shape of vorticity tendency are the β and the stretching term. While, at the outset, the β term resembles the tendency, stretching limits its southward extent, especially on the eastern side of Madagascar, where the convergence/divergence associated with this QBWO is noted to be strongest ( Figure   3). This gives the tendency a more east-west orientation. In other words, the southward movement of this mode would be much 390 faster without strong stretching; so, it can be said that the convectively coupled nature of this mode that gives rise to the strong stretching term essentially slows down the southward movement of the QBWO mode.The horizontal advection, which is not as dominant as these two aforementioned terms mostly plays a damping role and its inclusion leads to a better match with the vorticity tendency. Figure 13 adopts a Lagrangian perspective and depicts the temporal evolution of composite mean of the dominant terms in the 395 vorticity budget in the lower troposphere (averaged over 850 to 600 hPa) following the track of the system shown in Figure   3. On Day −9, a negative vorticity anomaly is visible just south of the equator. Consistent with the Hovmöller diagrams in Figures 4-6, over the course of the next week, the anomaly propagates in a southwest direction. This is followed by a positive vorticity anomaly that appears in a similar location and follows a similar track. As is clear in Figure 13, horizontal advection is not particularly strong and is scattered inside the vorticity anomaly contours. Though the stretching term is somewhat large, 400 particularly slightly away from the equator, as expected from our discussion of Figure 10-12, it is more or less in phase with the vorticity anomaly, and so it can't be responsible for the propagation of the vorticity anomaly (Wang and Chen, 2017), rather it mainly helps in local enhancement of the vorticity anomaly. The only term that is coherent and leads the vorticity anomaly is β; in fact, this leads the vorticity anomaly by approximately 4-5 days or about a quarter of a cycle. Interestingly , though there is a clear lead-lag relation between the β term and vorticity anomalies throughout the track, the tendency of β term suggests that 405 it is slightly faster than the movement of vorticity anomalies along the track, especially away from the equator. This matches with our observations in Figures 10-12, discussed above. Thus, overall, this lower level along-track perspective is consistent with the vertical structure of the system in Figure 9, and reinforces the role of β in the propagation of the QBWO. Once again, these results are consistent with findings regarding the QBWO over the SCS in the boreal summer (Wang and Chen, 2017), but contradict the claim made by Fukutomi and Yasunari (2013) who probed intraseasonal disturbances moving over the SWIO.

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They attributed southward movement mainly to the horizontal advection of transient eddy vorticity by the northerly mean flow, but here, in our analysis, the role of horizontal eddy advection is not prominent and the northerly mean flow is absent in the region where the southward movement of the QBWO is most apparent.

A QBWO case study and cyclogenesis
We now explore a particular QBWO episode from the boreal winter season of 2008-09; the aim is to elucidate the propagation 415 and evolution of this system and its connection with the genesis and track of TCs. As per convention, the location of cyclogenesis is defined by the coordinates where a named TC is estimated to attain tropical depression status (Bessafi and Wheeler, 2006). In the following, we show the position of 3 TCs from its depression stage to the point up to which the system retains at least Tropical Storm status as defined by JTWC. Note that we have shown the location of TCs at 0000UTC for a given day. Till now we have focused on composites of the QBWO and it is instructive to examine particular cases for a look at the 420 details of the systems' formation and propagation. In this context, Figure 14 shows the evolution of the QBWO wavepacket in which consecutive high and low vortices are generated near the equator, and then continue their journey to the southwest in the Southern Hemisphere. The features in Figure 14 are in excellent agreement with those identified in the composite of the QBWO (Figure 3). Note that this particular sequence of disturbances lasted approximately 2.5 months and Figure 14 shows a specific period from late January to early February of 2009, covering slightly more than one complete cycle of a QBWO. of above-average convection that covered Madagascar, and below-average convection is associated with the high-pressure area to the northeast. Inside the low-pressure zone, two nascent tropical depressions can be observed, marked by yellow and orange 430 dots, which eventually became tropical storm Fanele (yellow dot) and Eric (orange dot), respectively. The red contours in this plot are the zone of strongest negative (cyclonic in Southern Hemisphere) vorticity, and clearly, both these storms are within regions of largest vorticity anomalies associated with the QBWO. By January 21, the cyclonic circulation near Madagascar weakened, the anticyclonic vortex with positive OLR anomalies is displaced to the southwest, and to the north we see hints of a new QBWO low forming just south of the equator (between 60 • -90 • E), with weak convection and anomalous westerly winds.

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In this period, Fanele moved very slowly towards the east, Eric moved southward and still remained within the zone of QBWO convection. After 3 days, by January 24, the old cyclonic circulation and the TCs within it disappeared, the anticyclonic lobe moved west-southwestward towards northern Madagascar, and the evidence of a new low with strengthened and expanding negative OLR anomalies and strengthened westerly wind anomalies can be observed just south of the equator.The anomalous westerly wind also extends above the equator, and one can see a hint of anomalous convection associated with it, albeit weaker 440 than that of the south of the equator. By January 27, the high intensified and moved further southwest engulfing almost all of Madagascar with a large and well-formed anticyclonic vortex and associated positive OLR anomalies. Simultaneously, the newly formed low that emerged near the equator continued to intensify as it moves westward. It is worth noting that the linear shallow water solution for ER waves shows convergence one quarter wavelength east of the low (Matsuno, 1966), this pattern is reflected to some extent with strong negative OLR anomalies east of the low; a feature that has also been observed in ER 445 waves (Molinari et al., 2007) and the boreal summer QBWO (Chen and Sui, 2010). The above-average convection over the equator is still visible, though it remained almost stationary, and then decayed in the next few days.
The dominant pattern in the south of the equator described above repeats through the following days shown in Figure 14, though of course with the sense of anomalies reversed in the next cycle of the oscillation. More strikingly, on February 2, another tropical depression (eventually TC Gael) can be seen inside the low near 15 • S, 70 • E, i.e., within the strong negative OLR 450 anomalies in the northeast sector of the low-pressure lobe of the QBWO. Like Fanele and Eric, this system also formed within the region of strongest vorticity anomalies. By February 5, the low intensified further, expanded in scale with a well-defined cyclonic vortex, moved further southwestward and convection associated with it covered most parts of Madagascar and made inroads into southeast Africa. Concomitantly, the depression intensified into a TC (named Gael) and moved southwestward.
As the QBWO wavepacket evolved, TC Gael moved southwards inside its circulation gyre towards the coast of Madagascar 455 (February 8). Finally, by February 11, i.e., in the last subplot of Figure 14, the cyclonic anomaly near Madagascar almost disappeared and TC Gael moved towards the southeast and transitioned to an extratropical disturbance (not shown). In greater detail, Figure 15 shows unfiltered OLR and winds at 850 hPa at 0000 UTC of February 5 and February 8, and contours of 14-30 days filtered OLR anomalies to showcase the movement of TC Gael under the influence of QBWO. In fact, on February 5, almost the entire TC with its strongest winds can be seen within the outer contour of 14-30 days filtered OLR, and the core 460 is inside the inner contour of the negative QBWO lobe. On February 8, negative OLR anomalies associated with this low are weaker, still, most of the TC is contained inside the outer contour of these anomalies, with the centre still inside the inner contour.
In addition to these three TCs, as seen in Figure 16, other depressions that matured into TCs were also formed within this QBWO wavetrain. Specifically, TCs Cinda, Dongo, Hina and Izilda can be seen in the negative OLR lobes of the QBWO 465 wavetrain on December 15, January 9, February 21 and March 24 respectively 1 (marked with red, orange, yellow and gold color dots, respectively, in Figure 16). These four cyclones were born as depressions inside large anomalous vorticity zones associated with the QBWO lows; this is made clear in Figure 16 where regions of strongest cyclonic vorticity are marked with red contours. Together, all seven depressions considered here originated inside negative OLR anomalies of less than −10W/m 2 , and in regions of strong vorticity, thus satisfying most of the criteria used to assess whether a storm is associated 470 with ER activity on a quasi-biweekly timescale (Molinari et al., 2007) 2 . Further, we also note that all seven cyclogenesis events described here happened inside the region of large background cyclonic vorticity (Figure 7). Even though this examination was of a particular winter season where QBWO activity was exceptionally long-lasting, we have observed the birth of depressions and their maturity into TCs inside the QBWO wavetrain in numerous years. For example, one of the most intense TCs in the recorded history in this basin, Cyclone Gafilo in 2004, was also born and moved under the influence of a QBWO wavetrain. As 475 seen in the composite in Figure 3 and 7, convectively coupled QBWO lows become strongest in regions of high background vorticity, thus superposition of the background cyclonic circulation and QBWO cyclonic circulation possibly makes the area very conducive for cyclogenesis. It is worth mentioning that there are also cases where depressions that matured into cyclones were born outside the QBWO envelope, but eventually their movement was influenced by the environmental quasi-biweekly circulation anomalies.
Additionally, OLR anomalies associated with waves serve as pre-existing convective disturbances from which TCs can be born, and the mean upward motion associated with moist convection can further aid cyclogenesis (Frank and Roundy, 2006;485 Bessafi and Wheeler, 2006). In the SWIO, the influence of gravest ER wave modes on cyclonic activity has been noted, and the modulation of cyclogenesis is most readily attributable to large variations in low-level, off-equatorial vorticity and OLR by these ER waves (Bessafi and Wheeler, 2006). The previous sections emphasized similarities between the QBWO 1 Here, we have shown the plots of the days when the tropical depressions are first detected at 0000UTC. 2 If a TC is not born by 0000UTC of the days shown here, rather it starts as a depression at an earlier time, we confirm it's genesis location still satisfies the criteria mentioned above. This also applies for the TCs shown in the case study plot of Figure 14.  and the gravest ER wave which is known to influence cyclogenesis in SWIO (Bessafi and Wheeler, 2006). Indeed, much like the sequence of events depicted for the seven TCs within the QBWO in 2008-09, Bessafi and Wheeler (2006) found that 490 cyclogenesis that happens during off-equatorial ER wave activity occurs inside the cyclonic vorticity and convective anomalies.
Further, they also noted that, once born, systems move systematically westward with the ER wave (indeed, TCs Gael, Eric, Cinda and Hina initially moved westward). Thus, much like the connection of QBWO to cyclogenesis in other tropical basins (Ling et al., 2016;Zhao et al., 2016), here too, quasi-biweekly variability clearly influences the birth and evolution of TCs.

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In this study, we have identified a convectively coupled quasi-biweekly signal in the SWIO during the boreal winter. At the outset, we note that regular quasi-biweekly oscillations are observed almost every year in this region, usually during the second half of the winter season. In fact, this intraseasonal variability in the SWIO is contained within an envelope of high precipitable water. A composite drawn from 10 years of data shows that the QBWO exhibits distinct propagation characteristics in filtered OLR and low-level circulation. Specifically, the system starts near the equator, west of Sumatra, and then propagates southwest   The plots are shown for the day when the tropical depression was first detected at 0000UTC, as defined by the JTWC. Red contours are of 14-30 day vorticity anomalies of the respective days. Only negative (cyclonic in the Southern Hemisphere) anomalies are contoured, the value of the outer contour is −4 × 10 −6 s −1 , and the inner contour is −8 × 10 −6 s −1 .
The vertical structure of the QBWO shows a nearly barotropic structure when it is initially observed near the equator, a first baroclinic mode profile emerges as the system couples with moist convection and slowly moves away from the equator, and finally, by about 35 • S, an equivalent barotropic structure re-emerges when the oscillation weakens at the end of its life-cycle.
Further, near the equator, vertical velocity and vorticity extrema are not aligned. In fact, the maximum (minimum) vertical 510 pressure velocity is located to the northeast of vorticity maximum (minimum), whereas away from the equator, these two are aligned. With regard to the dynamics at play, a vorticity budget analysis showed that the β effect is the main contributor in the southwestward propagation of QBWO vorticity anomalies. The roles of stretching and horizontal advection are also important to determine the spatial structure of the vorticity anomalies in the lower troposphere. Further, stretching, due to convergence/divergence slows down the southward propagation speed of the QBWO. Thus, we see the physical manifestation 515 of moist convective coupling in reducing the speed of this mode. Further, this analysis allows us to hypothesize that differential planetary rotation, coupling with moisture and horizontal rotational advection are the minimal ingredients required for the QBWO.
These features, i.e., the wavenumber, phase speed, and time-period fall within the range reported for convectively coupled gravest ER waves (Wheeler and Kiladis, 1999;Wheeler et al., 2000;Kiladis et al., 2009;Janicot et al., 2010). Moreover, the 520 position of strongest convection is also similar to observations of ER waves (Wheeler et al., 2000;Molinari et al., 2007), and agrees with simplified moist shallow water simulations (Suhas and Sukhatme, 2020). The baroclinic nature of the QBWO while strongly coupled with convection, and near-barotropic structure while loosely coupled/uncoupled with convection are also observed in ER waves (Wheeler et al., 2000;Yang et al., 2007;Kiladis et al., 2009). While this agreement with ER waves is encouraging, certain features need to be kept in mind. Quite conspicuously, the QBWO is restricted to the Southern

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Hemisphere in this season. Though idealized ER waves are symmetric about the equator (Matsuno, 1966), and studies have observed symmetric ER waves (Kiladis and Wheeler, 1995;Chatterjee and Goswami, 2004), this kind of asymmetric wave structure which is purely dominated by one hemispheric component is anticipated and documented in different background flows (Wheeler et al., 2000;Molinari et al., 2007;Chen and Sui, 2010). With regard to propagation, the QBWO moves westward and poleward, whereas ER waves on a background state of no flow are equatorially trapped. In reality, Rossby waves triggered 530 in the tropics can leave the equatorial wave-guide under the influence of non-zero zonal mean flows (Lau and Lim, 1984;Sardeshmukh and Hoskins, 1988;Zhang and Webster, 1989;Jin and Hoskins, 1995;Molinari et al., 2007;Monteiro et al., 2014). In fact, this poleward motion is consistent with the propagation of the boreal summer QBWO (Chatterjee and Goswami, 2004; Kikuchi and Wang, 2009;Chen and Sui, 2010;Wang and Chen, 2017). Taken together, the structure, features and dynamics of the QBWO in the boreal winter has many similarities with its Northern Hemisphere counterparts, both of which 535 appear to be consistent with convectively coupled ER waves that are modified by suitable background states.
Though the principal features of the QBWO match with convectively coupled ER waves, the genesis of these oscillations requires further study. Convective feedback mediated by boundary layer convergence does take a step in this direction (Chatterjee and Goswami, 2004), and idealized models also suggest that easterly vertical shear traps the ER wave in the lower troposphere and helps growth through diabatic heating Xie and Wang, 1996). Further, when vertical shear is asym-540 metric about the equator, the unstable ER wave is constrained to the hemisphere where the easterly shear is prominent Xie and Wang, 1996). Such a vertical shear is present between 0 • -10 • S in the SWIO where the QBWO starts to grow. In addition to the winds and shear, the concentration of PW in the Southern Hemisphere in the boreal winter possibly helps to facilitate the coupling with moisture south of the equator in this season. Indeed, building on the interaction of moisture gradients with waves (Sobel et al., 2001;Sukhatme, 2014;Monteiro and Sukhatme, 2016), recent work has uncovered newer 545 routes of genesis such as moisture-vortex instability (Adames and Ming, 2018;Adames, 2021) or enhancement of barotropic processes Boos, 2019, 2021) that can play a role in the growth of large-scale moist systems. Thus, a holistic theory for the QBWO, will, in addition to the minimal ingredients listed above, possibly include interaction with seasonal background shear and moisture gradients. It is worth noting that general circulation models still have difficulties in producing an accurate QBWO (Jia and Yang, 2013;Wang and Zhang, 2019). An understanding of the basic mechanisms involved in the QBWO 550 will help diagnose the issues that plague these efforts, and will contribute to enhanced intraseasonal prediction capabilities, especially in the context of Madagascar and parts of south-east Africa, where the boreal QBWO has significant influence. Finally, convergence, moist coupling and large vorticity anomalies of the QBWO generate a favourable environment for the birth of tropical depressions, some of which go on to intensify in cyclones. Specifically, using the case study of 2008-09 winter, we showed the repeated genesis of depressions inside QBWO lows, preferentially in the NE sector.We have shown seven of 555 these systems that evolved into TCs. In particular, the influence of the QBWO environment on the birth and propagation of TC Fanele, Eric and Gael were examined in detail. Indeed, the convective environment provided by the QBWO in conjunction with the vorticity of the background flow appears to provide the most suitable conditions for cyclogenesis. The connection between ER waves and TC genesis is well established (Frank and Roundy, 2006;Bessafi and Wheeler, 2006;Molinari et al., 2007;Schreck et al., 2012), and the interpretation of the QBWO as a suitably modified grave ER mode adds merit to the 560 possibility of cyclones preferentially forming within the zone of strong cyclonic vorticity anomaly and convection associated with the Rossby gyres. In the SWIO, Bessafi and Wheeler (2006) have reported instances of cyclogenesis in both east and west of the ER low, but the most probable region is again northeastward of the centre of the ER low which is in agreement with our observation of cyclogenesis in the QBWO. Though we focused on one season, it is important to note that the genesis of depressions and their conversion to TCs within the QBWO envelope was observed in other seasons too. In fact, the symmetry 565 imposed on ER wave detection (Bessafi and Wheeler, 2006) can be relaxed due to the hemispheric preference of the QBWO, and this can potentially lead to the identification of more systems spawned in these moist convective envelopes, thus enhancing the predictability of a larger number of depressions and cyclones in the SWIO.
Code and data availability. All data used in this study is publicly available. NCEP-NCAR reanalysis can be accessed from https://psl.noaa.