# Northward Propagating versus Non-propagating Boreal Summer Intraseasonal
Oscillations

Sambrita Ghatak Corresponding author: Sambrita Ghatak<EMAIL_ADDRESS>Centre for Atmospheric and Oceanic Sciences, Indian Institute of Science,
Bangalore, India.  Divecha Centre for Climate Change, Indian Institute of
Science, Bangalore, India.  These authors contributed equally to this work.
Jai Sukhatme  Centre for Atmospheric and Oceanic Sciences, Indian Institute of
Science, Bangalore, India.  Divecha Centre for Climate Change, Indian
Institute of Science, Bangalore, India.  These authors contributed equally to
this work.

###### Abstract

The Boreal Summer Intraseasonal Oscillation (BSISO) is a pronounced mode of
tropical intraseasonal convective variability during the boreal summer. One of
the most prominent features of the BSISO is the northward movement of
convection in the South Asian monsoon region. Using long-term observational
and reanalysis data, we identify two types of BSISO events, one which
propagates northward over South Asia from the equatorial Indian Ocean, and the
other which doesn’t. By investigating the difference between these two types
of events, we identify the critical mechanisms involved in northward
propagation.

A moisture budget reveals that for propagating cases when organized convection
first appears over the equatorial Indian Ocean, easterlies on the northern
flank of the Rossby wave response to enhanced convection (cyclonic) as well as
those on the southern flank of the Rossby wave response (anticyclonic) to the
suppressed convection further north act on the climatological moisture
distribution, and rapidly moisten the atmosphere over the southern Arabian
Sea. This results in the characteristic northwest-southeast-oriented
convection observed in the BSISO. Now, as this tilted belt of enhanced
convection is present south of the previous cycle of suppressed convection
associated with subsidence, in the presence of background easterly vertical
shear of the monsoon winds, a latitudinally tilted vortex tilting term is
generated due to the meridional gradient in vertical velocity. The generation
of positive vorticity anomalies over the Arabian Sea more than over the Bay of
Bengal, leads to a tilted gyre north of the convective anomaly. As a result,
anomalous winds over the northern Indian landmass, particularly north of 20N
become south-easterly. These winds tap into the north-westward moisture
gradient that is present over much of the northern Indian landmass and help
move the convection further north over India. Moreover, the south-westerly
background monsoon winds advect anomalous moisture, thus initiating convection
over the Bay of Bengal.

For non-propagating cases, though a well-formed Rossby gyre results as a
response to the nascent convection in the equatorial Indian Ocean, easterlies
over the Arabian Sea are much weaker and are unable to moisten the atmosphere
sufficiently to initiate strong convection over the southern Arabian Sea. In
the absence of strong vertical velocity due to a lack of convection, the
meridional gradient of vertical velocity is weak, and the background vertical
shear does not generate sufficient tilting over the northern Arabian Sea. In
all, the convective wind response stalls, and the large-scale convection does
not propagate north of 15N. Taken together, this work shows that the northward
propagating BSISO over South Asia is a moisture mode acting under the
influence of background vertical shear, where vortex tilting as well as
horizontal advection work hand in hand, and moistening over the Arabian Sea
due to the strong easterly wind anomalies acting on the mean moisture gradient
is critical for the BSISO to propagate over the Indian landmass.

##  1 Introduction

Intraseasonal oscillations (ISOs) in the tropical atmosphere exhibit
pronounced seasonality (Adames et al.,, 2016; Jiang et al.,, 2018). While the
Madden Julian Oscillation (MJO) is the dominant ISO signal during boreal
winter, the Boreal Summer Intraseasonal Oscillation (BSISO) is the most
significant intraseasonal signal during northern hemisphere summer,
particularly in the Indo-pacific sector (Jiang et al.,, 2018; Chen and Wang,,
2021). Like MJO in boreal winter, the BSISO is thought to be one of the most
important sources of sub-seasonal variability and is known to influence
various weather systems on different scales (Chen and Wang,, 2021). Though
both the MJO and BSISO most often develop in the Indian Ocean and have similar
timescales (Madden and Julian,, 1971, 1972), both have a time period within
30-60 days, they differ markedly in their spatial pattern. While MJO is
largely symmetric about the equator and predominantly characterized by
equatorial eastward propagation, the spatial structure and propagation
characteristics of BSISO are more complicated (Chen and Wang,, 2021; Wang and
Sobel,, 2022). Similar to MJO, the BSISO also has an equatorial eastward
moving component (though much weaker) that moves from the Indian Ocean to the
western Pacific Ocean, but unlike MJO, the most prominent feature of BSISO is
its northward propagation from the equatorial Indian Ocean over South Asian
Monsoon region, and northwestward propagation from the equator over western
Pacific (Wang and Sobel,, 2022). Traditionally, the MJO and BSISO are seen as
separate low-frequency ISO modes with similar time scales, the conceptual
boundary between these two is not very clear (Wang and Sobel,, 2022), and a
few recent studies don’t see BSISO and MJO as separate phenomena (Jiang et
al.,, 2018; Wang and Sobel,, 2022). These studies treat BSISO as a “northern
summer incarnation of the MJO” (Wang and Sobel,, 2022). Thus, along with MJO,
understanding BSISO can also be thought of as one of the fundamental questions
in tropical atmospheric dynamics.

The BSISO has a profound influence on global weather systems and extremes,
such as floods and droughts (Mooley and Parthasarathy,, 1983), tropical
cyclones (Kikuchi and Wang,, 2010), monsoon low-pressure systems (Goswami et
al.,, 2003). Particularly in South Asia, the BSISO heavily impacts the active
and break cycles of the Indian monsoon (Pillai and Sahai,, 2014). By impacting
monsoon onset, active-break phases, low-pressure systems, and depressions, it
dictates the overall pattern of monsoon rainfall (Goswami and Xavier,, 2005).
As South Asia is heavily dependent on monsoon rains, and this region also
faces a myriad of disasters during the rainy season, understanding and
successfully predicting BSISO is of great social and economic concern and
remains a significant challenge (Neena et al.,, 2017). Because of its impact,
there have been many studies in the last few decades to understand the BSISO,
including theoretical, modeling, and observational perspectives. While
progress has been made, the system remains elusive, and particularly the
mechanism behind its striking northward movement has not been clearly
understood yet (Wang and Sobel,, 2022).

Over the South Asian Monsoon Region (SAMR), the northward propagating BSISO
was first observed by Yasunari, (1979) and Sikka and Gadgil, (1980). Broadly,
there are two schools of theories based on simplified models that attempt to
produce northward propagating equatorial modes (Jiang et al.,, 2018; Wang and
Li,, 2020). One avenue is to understand the BSISO as a modified equatorial
Rossby wave that interacts with the monsoonal background flow (Wang and Li,,
2020). There are variations within this school of thought, but the basic
understanding of northward propagation of convection is via moisture
convergence in the boundary layer (Jiang et al.,, 2004; Bellon and Sobel,,
2008). On the other hand, recently, based on the “moisture mode” theory (Sobel
et al.,, 2001; Sobel and Maloney,, 2013; Sukhatme,, 2014), it has been shown
that prognostic moisture is essential to produce northward propagating modes,
and the perturbation winds of Rossby response act on the mean gradient of
moisture to give rise to northward movement (Adames et al.,, 2016; Jiang et
al.,, 2018; Chen and Wang,, 2021). While successful to some extent, these
theories come with their own set of caveats when it comes to capturing the
full set of features associated with the northward propagation of the BSISO.

In this paper, inspired by the work on MJO (Kim et al.,, 2014), we have
identified two types of BSISO events, one where the convection moves northward
to South Asia from the Equatorial Indian Ocean (EIO), and one where convection
does not propagate northward in spite of a strong start at the EIO. We
investigate the differences between the propagation mechanisms of these two
categories and identify the critical mechanisms behind the northward
propagation. Specifically, we employ a “moisture mode” framework, where
moisture dictates the convection, as well as a vorticity budget analysis to
understand the coupling with circulation.

##  2 Data and Methodology

Daily data from the ERA5 reanalysis (Hersbach et al.,, 2020) project serve as
the main data set for this study. Specifically, we have used 25 years of
horizontal winds, vertical velocity, and specific humidity data at 17 pressure
levels (1000 to 200 hPa) with an interval of 50 hPa. The horizontal resolution
of the data used in calculations is 2.5∘. Our analysis spans the boreal
summer, i.e., May through October (MJJASO) from 1985 to 2009. 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 and moisture
budgets are computed using Windspharm package (Dawson,, 2016). Daily, 2.5∘
horizontal resolution 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).

To isolate the BSISO signal, we used a filter with a 25-80 day band, following
Lawrence and Webster, (2002). As there is a prominent 10-20 day mode in the
same region(Chatterjee and Goswami,, 2004), we use a lower cutoff greater than
20 days, though slightly changing the filter cutoff doesn’t affect our
results. We use the Lanczos band-pass filtering method (Duchon,, 1979), and
prior to filtering, the annual cycle of the time series in question is removed
by subtracting the mean and the first three Fourier harmonics. This annual
cycle has been called the background signal in this paper.

To distinguish between propagating and non-propagating BSISO events, we used
two reference boxes, one over EIO (70∘-90∘E, 0∘-5∘N), and another over Indian
landmass (70∘-90∘E, 17.5∘-22.5∘N). The standard deviation of box-averaged OLR
in the EIO is $\sim$ 18 W m-2 and over the land is $\sim$ 12 W m-2. We define
a BSISO event to be propagating if the lowest value of box-averaged 25-80 day
filtered OLR anomaly is below -18 W m-2 in the EIO box, and after attaining
the lowest value in the EIO, it attains its lowest value over the land box
within next 20 days. The lowest value in the land box must be below -13.5 W
m-2, which is substantially lower than one standard deviation of this region,
and three-forth of the standard deviation of the EIO box. These criteria allow
us to isolate cases that propagate northward with a substantially strong
convective signal. The time interval between the EIO box minima to land box
minima for all of our propagating cases is 10-20 days. Using these criteria,
we obtain a total of 25 propagating cases from 25 years. Note that, Day 0 is
defined to be when the box-averaged OLR anomaly attains a minima in the EIO.

Similarly, to isolate non-propagating events, we use the same criteria over
the EIO box, but constrain the lowest value in the land box to be above -6 W
m-2, i.e., one-third of the standard deviation of the EIO box, and half of the
standard deviation of the land box. Thus, we are able to isolate cases that
started with almost an equal strength in the EIO but couldn’t propagate into
the Indian land region with substantial convective signal. This resulted in 14
such cases from 25 years of data. Our criteria are quite strict for isolating
propagating and non-propagating cases, but they identify very distinct cases,
which is helpful for comparing their propagation characteristics. We confirm
that the results are insensitive to slight changes in the box size, location,
and threshold values.

After isolating the strong propagating and non-propagating cases, we construct
composites. To understand the moist processes associated with the movement of
convection, and the evolution of circulation, we perform a moisture and
vorticity budget analysis, respectively. The terms in the budget are
calculated first from the individual cases and then averaged to make the
composites. Detailed descriptions of budgets are given in their respective
sections. For all the constructed composites, we have performed significance
testing, and we have only shown signals that are statistically significant
signal at a 95% confidence level.

##  3 Horizontal Structure of the two types of BSISO events

In this section, we present the horizontal composite characteristics of the
propagating and non-propagating BSISO events. We begin with the propagating
composite which is shown in Figure 1; specifically, we show OLR and 850 hPa
horizontal wind anomalies with an interval of four days. On Day -12, we see a
pair of anticyclonic gyres, one in each hemisphere. These two gyres are not
symmetric, the southern one is more zonally oriented, while the Northern
hemisphere anticyclonic gyre has a clear NW-SE tilt. The OLR anomaly
associated with the circulation is positive (indicating suppressed convection)
and it also has a similar NW-SE tilt. The strongest OLR anomaly is seen over
the Equatorial Indian Ocean (EIO), particularly to the eastern side, and over
the Arabian Sea (AS). The signals visible in our domain of interest can be
understood as a pair of Rossby gyres that straddle the equator to the west of
anomalous convective activity, i.e., they are part of a Gill-type response
(Jiang et al.,, 2018; Chen and Wang,, 2021). These are associated with
easterly wind anomalies along the equator, and westerly wind anomalies away
from the equator. To the east, there exists a Kelvin wave response (not
shown), but here we focus only on the Rossby gyre as our interest is in the
northward propagating BSISO over India, and this region is dominated by the
Rossby part of the circulation. An immediate question that one can ask is, why
the Northern Hemisphere Rossby response is stronger and tilted from NW to SE?
This will turn out to be a central question as we proceed in this paper, and
it will be answered later, particularly in the vorticity budget analysis.

On Day -8 (Figure 1), the Northern hemisphere anticyclonic gyre becomes
compact, and moves slightly northward, while in the EIO, strong easterlies
continue to prevail. The positive OLR anomalies move further North and engulf
the entire AS, the Bay of Bengal (BOB), and a significant part of the Indian
landmass. While over the EIO, a hint of enhanced convection (negative OLR
anomaly) appears. The enhanced convection gets stronger by Day -4, and it
crosses 10N into the AS, simultaneously, the existing positive OLR anomalies
in the AS recede. Interestingly, over the BOB, the positive anomalies
(suppressed convection) don’t recede as much, thus the area of suppressed
convection gets tilted. In the wind anomalies, we see a new cyclonic Rossby-
type gyre in the EIO, while the anticyclonic circulation continues over the
land region, thus, between 5-20N, we notice very strong anomalous easterlies.
On Day 0, the Rossby gyre in the EIO gets stronger and very well-marked with
the strengthened convection anomaly; further, a weak Rossby-type circulation
is also visible south of the equator, resulting in strong easterlies between
10-20N, and westerlies near the equator. This can again be understood as a
modified Gill-type response, but now with enhanced convective heating.
Interestingly, similar to Day -4, convection moves north into central AS, but
it doesn’t enter the Bay Bengal. Thus, the convection that started with a
zonally oriented structure in the EIO on Day -8, progresses into the AS by Day
0, and a clear NW-SE tilted structure gets established.

In Figure 1, on Day 4, convection enters deep into the northern AS, and it
also moves slightly north over the BOB. The most interesting feature of this
day is in the circulation pattern, the cyclonic Rossby gyre that formed over
the EIO in response to the enhanced convection now gets abruptly tilted from
NW to SE and moves north. In other words, the cyclonic vortex quickly “jumps”
north into the AS between Day 0 and Day 4, but in contrast, it moves slowly in
the BOB sector. On Day 8, anomalous convection appears over peninsular India,
and also over the north-west of India. The tilted structure of the vortex
becomes more prominent and moves further north, and the south-easterlies over
the land become more prominent and stronger. Over the EIO, we now see strong
westerlies associated with this cyclonic vortex, and the convection dies down,
so essentially, the whole convective belt has moved north from the EIO. On Day
12, anomalous convection covers almost the entire Indian landmass. In the EIO,
the next cycle of the BSISO starts as positive OLR anomalies appear over the
region. Indeed, this leads to the period of this mode as being approximately
40 days.

Shifting our focus to the composite of the non-propagating cases (Figure 2) —
on Day -12, as in Figure 1, we see an anticyclonic Rossby gyre associated with
suppressed convection north of the equator and its southern hemisphere
counterpart. But, note that the southern gyre is rather weak, indeed,
suppressed convection is much weaker compared to the propagating cases, and it
is limited to 20N. On Day -4, the area of enhanced convection gets bigger and
stronger, and a small Rossby gyre comes into being as a response to this
heating. Interestingly, the area of suppressed convection north of the nascent
enhanced convection doesn’t weaken and remains almost stationary. On Day 0,
convection strengthens, and the Rossby gyre is more prominent with westerlies
over the EIO and easterlies between 10-20N. The difference with the Rossby
gyre of propagating cases is in their extent; specifically, the easterlies
associated with the gyre of the propagating composite extended west of 70E,
while for the non-propagating cases, it is mostly confined to the east of 70E.
On Day 4, enhanced convection remains stationary (though slightly weaker),
along with the Rossby gyre, while the area of suppressed convection gets much
weaker. In stark to the propagating cases, in spite of having a strong
convective signal in the EIO, the BSISO doesn’t propagate northward but starts
to weaken. Subsequently, the convective signal disappears, and a new area of
suppressed convection appears over the EIO.

Figure 1: Composite of $25-80$ day filtered OLR (W m-2; shading) and 850 hPa
wind anomalies (quivers) for the boreal summer (MJJASO) from Day $-12$ to Day
$20$ for the propagating cases. OLR and wind vectors shown are statistically
significant at 95% confidence level. Figure 2: Same as Figure 1, but for non-
propagating cases. Figure 3: Composite of 25-80 day filtered column-integrated
specific humidity (scaled by the latent heat of vaporization L) ($10^{6}$J
s-2; shading) and 850 hPa wind anomalies (quivers) for the boreal summer
(MJJASO) from Day -12 to Day 20 for the propagating cases. Wind vectors shown
are statistically significant at 95% confidence level. Figure 4: Same as
Figure 3, but for non-propagating cases. Figure 5: Contours of the composite
mean of 25-80 day anomaly terms in Equation 1 (scaled by the latent heat of
vaporization, $L$) and their combinations (for column process) for propagating
cases on (a) Day -8 and (b) Day -4. Units of terms are W m-2. The 850 hPa wind
anomalies are overlaid for reference. Wind vectors shown are statistically
significant at 95% confidence level. Figure 6: Same as Figure 5, but on (a)
Day $4$ and (b) Day $8$ Figure 7: Same as Figure 5, but only for Day $0$ of
the composite of non-propagating cases.

##  4 Moisture budget

Tropical convection is known to be tied with column-integrated moisture and
the environmental moisture distribution on various timescales (Bretherton et
al.,, 2004). Many studies regarding MJO/BSISO have shown coherence between OLR
or precipitation anomalies with column-integrated moisture (specific humidity)
anomalies, or sometimes moisture anomalies lead precipitation (Kiranmayi and
Maloney,, 2011; Adames and Wallace,, 2015; Kim et al.,, 2014; Jiang et al.,,
2018). Thus, a column-integrated moisture budget has been used to understand
the processes involved in BSISO (Adames et al.,, 2016; Chen and Wang,, 2021)
and MJO (Adames and Wallace,, 2015; Adames et al.,, 2016) dynamics. Moist
static energy (MSE)/Moist entropy (ME) budgets have also been employed (Sobel
et al.,, 2014; Jiang et al.,, 2018; Wang and Li,, 2020), as they include
additional energy fluxes that may affect convection and MSE/ME are nearly
conserved variables, though many of these studies concluded that MSE/ME
anomalies are in fact dominated by moisture anomalies. Following this line of
work, the “moisture mode” framework has emerged as a promising avenue to
understand certain large-scale moist tropical systems, which at the broadest
level means that these modes of variability are dictated by moisture anomalies
and that these modes would not exist in any mathematical model that does not
contain a prognostic equation for moisture (Sobel et al.,, 2001, 2014; Sobel
and Maloney,, 2013; Sukhatme,, 2014; Kim et al.,, 2014).

We begin our moisture budget analysis of the BSISO by examining OLR and
column-integrated specific humidity. Specifically, Figures 3 and 4 show the
25-80 day filtered column-integrated (1000 to 200 hPa) specific humidity
anomalies for propagating and non-propagating BSISO cases, respectively.
Comparing with Figure 1 and Figure 2, we clearly see that BSISO-related
specific humidity and OLR (convection) anomalies are collocated. Specifically,
large negative OLR anomalies associated with strong convection are accompanied
by large positive anomalous column-integrated specific humidity and vice-
versa. Thus, an understanding of how the column-integrated moisture evolves
should provide insight into the evolution of convection. The relevant equation
reads,

$[\frac{\partial q^{\prime}}{\partial
t}]=-[(\textbf{V}.\nabla_{h}q)]^{\prime}-[(\omega\frac{\partial q}{\partial
p})]^{\prime}-P^{\prime}+E^{\prime}+R,$ (1)

where $q$ is the specific humidity, $\textbf{V}=u\textbf{i}+v\textbf{j}$ is
the horizontal wind, ${\nabla_{h}=\textbf{i}(\frac{\partial}{\partial
x})+\textbf{j}(\frac{\partial}{\partial y}})$ is the horizontal gradient
operator, $P$ is precipitation, $E$ is evaporation, and $\omega$ is the
vertical velocity in pressure co-ordinates. Here, prime denotes a 25-80 day
anomaly. $R$ is the residual in the budget (Adames and Wallace,, 2015). The
square bracket represents mass-weighted vertical integrals, calculated from
1000 to 200 hPa. The last three terms of the R.H.S are usually bundled
together as,

$-[Q_{2}]^{\prime}/L=-P^{\prime}+E^{\prime}+R,$ (2)

which is called the column-integrated “apparent moisture sink” (Adames and
Wallace,, 2015). The last four terms in Equation 1 are together called
“column-processes” (Chikira,, 2014). Further,

$C^{\prime}=-[(\omega\frac{\partial q}{\partial
p})]^{\prime}-P^{\prime}+E^{\prime}+R=-[(\omega\frac{\partial q}{\partial
p})]^{\prime}-[Q_{2}]^{\prime}/L.$ (3)

Hence, this term can be calculated directly by subtracting horizontal
advection from moisture tendency. As precipitation and evaporation are not
defined at pressure levels, the moisture budget equation at a single pressure
level is often written as,

$\frac{\partial q^{\prime}}{\partial
t}=-(\textbf{V}.\nabla_{h}q)^{\prime}-(\omega\frac{\partial q}{\partial
p})^{\prime}-Q^{\prime}_{2}/L,$ (4)

which we have used for our vertical structure investigation. Moreover, the
vertical moisture advection term can be broken down into,

$(\omega\frac{\partial q}{\partial p})^{\prime}=\frac{\partial(\omega
q)^{\prime}}{\partial p}+(q\nabla_{.}{\textbf{V}})^{\prime},$ (5)

where the first and second terms are the vertical and horizontal convergence
of moisture flux, respectively. Note that as many previous studies regarding
MJO/BSISO use MSE/ME budgets, in this paper, we multiply all the budget terms
with $L$, the latent heat of vaporization, as it will be useful to compare our
results to those studies.

The composite moisture budgets for the propagating BSISO cases on Day -8 and
Day -4, and Day 4 and Day 8, i.e., as the BSISO develops and propagates, are
shown in Figures 5 and 6, respectively. One can see the first hint of
northward movement of moisture anomaly (as well as convection) — as in Figure
1 — from the Equatorial Indian Ocean (EIO) to Southern Arabian Sea (AS)
happens between Day -8 and Day -4. This northward movement over the AS
continues, and on Day 0, we see the positive moisture anomaly has almost
engulfed the AS up to 20N. Strikingly, from Day -8 to Day 0, there is almost
no northward movement of convection over the Bay of Bengal, this results in
the characteristic NW-SE tilted convection band associated with the developing
BSISO.

To understand the reason behind this preferential northward propagation over
the AS at this stage, we focus on Figure 5, where we have plotted the terms of
moisture budget (Equation 1) and the combination of the terms that contribute
to “column-process” (Equation 3) for Day -8 and Day -4. Note that residual is
included in $C^{\prime}$. In Figure 5(a), we see that the moisture tendency on
Day -8 has entered the southern AS, as expected from the discussion above. The
pattern of moisture budget terms indicates that horizontal advection is the
main contributor to the moisture tendency in the AS sector, though horizontal
advection is not the dominant term in the budget, as shown previously for the
BSISO (Adames et al.,, 2016; Jiang et al.,, 2018; Wang and Li,, 2020; Chen and
Wang,, 2021). As expected, precipitation and vertical advection are the
dominant terms in the budget, but they cancel each other to a large extent.
The large precipitation and vertical advection signal is due to the negative
moisture anomaly and anomalous subsidence associated with the gyre of the
previous cycle of suppressed BSISO convection north of the newly born
convective anomaly over the EIO. Evaporation, though small in magnitude,
opposes the moistening, because the easterly wind anomalies associated with
the BSISO act against the climatological south-westerly monsoonal mean flow
and slow down the overall flow in the AS as well as BOB. This indicates that
the wind-induced surface heat exchange (WISHE) mechanism is not applicable to
the northward propagation of BSISO. Amongst “column-process” terms, vertical
advection dominates and we get a net negative value over AS and BOB, with a
minor positive contribution over the EIO. Both “column-process” and horizontal
advection moisten the EIO, while the “column-process” dries the AS and BOB. In
BOB, the magnitude of horizontal advection is close to the opposing “column-
process”, and in all, we see a drying tendency in the north and weak
moistening in the southern BOB. But over AS, horizontal advection is
considerably stronger, and it wins over the drying “column-process”, and the
net result is a moistening of the atmosphere over the AS. This is the primary
cause for the preferential movement of moist convection over the AS at this
stage in its development, and results in the NW-SE tilted structure of the
BSISO.

The moisture budget for Day -4 (Figure 5b) tells a very similar story, though
the “column-process” is a little weaker and horizontal advection is little
stronger over the AS, so now we have stronger moistening over AS and the BSISO
moves further north. Over BOB, though the “column-process” is strong, the
horizontal advection also becomes slightly larger, and this causes some
moistening, particularly in the southern sector of the BOB. These findings, at
this stage of the BSISO, are consistent with the MSE budget analysis of Jiang
et al., (2018). In peninsular India, we see a slightly different moistening
process. Unlike AS and BOB, the horizontal advection on Day -8 and Day -4
dries the region. Yet, we find overall moistening as reflected in the tendency
term, indeed, this is due to “column-process”, more specifically, due to
vertical advection. A similar pattern was also identified by Jiang et al.,
(2018) who speculated that this is probably due to topographic influence.

Next, we focus on the moistening over the Indian landmass, particularly beyond
20N. To the best of our knowledge, previous studies regarding northward
propagating BSISO do not explain the moisture dynamics beyond 20N, where the
BSISO influences the Indian monsoon active and break cycle. As seen in Figure
3, though the positive moisture anomaly enters the Indian landmass beyond 20N
on Day 4, the most striking moistening happens between Day 4 and Day 12. To
understand the moistening process on Day 4 and Day 8, we examine the moisture
budget in Figure 6. On both days, we see a very strong moisture tendency
covering almost all the Indian landmass. Similar to Day -8 and Day -4,
horizontal advection is the main contributor to the positive moisture
tendency. On both days, we see “column-process” (again, mainly due to vertical
advection, and to some small extent, evaporation) induces drying at the North-
West corner in the Northern AS and desert region of India, but that is much
weaker than the large horizontal advection. On both days, the BOB also shows a
large positive moisture tendency, and it is also due to horizontal moisture
advection. Interestingly, on Day 8, we see slight moistening by horizontal
advection over peninsular India, but the drying associated with “column-
process” is larger and results in a net weak drying tendency in this region.

For the non-propagating cases, the composite in Figure 4 shows that from Day
-8 to Day 0, the anomalous moisture distribution remains almost unchanged,
except for some strengthening of positive anomaly over the EIO. On Day 4, we
see a sign of moistening over the AS, but the positive moisture anomaly fails
to penetrate into the AS. The situation remains almost unchanged on Day 8,
though by Day 12, we see the sign of a very weak positive moisture anomaly
over the AS. Indeed, when compared to the propagating cases, this moistening
is negligible. Further, over the EIO, positive moisture anomalies start to
weaken from Day 0 onwards and almost vanish by Day 8. This is also evident in
the OLR signal in Figure 2. As we see the first well-organized and strong
circulation on Day 0, we focus on the moisture budget of day Day 0 for non-
propagating BSISO composites to find out why the convection fails to propagate
in the AS.

The moisture budget on Day 0 for the non-propagating cases is shown in Figure
7. As in the propagating BSISO cases, the tendency is dominated by the
horizontal advection and the “column-process” (mostly by vertical advection)
acts against it to reduce the amount of moistening. But here, the tendency is
much weaker than the propagating cases, particularly over the Southern AS.
This weak tendency is caused by the weak horizontal advection term (in some
areas near 10S, it is even slightly negative), particularly in the southern
region of the Arabian Sea. This weak moistening is the reason behind the
inability of the convection to move into the AS. Interestingly, the moistening
is slightly stronger in the Northern AS, which is also reflected in the fact
that from Day 0 to Day 4, the negative anomaly in the Northern AS vanishes,
but the positive anomaly fails to penetrate into the Southern AS. Over Indian
peninsula, advection is negative, and “column-process” (dominated by vertical
advection) is positive, and we see a net weak positive tendency. Finally, over
the EIO, horizontal advection induces drying, and that eventually kills the
convection in that region.

###  4.1 Vertical structure

Having understood the column-integrated moisture budget, we now examine the
vertical structure of important variables associated with BSISO. From the
discussion above, the critical difference between the propagating and non-
propagating cases stems from their ability/inability to penetrate into the AS,
thus, here we focus on the AS sector (60-72.5E). Figure 8 shows various terms
of moisture budget and a few other important variables on Day -8 of
propagating BSISO cases. We decomposed vertical advection into two parts
including horizontal moisture convergence, shown in Equation (6), as we want
to categorically focus on the boundary layer moisture convergence, which is
thought to be critical in northward propagation in many theories (Jiang et
al.,, 2004; Bellon and Sobel,, 2008), and used as a cornerstone in many
modeling studies (Yang et al.,, 2019) and model validations (Neena et al.,,
2017). Moreover, the vertical structure enables us to examine whether the
BSISO has a pronounced tilt which is a characteristic of the MJO (Adames and
Wallace,, 2015) and is implied by certain theories concerning the propagation
of the BSISO (Jiang et al.,, 2004).

As seen in Figure 8, on Day -8, the positive moisture anomaly is located over
the EIO, south of 10N, and a negative moisture anomaly is present to the north
over the AS. Both anomalies reach up to 400 hPa, above which we don’t see any
major moisture signal. One should note that the strongest moisture anomaly
signal is not in the boundary layer, but just above it in the free-
troposphere. As expected, the positive moisture tendency is in front of the
positive moisture anomaly, and interestingly, it is also strongest just above
the boundary layer, in the free troposphere between 850-600 hPa. As noted in
the previous section, the main contributor to the tendency is horizontal
advection, while “column-process” acts against it to reduce the moistening.
The main contributor to the “column-process” is vertical advection, which is
stronger than the opposing apparent moisture sink. Interestingly, horizontal
advection and “column-process”, are equally strong in the boundary layer, and
cancel each other, while in the free troposphere, horizontal advection is
stronger, so the net tendency is positive. Vertical velocity strongly aligns
with vertical advection, indicating that the vertical advection is determined
by the anomalous subsidence over the AS and ascent over the EIO. Now, to
examine the role of horizontal moisture convergence, we look at the
decomposition of vertical advection. In the boundary layer, in front of the
convection (positive moisture anomaly), we see very strong boundary layer
moisture divergence. So, boundary layer convergence cannot play a significant
role in northward propagation, as is assumed in many theory and modeling
studies (ref). Above the boundary layer, there is a small positive
contribution of horizontal moisture convergence, but it is opposed by strong
vertical moisture flux convergence. Thus, unlike the MJO here a tilt is
clearly absent, and contrary to expectations from Jiang et al., (2004), the
moisture anomaly as well as vertical velocity have a more or less upright
structure in the BSISO.

###  4.2 Process of moistening

To identify the specific processes responsible for the anomalous horizontal
advection that causes the northward movement of convection, we decompose it
into several terms consisting of BSISO-scale and background state wind and
moisture components,

$(\mathbf{V}.\nabla_{h}q)^{\prime}\approx(\mathbf{\bar{V}}.\nabla_{h}q^{\prime})^{\prime}+(\mathbf{V}^{\prime}.\nabla_{h}\bar{q})^{\prime}+(\mathbf{V}^{\prime}.\nabla_{h}q^{\prime})^{\prime},$
(6)

where prime means the BSISO-scale perturbation (25-80 day filtered anomaly),
and bar refers to the seasonal background (mean and first 3 harmonics). Though
this background is not constant, it is slowly evolving. Of course, there are
contributions from other timescales, but they are much smaller than the terms
shown, so Equation (6) is a very good first-order approximation. In fact, even
the last term in RHS is much smaller than the first two terms, and we have
observed that these two terms together capture most of the BSISO advection
anomaly. Physically, the first term in the RHS should be understood as the
background moisture advection by the anomalous BSISO wind, and the second term
should be understood as the anomalous BSISO moisture advection by the mean
monsoon background wind.

In the context of moistening in the lower troposphere, we focus on one level
(namely 700 hPa). We have chosen this level, as this is where both moisture
tendency and moisture advection are strong as seen in Figure 9. We also
confirmed that the column-integrated version of this decomposition paints a
very similar picture. In Figure 9 we study the AS sector (the region where
northward propagation of convection advances rapidly) on Day -8 for the
propagating cases. For moistening over the Indian landmass to the North of
20N, i.e., the second stage of northward movement of the BSISO, we focus on
Day 8 in Figure 10. Finally, to understand the reason for weak advection in
the AS in the non-propagating cases, we present Day 0 of the non-propagating
composites in Figure 10.

From Figure 9, it is clear that on Day -8 of the propagating cases composite
the background moisture advection by the BSISO winds plays a dominant role in
the total horizontal advection over the AS sector, thus this term is primarily
responsible for the northward movement of convection over AS. The second term,
that is the anomalous BSISO moisture advection by the background monsoon winds
has a small contribution to the west of 70E, but it has a negative
contribution along India’s west coast and peninsular region. Overall, the
former is much larger along the west coast, so in total, the entire region
over the AS has a positive signal. In the BOB, both terms have weak
contributions, and over the peninsular region advection of the background
moisture by BSISO winds dominates, so we have a net negative anomaly when the
terms are added together. Further north, as seen in Figure 10, the moistening
north of 20N is again dominated by the background moisture advection by the
BSISO wind anomalies. Advection of anomalous BSISO moisture by background
monsoon winds tries to dry the northwestern desert region north of 20N, but it
can’t overcome the strong moistening by eddy advection of background moisture.
The story is different in the peninsular Indian region and BOB, here,
background wind advection of BSISO moisture anomalies induces strong
moistening and dominates the total moisture advection.

Finally, for the non-propagating BSISO cases, as seen in Figure 11, we have
net negative moisture advection in the southern AS sector, from the west coast
of India to 65E, which as discussed before is the reason behind the failure of
the non-propagating cases to effectively penetrate into the AS. In the
Northern AS, moisture advection is very weak and close to zero. In fact, the
advection of background moisture by anomalous BSISO winds is much weaker and
limited (close to the coast, east of 70E) compared to the propagating cases,
as seen in Figure 9. Further, the advection of BSISO moisture anomalies is
slightly stronger than the propagating cases and essentially offsets any
moistening by the advection of background moisture. In fact, this induces a
small net negative moisture advection in the Southern AS. So, overall,
comparing Figures 9 and 11, the primary cause behind the failure of non-
propagating cases to penetrate into the AS is weaker and limited advection of
background moisture by BSISO winds. This is particularly true west of 70E
where we see almost no moistening by this term, while for the propagating
cases, there are considerable positive contributions all over the Southern AS.

To demonstrate how the BSISO wind anomalies advect background moisture and
monsoon winds advect BSISO moisture anomalies in their respective places of
dominance, we plot 700 hPa background moisture anomaly along with 700 hPa
BSISO wind anomalies as well as 700 hPa BSISO moisture anomalies with
background wind in Figures 12, 13 and 14 on Day -8, Day 8 for the propagating
cases and Day 0 for the non-propagating case.

In the first stage, i.e., when convection enters the AS, on Day -8, for
propagating cases (Figure 12), we see very strong easterlies from the
equatorial region up to 15N, covering the whole AS and peninsular India. These
are associated with the off-equatorial suppressed BSISO convection and can be
thought of as a part of the Rossby component of a Gill-type response. These
easterlies act upon the sharp zonally oriented gradient of background moisture
over the AS and moisten the southern AS region. Interestingly over the BOB,
the gradient of background moisture is more meridionally oriented, but the
wind anomalies are north-easterly, so the advection of moisture is much
weaker, thus the BSISO moisture anomaly (convection) moves much quicker over
the AS than the BOB. This, as mentioned, establishes the characteristic NW-SE
tilted convection band that is evident from Day 0 to Day 8. On the other hand,
the negative BSISO moisture anomaly associated with the suppressed convection
is stronger over the AS than peninsular India, so background westerly monsoon
winds cause dry advection near the coast and over peninsular India. On Day -4
(not shown), we have equally strong easterlies between 5N to 20N, as, along
with the suppressed convection of BSISO, the emerging convection over the EIO
induces a new modified Gill-type response with an equatorial Rossby signal in
the Indian Ocean. This signal persists up to Day 0 and continues to moisten
the AS.

In the second stage, i.e., northward movement over the Indian landmass, on Day
8 (Figure 13), we see that the new Rossby gyre associated with the enhanced
convection has a clear tilt from North-West to South-East (which is first
visible on Day 4), and a well-formed vortex can be seen over the AS.
Associated with this gyre, the wind anomalies over India are south-easterly,
and aligned with the background moisture gradient (the background moisture
decreases from the head BOB-Bangladesh-Myanmar region towards the desert
region in the North-West of India). This wind taps in the moisture gradient
and advects moisture from the BOB region to India north of 20N. Further, on
Day 8, the background monsoon wind, which is south-easterly in the BOB, acts
upon the anomalous moisture gradient in the same direction and moistens the
Bay, thus the moisture anomaly and convection move further northward towards
the North Bay of Bengal. Similarly, westerly monsoon winds advect anomalous
moisture from AS towards the peninsular India. Note that, by Day 8, as the
Rossby gyre is tilted and moves northward, the anomalous winds over the EIO as
well as southern AS, become westerly, and these act against the background
moisture gradient to dry the region. As a result, the whole tilted band of
anomalous moisture (convection) moves further north.

Overall, for northward propagation, various moistening processes play a role
at different stages of BSISO and at different locations. First, when the BSISO
convection signal starts over EIO, anomalous easterlies advect background
moisture into the AS and push convection northward into the AS. Then, the
Rossby gyre associated with the BSISO tilts from the North-West to the South-
East, and the anomalous south-easterly winds tap the existing background
moisture gradient to moisten the lower troposphere above landmass beyond 20N,
and thus the convection moves northward into the Indian land region. During
this stage, when the BSISO convection has moved northward deep into the AS
(but not so much in the BOB), the background monsoon winds advect the moisture
into the BOB, thus the convection moves northward towards the northern BOB.

Given these observations, we try to settle the debate in the literature about
the process of moistening regarding the BSISO in South Asia. As noted by
Kikuchi, (2021), studies have claimed different terms to be dominant, and
there is no consensus about which processes play the most significant role. As
suggested by Kikuchi, (2021), these discrepancies arose because studies
averaged the terms over different regions, whereas as we have seen, differing
processes are in action in various regions and stages of the BSISO. While
Jiang et al., (2018) showed the dominant term to be the background moisture
advection by BSISO winds, Wang and Li, (2020) claimed that background winds
advecting BSISO moisture anomalies are more important. As seen in the previous
discussion, $(\mathbf{V}^{\prime}.\nabla_{h}\bar{q})^{\prime}$ is dominant
over the AS, but $(\mathbf{{\bar{V}}}.\nabla_{h}q^{\prime})^{\prime}$ is
dominant over the BOB, and also, it picks up slightly later than the
moistening of the AS. As Jiang et al., (2018) took a large box comprising both
AS and BOB, their result is dominated by the process that moistens the AS.
Also, by focusing on a particular day, they missed different processes of
moistening that are important during different stages of the BSISO. On the
other hand, Wang and Li, (2020) averaged across the BOB and claimed the
dominance of the background wind advection term. To the best of our knowledge,
the only study that showed the importance of both terms is Adames et al.,
(2016), though they suggested that the BSISO moisture anomaly advection by
background flow only causes eastward movement, and it is dominant near the
western north Pacific region.

Equally important is our finding that the moistening proceeds in stages, and
in fact, the moistening over peninsular India is quite distinct. It was
assumed that the moistening over the AS happens due to advection by the BSISO
easterlies, and land also gets moistened by the same process (Adames et al.,,
2016), but that is not the case, in fact, the anomalous moisture advection is
negative at this phase over the peninsular India, which gets moistened due to
stronger “column-process”. Moreover, to the best of our knowledge, no study in
the context of BSISO has identified the moistening process over the land
region north to 20N, though we see that convection reaches as far north as
30N. Some studies (Prasanna and Annamalai,, 2012; Pillai and Sahai,, 2014) in
the context of active/break cycles of monsoon identified anomalous moisture
advection over the land region, but they didn’t pinpoint how the anomalous
moistening process occurs, except for the drying (break) case, where they
speculated that dry air advection from the desert region might play a crucial
role. As discussed earlier, we have clearly demonstrated that there exists a
strong north-westward background moisture gradient running from the moisture-
rich north BOB towards the desert region of northwest India, and before the
enhanced (suppressed) convection phase of BSISO reaches there, strong
anomalous South-Easterlies (North-Westerlies) moisten (dry) the landmass by
advection. These South-Easterlies (North-Westerlies) are associated with the
modified Rossby response to the enhanced (suppressed) convection, which is
tilted toward the Northern AS in the northwest. As previous studies didn’t
focus on the moistening beyond 20N, they also didn’t ask the question as to
why and how the Rossby response gets tilted to generate the South-Easterlies
(North-easterlies) which results in moistening (drying) over that region. In
the next section, we will try to solve this puzzle.

To understand why horizontal moisture advection is weak for non-propagating
cases, we examine Figure 14. Here too, we clearly see the Rossby gyre
associated with the Gill-type response and prominent easterlies, but it is
comparatively weaker than the propagating cases, and limited to the East of
70E. Even near 70E, the winds turn at the edge of the gyre, so they are more
north-easterly than easterly. These wind anomalies can’t successfully tap the
moisture gradient present in the AS, and fail to moisten the region. Moreover,
due to the lack of strong moistening before Day 0, the negative moisture
anomaly of the dry cycle over AS is quite strong, and the background
westerlies act upon that to give rise to strong negative advection near the
coast. Over the EIO, background westerlies work against the moisture gradient
associated with the nascent convection to dry the region.

Thus, in contrast to the suggestion by Jiang et al., (2018), strong easterlies
over India don’t guarantee robust northward propagation. In fact, we see the
critical condition is the extent of these easterlies, which need to extend far
beyond 70E to amply moisten the AS. Why the strong moistening of AS is
critical for the BSISO to reach further North into the South Asian land
region? This question takes us back to the previous question of sudden tilt in
the Rossby response (as seen between Day 0 to Day 8), as we have seen that the
South-easterlies associated with the tilted Rossby response are the reason
behind the moistening of most of the land region. So, the question boils down
to, why we don’t get the tilted Rossby structure in the non-propagating BSISO.

Figure 8: Pressure-latitude profile of anomalous moisture budget terms in
Equation 4 (scaled by latent heat of vaporization L), components of anomalous
vertical advection decomposition as shown in 6 (scaled by the latent heat of
vaporization L), and anomalies of a few other important variables averaged
over target region of Arabian Sea (60∘-72.5∘E) on day$-8$ for propagating
cases. The upper panel shows (from left): specific humidity, moisture
tendency, the sum of vertical moisture advection and apparent moisture sink,
and horizontal moisture advection. Middle panel shows (from left): vorticity,
horizontal moisture convergence, vertical moisture flux convergence, and
vertical moisture advection. Lower panel shows (from left): apparent moisture
sink, divergence, and vertical velocity in pressure coordinates. Moisture
tendency contour is overlaid on moisture budget terms. Units for specific
humidity(moisture) is J kg-1 and for all other terms are W kg-1

.

Figure 9: Anomalous horizontal advection term and its linearly decomposed
primary contributor terms and their combination (all scaled by L) at 700 hPa
as shown in Equation 6, for Day $-8$ of the composite of propagating cases.
Units of terms are W kg-1. The 700 hPa wind anomalies are overlaid for
reference. Wind vectors shown are statistically significant at 95% confidence
level  Figure 10: Same as Figure 10, but for Day $8$. Figure 11: Same as
Figure 9, but for Day $0$ of the non-propagating cases.  Figure 12: Background
specific humidity (g kg-1) and 25-80 day filtered wind anomalies at 700 hPa on
Day$-8$ of the propagating composite. Wind vectors shown are statistically
significant at 95% confidence level.  Figure 13: Same as Figure 13, but for
Day $8$. Figure 14: Same as Figure 13, but for Day $0$ of non-propagating
composite.

##  5 Vorticity budget

Having examined the moistening processes, we now focus on the BSISO
circulation. During the initial stage of the propagating cases, when the BSISO
appears over the EIO, easterlies associated with the previous dry cycle and
the new enhanced convection moistens the AS, thus the convection moves into
AS. Once the convection enters deep into the AS (but not that far in BOB), the
slanted structure of convection gets established, and the BOB moistening by
background south-westerlies begins. But the question remains, how the Rossby
gyre (that was initially established as a part of the modified Gill-type
response associated with equatorial convection) tilts North-West to generate
the South-Easterlies over the land region which in turn moisten the vast
expanse of land in India? The other relevant question is, for non-propagating
cases, why does the Rossby gyre not show a North-West tilt, and thus doesn’t
moisten land region over India? To understand this, here we appeal to
vorticity budget analysis. The column-integrated version of the relevant
equation reads (Wang and Chen,, 2017),

$\langle\frac{\partial\zeta^{\prime}}{\partial
t}\rangle=\langle(-\omega\frac{\partial\zeta}{\partial
p})\rangle^{\prime}+\langle(-\textbf{V}.\nabla_{h}\zeta)\rangle^{\prime}+\langle(-v\frac{\partial
f}{\partial y})\rangle^{\prime}+\langle-(\zeta+f)D]\rangle^{\prime}+\langle
T\rangle^{\prime}+\textrm{residual},$ (7)

where, $\zeta=(\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y})$
and $D=(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y})$ are the
relative vorticity and divergence, respectively.
$\textbf{V}=u\textbf{i}+v\textbf{j}$ is the horizontal wind,
${\nabla_{h}=\textbf{i}(\frac{\partial}{\partial
x})+\textbf{j}(\frac{\partial}{\partial y}})$ is the horizontal gradient
operator, $f$ is Coriolis parameter and $\omega$ is the vertical velocity in
pressure co-ordinates. Prime denotes a 25-80 day anomaly as defined earlier.
$T$ is given by $(\frac{\partial\omega}{\partial y})(\frac{\partial
u}{\partial p})-(\frac{\partial\omega}{\partial x})(\frac{\partial v}{\partial
p})$, which is tilting term. In this analysis, we separately show these first
and second terms of the tilting, as there are conflicting views regarding
which term is important in the BSISO. Here, we call the first term $T_{1}$ and
the second term $T_{2}$, so $T^{\prime}$ reads
$(T_{1}^{\prime}-T_{2}^{\prime})$. $[-(\zeta+f)D]$ represents the stretching
term, $\frac{\partial\zeta}{\partial t}$ is the local tendency of the relative
vorticity, $(-\textbf{V}.\nabla_{h}\zeta)$ and
$(-\omega\frac{\partial\zeta}{\partial p})$ represent the horizontal and
vertical advection of relative vorticity, respectively, and $(-v\frac{\partial
f}{\partial y})$ is the vorticity generation due to the $\beta$ effect.

Figure 12 shows the terms comprising the lower-tropospheric vorticity budget
and their combinations on Day 0 of the propagating cases. We chose Day 0
because, from Day 0 to Day 4, we see the abrupt tilting of the Rossby gyre
towards North-West (associated with which is a well-formed vortex over the
AS), which was zonally oriented on Day 0 (Figure 1). In other words, positive
vorticity anomalies traveled northward much faster in the AS than in the BOB.
In Figure 12, we see the vortex of positive vorticity (associated with the
Rossby response of Equatorial convection) up to 15N, which is zonally oriented
as expected. The tendency has a clear NW-SE tilt, which is also expected as
discussed above. Clearly, the prime contributor to this NW-SE tilted tendency
is $T_{1}^{\prime}$ (the component of the tilting term associated with the
meridional gradient of vertical velocity). The tendency as well as
$T_{1}^{\prime}$ are particularly strong over the AS, compared to the BOB,
which causes the generation of cyclonic vortex over the AS on Day 4 and Day 8.
Interestingly, quite similar to the moisture budget, $T_{1}^{\prime}$ is the
main contributor to the tendency, but it is not the largest term. The largest
terms in this budget are the stretching and the horizontal advection, and they
mostly cancel each other. We have added the stretching, horizontal advection,
and $\beta$ term (advection of planetary vorticity), their combination is
close to zero over the AS, where the tendency is the strongest. The vertical
advection (not shown) term is negligible over the AS and BOB but has a small
positive contribution over the land. As seen, $-T_{2}^{\prime}$ is also
negligible, but we show it here as it was suspected to be important in BSISO
propagation (Dixit and Srinivasan,, 2011; Karmakar et al.,, 2022). As found by
most of the vorticity budget studies, the residual (not shown) is non-
negligible, but it is weak and negative over the region of strongest positive
tendency over the AS and BOB, so it doesn’t jeopardize our understanding.
Above all, the contribution from all the terms except $T_{1}^{\prime}$ is
shown at the bottom right panel of Figure 12 (it includes the terms not
explicitly shown in the figure) and it mostly yields negative values over the
region of positive tendency, but $T_{1}^{\prime}$ is much larger than the
negative contribution from all other terms, thus resulting in a positive
vorticity tendency. In essence, we can conclude that $T_{1}^{\prime}$ is the
term that dictates the NW-SE slanting of the Rossby gyre as seen from Day 0 of
the propagating composite. Near the equator, horizontal advection contributes
to a negative tendency, so the whole gyre moves North, of course with the
characteristic tilt explained above. A similar process also holds on Day 4
(not shown), which tilts the gyre even more and generates stronger South-
easterlies over the land region. The importance of the tilting term behind
propagation has been previously noted by a couple of recent studies (Li et
al.,, 2021; Karmakar et al.,, 2022).

To understand why the Rossby gyre doesn’t tilt and move north into the AS for
non-propagating cases, we focus on the Day 4 vorticity budget shown in Figure
13. We chose this day because, on Day 4, a clear Rossby signal is evident over
EIO and Southern India, but it fails to propagate and weakens by Day 8 (Figure
2). As seen in Figure 13, $T_{1}^{\prime}$ is almost absent over the AS,
except for a small positive patch below 15N, and the tendency term also
reflects a similar pattern. Cancellation between stretching and horizontal
advection is also present like the propagating cases, and when added with the
$\beta$ term, their cumulative contribution over the AS is close to zero.
Comparing with the propagating cases, we can conclude that the vortex doesn’t
propagate into the AS, and fails to generate the NW-SE tilted Rossby gyre due
to a non-existent $T_{1}^{\prime}$ term in the Northern AS. Over the Indian
landmass, we see a contribution from $T_{1}^{\prime}$, but it is not strong
enough to counteract the opposing effects by other terms, though it does
generate a small positive tendency, thus the gyre moves slightly North over
land (Figure 13), but it can’t generate the South-easterly wind as the gyre
doesn’t get tilted. Near the equator, horizontal advection primarily
contributes to the negative tendency to weaken the cyclonic vortex.

###  5.1 Process of tilting

Finally, the question boils down to, why a strong tilting term (here,
$T_{1}^{\prime}$) gets generated over the Northern AS region for propagating
cases once the Rossby signal associated with the nascent convection in the EIO
region gets firmly established, while this doesn’t happen for the non-
propagating cases. To understand this, similar to Equation 3, we break
$T_{1}^{\prime}$ into components comprising background and BSISO-related
anomaly fields. Here, we only show ${(\frac{\partial\omega^{\prime}}{\partial
y})(\frac{\partial\bar{u}}{\partial p})}$, which is the dominant term
controlling $T_{1}^{\prime}$, as seen in Figure 12. Physically, this term
comprises the meridional gradient of anomalous vertical velocity and vertical
shear of background zonal wind.

To investigate the $T_{1}^{\prime}$ term, we again focus on a single level
(700 hPa), which is a representative level for the lower free troposphere, and
was also the level chosen for understanding the moistening process. In Figures
14a and 14b, we have shown $T_{1}^{\prime}$ its components, and other relevant
fields at 700 hPa. Looking at Figure 14, we see most of the $T_{1}^{\prime}$
is captured by ${(\frac{\partial\omega^{\prime}}{\partial
y})(\frac{\partial\bar{u}}{\partial p})}$ for both the propagating and non-
propagating cases, so we separately look at vertical shear of background zonal
wind and meridional gradient of anomalous vertical velocity to understand the
processes involved. The vertical wind shear is very similar for both cases, so
it is not the reason behind the difference between propagating and non-
propagating cases. Clearly, the difference arises from
${(\frac{\partial\omega^{\prime}}{\partial y})}$, which takes the shape of the
${(\frac{\partial\omega^{\prime}}{\partial y})(\frac{\partial\bar{u}}{\partial
p})}$ and $T_{1}^{\prime}$ term for both the categories. Just like
$T_{1}^{\prime}$, this term is positive north of the convection, and very
strong over the Northern AS for the propagating cases, while for the non-
propagating cases, it is limited to the land and the BOB, and essentially non-
existent over the AS. The vertical shear of background zonal wind is also
strongest over the Northern AS, so it amplifies $T_{1}^{\prime}$ over the
region even more. ${(\frac{\partial\omega^{\prime}}{\partial y})}$ is also
strong over the BOB, but weaker background shear makes the tilting
comparatively weak for both cases.

To explain why ${(\frac{\partial\omega^{\prime}}{\partial y})}$ is strong over
the northern AS for propagating cases, but not so for the non-propagating
cases, we shift our focus to the orientation of $\omega^{\prime}$. For the
propagating cases, by Day 0, anomalous negative values associated with
ascending motion engulf all the EIO as well as the Southern AS, while for the
non-propagating cases, even on Day 4, this is limited to the EIO, and to some
extent peninsular India, with much weaker magnitude. The distribution of
$\omega^{\prime}$ is highly collocated with the distribution of column-
integrated positive moisture anomaly, as high values of anomalous column-
moisture cause convection that manifests in ascending motion. Though
$\omega^{\prime}$ and column-integrated moisture anomaly for propagating cases
are highly coherent over the EIO and Southern AS, in the Northern AS, moisture
has a slight lead, which might help in preconditioning the region for
convection.

To the north of the area of the ascending motion, we find an area of positive
vertical velocity anomaly (descending motion) for both categories. This area
has a similar orientation for both categories except for the AS. For both
categories, it runs much south over the BOB, almost up to 10N, but over the
land, it is confined within 15-20N, so it also has a similar tilt. Over the
AS, for the propagating cases, this is confined in near 20N, but for the non-
propagating cases, weak anomalous descending motion is visible up to the
southern AS. The descending motion for both categories is associated with the
suppressed BSISO convection and accompanied by negative or near-zero moisture
anomalies. Thus, a strong gradient of vertical velocity anomaly exists over
the Northern AS region for the propagating cases, while it doesn’t for the
non-propagating cases.

Figure 15: 600-850 hPa(lower free-troposphere) integreated vorticity anomaly
and dominant vorticity budget terms as shown in Equation 1 and their
combinations, on Day $0$ of the propagating composite. Unit of column
integrated vorticity is kgm-2 s-1 and of budget terms are kgm-2s-2. Figure 16:
Same as Figure 16, but for Day $4$ of non-propagating composite. Figure 17:
(a)Various important terms associated with anomalous tilting on Day0 at 700
hPa for propagating cases, Clockwise(from top left): Dominant part of tilting
term anomaly $T_{1}^{\prime}$, its’ dominant linearized component, anomalous
vertical velocity, vertical shear of background zonal wind, meridional
gradient of anomalous vertical velocity at 700 hPa and column-integrated
specific humidity anomaly, for propagating composite on Day $0$. Units are
s-2, s-2,Pa s-1,m Pa-1,Pa (ms)-1 and J s-2 respectively. (b)Same as (a), but
for Day 4 of non-propagating composite.

##  6 Conclusions

In this study, we have investigated the mechanism behind the northward
propagation of BSISO over South Asia using the “moisture mode” framework. We
have identified two types of BSISO events, one propagates northward to South
Asian landmass from EIO, while the other type doesn’t. Comparing their
propagation dynamics, we identified the critical mechanisms behind Northward
propagation. We confirm that both types of BSISO convection anomalies are
generally collocated with the column-integrated moisture anomalies. A moisture
budget analysis was performed to understand the evolution of anomalous
moisture, that dictates the evolution of anomalous convection. Our results
suggest that, for propagating cases, easterlies on the southern flank of the
anticyclonic Rossby gyre associated with the previous cycle of suppressed
convection, as well as the easterlies in the north flank of the cyclonic
Rossby gyre associated with the new area of enhanced convection over the EIO
engulf most of the AS region. This aligns with the background gradient of
moisture and moistens the Southern AS region by advection. Over BOB, the
background moisture gradient is mostly meridional while BSISO wind is north-
easterly, thus the moistening due to advection is weaker. ’Column-process’
acts against this moistening, but the advection is stronger. At this stage, as
we have stronger moistening over the AS, the convection quickly enters into
the AS from the EIO, but it takes more time to enter the BOB. Thus, we get the
initial NW-SE tilted band of convection.

At this stage, as a tilted belt of strong convection is present behind the
area of suppressed convection associated with subsidence, a tilted belt of a
meridional gradient of anomalous vertical velocity comes into being, from the
Northern AS to the north-west, to the Southern BOB to the south-east. The
vertical easterly shear in the background monsoon wind acts upon this gradient
to generate an NW-SE slanted vortex tilting term, which dominates the
vorticity tendency and thus leads to the vorticity anomaly. Thus, the cyclonic
Rossby gyre associated with the enhanced BSISO convection gets a clear NW-SE
tilt while moving northward from the EIO. So, the characteristic tilted vortex
comes into being. On the northern flank of the tilted Rossby gyre, anomalous
south-easterlies advect the background moisture from the moisture-rich head
BOB region in the southeast towards the dry desert region in the northwest.
Thus, again the anomalous BSISO wind taps the background moisture gradient and
moistens the vast expanse of land north of 20 N, and the convection jumps into
the aforementioned region. On the southern flank of this Rossby gyre,
westerlies advect dry air in the EIO, thus the convection dies down, and the
entire band of convection appears to jump from the equatorial region to the
off-equatorial region, above 10N. Over the BOB, the moistening process is
different. Once the tilted structure of convection comes into being, the
background south-easterly monsoon wind moistens the BOB and helps the
convection to take place.

For the non-propagating BSISO cases, while the nascent convection starts to
gain strength over the EIO, easterlies over the Arabian Sea are much weaker,
thus they can’t properly moisten the region over the southern AS to initiate
strong convection. In the absence of strong convection behind the zone of
subsidence associated with suppressed convection, the meridional gradient of
vertical velocity is almost absent. Hence, in spite of the presence of strong
easterly vertical shear of background zonal wind, a strong vortex tilting term
doesn’t get generated. As a result, the convection stalls over the EIO, and
the westerlies in the southern flank of the Rossby gyre of the enhanced
convective signal eventually kill the convection.

Overall, we can claim that the northward propagation of BSISO over South Asia
is a moisture mode acting under the influence of the background vertical shear
of the zonal monsoon wind. It is a classic case of convectively coupled
dynamics, where moisture and circulation influence each other to dictate the
propagation of convection. While the vertical shear of the background zonal
wind and the zonal gradient of background moisture over the AS are necessary
conditions for northward propagation, they are not sufficient. The critical
difference between the propagating and non-propagating cases arises from the
strength and extent of easterlies over the southern AS when new convection
starts in the EIO, as moistening over the southern AS by this easterlies is
critical behind the propagation.

While previous studies highlighted the important role of vertical shear (Jiang
et al.,, 2004; Li et al.,, 2021; Karmakar et al.,, 2022) as well as moisture
advection (Adames et al.,, 2016; Jiang et al.,, 2018; Chen and Wang,, 2021;
Wang and Li,, 2020) with uncertainly as to which process of moisture advection
dominant, these two mechanisms were thought as either somewhat contradictory
(Yang et al.,, 2019), or independent (Li et al.,, 2021; Wang and Sobel,,
2022). Moreover, in the ’vertical shear mechanism’ (Jiang et al.,, 2004; Li et
al.,, 2021; Karmakar et al.,, 2022), the moistening process was dictated by
boundary layer moisture convergence, while the studies that followed the
’moisture mode’ framework (Adames et al.,, 2016; Jiang et al.,, 2018; Wang and
Sobel,, 2022), and understood the propagation by moisture advection, paid less
attention to the vertical shear of the background wind and its role in tilting
the Rossby gyre as a part of their mechanism. In this paper, we showed that
though vertical shear of background wind is essential, boundary layer moisture
convergence doesn’t play a role in moistening the area north of existing
convection to facilitate northward propagation. In fact, the strong moistening
happens above the boundary layer, in the free-troposphere, and it is dictated
by the moisture advection. On the other hand, only moisture advection, without
the role played by vertical shear, can generate a very limited Northward
propagation, up to the AS, but it can’t explain the moistening process beyond
20N. It is also unable to explain the observed tilt in the Rossby gyre. Here,
we claim that vortex tilting and the moisture advection process can’t be
looked at separately, in fact, they work hand in hand to facilitate northward
propagation of the BSISO.

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