# Intraseasonal synchronization of extreme rainfalls between North India and
the Sahel

Felix M. Strnad
Machine Learning in Climate Science, University of Tübingen, Germany
Kieran M. R. Hunt
Department of Meteorology, University of Reading, UK
National Centre for Atmospheric Science, University of Reading, UK
Niklas Boers
Earth System Modelling, School of Engineering & Design, Technical University
of Munich, Germany
Potsdam Institute for Climate Impact Research, Potsdam, Germany
Department of Mathematics and Global Systems Institute, University of Exeter,
Exeter, UK
Bedartha Goswami
Machine Learning in Climate Science, University of Tübingen, Germany

###### Abstract

The Indian Summer Monsoon (ISM) and the West African Monsoon (WAM) are
dominant drivers of boreal summer precipitation variability in tropical and
subtropical regions. Although the regional precipitation dynamics in these two
regions have been extensively studied, the intraseasonal interactions between
the ISM and WAM remain poorly understood. Here, we employ a climate network
approach based on extreme rainfall events to uncover synchronously occurring
extreme rainfall patterns across the two monsoon systems. We reveal strong
synchronization of extreme rainfall events during the peak monsoon period in
July and August, linking heavy rainfall over North India to that over the
Sahel with a lag of around 12 days. We find that La Niña-like conditions in
combination with the Boreal Summer Intraseasonal Oscillation and an enhanced
Tropical Easterly Jet (TEJ) foster the synchronization between the ISM and the
WAM. Convective clouds are transported by an intensified TEJ from southwestern
Asia toward North Africa, supporting anomalous deep convection over the Sahel
region.

Key points:

  * •

Climate networks reveal synchronous occurrence of extreme rainfall events in
North India and the Sahel.

  * •

Propagation pathways leading to the synchronization are identified using
multivariate latent space clustering.

  * •

The synchronization is driven by a combination of active BSISO, La Niña-like
conditions, and a strong Tropical Easterly Jet.

_Keywords_ Communities of rainfall extremes $\cdot$ Long-range rainfall
teleconnection $\cdot$ intraseasonal rainfall dynamics

##  1 Introduction

The Indian Summer Monsoon (ISM) and the West African Monsoon (WAM) are primary
drivers of boreal summer precipitation variability in tropical and subtropical
regions. The ISM is characterized by a strong meridional overturning
circulation, with a low-level monsoon flow from the Indian Ocean to the Indian
subcontinent and a return flow at upper levels (Bordoni and Schneider, 2008).
Similarly, the WAM is characterized by a low-level inflow of moist air from
the Atlantic Ocean, which converges with the dry, hot air from the Sahara
desert. Both the North Indian and Sahel regions exhibit substantial variations
in monsoon rainfall known as “active” and “break” phases. The active phase is
often associated with extreme rainfall events, which can have severe
socioeconomic impacts (Kotz et al., 2022).

The intraseasonal variability comes about through a complex interplay of
tropical and subtropical large-scale modes of variability (Di Capua et al.,
2020). For example, the rainfall dynamics in both North India and the Sahel
are known to be correlated to the intensity and location of the Tropical
Easterly Jet (TEJ) (Huang et al., 2019). The TEJ is a strong zonal wind
maximum in the upper troposphere that is located over the tropical Indian
Ocean and is mainly present during boreal summer months (usually
June–September). It is established due to the meridional temperature
difference between the Equatorial Indian Ocean and the Tibetan Plateau and
extends from the Pacific Ocean to the West Coast of the Sahel Zone (SZ)
(Koteswaram, 1958). Previous studies have found a strong connection between
the strength of the TEJ and ISM rainfall (Pattanaik and Satyan, 2000, Madhu,
2014, Huang et al., 2019, 2021). Through latent heat release, the TEJ becomes
stronger (weaker) during wet (dry) years of the ISM (Sathiyamoorthy et al.,
2007, Rao and Srinivasan, 2016). Conversely, a stronger upper-level jet
increases the vertical wind shear leading to more convective organization and
consequently to more rainfall over India. The physical mechanism underlying
the link between the TEJ and Sahel rainfall is less well understood, even
though the strong statistical correlation between the TEJ and Sahel rainfall
is well documented (Lemburg et al., 2019, Nicholson and Klotter, 2021). For
instance, several studies have shown that wet years in the Sahel are often
characterized by a regionally stronger TEJ even on interannual timescales
(Lemburg et al., 2019). A strong (weak) TEJ is conducive to wet (dry)
conditions and recent work has also shown that there is only a weak
relationship between TEJ variability and daily variations in convection over
the Sahel (Nicholson and Klotter, 2021). The authors conclude that the
intensity of the TEJ is not influenced by rainfall variations over North West
and Central Africa.

While the TEJ is influenced by strong convection over India, the occurrence of
extreme rainfall events in the Indo-Pacific region itself is substantially
influenced by another large-scale mode of variability: the Boreal Summer
Intraseasonal Oscillation (BSISO) (Kikuchi, 2021). The BSISO is a mode of
large-scale convective variability that originates in the Indian Ocean and
propagates northeastward across the Maritime Continent and the Western Pacific
(Kikuchi et al., 2012, Lee et al., 2013, Kiladis et al., 2014). This
oscillation plays a crucial role in the generation of deep convection and
interacts with the local circulation patterns over the Indian subcontinent,
e.g. by modulating the frequency and behavior of low-pressure systems (Hunt
and Turner, 2022). The ISM rainfall dynamic is further modulated, on
interannual timescales, by the El Niño Southern Oscillation (ENSO). Indian
rainfall is enhanced (reduced) during La Niña (El Niño) years, typically
explained by the modulation of the Walker circulation (Kumar et al., 2006).
The BSISO itself is modulated by ENSO with La Niña-like conditions leading to
an intensified northward propagation and more EREs in North India (Strnad et
al., 2023). Similarly, due to constructive (destructive) inference from the
Walker circulation in La Niña (El Niño) years, the TEJ intensifies (weakens),
and expands both horizontally and vertically (contracts spatially) (Nithya et
al., 2017). The modulation of the TEJ by ENSO is used to explain why El Niño
events reduce rainfall and foster the occurrence of droughts in Ethiopia
(Gleixner et al., 2017). This teleconnection mechanism is also present in some
global circulation models (Vashisht et al., 2021).

Even though the two monsoon systems of the ISM and WAM are both influenced by
the same global large-scale modes of variability, the occurrence of rainfall
in the two monsoon systems of the ISM and WAM is commonly still thought of as
being interconnected only on interannual to decadal timescales in the
framework of the ‘Global Monsoon’ (Wang and Ding, 2008, Geen et al., 2020).
Possible interactions between both monsoon systems on intraseasonal
timescales, however, have not been systematically investigated. In their
study, Boers et al. (2019) reveal a synchronization pattern of extreme
rainfall events (EREs) between North India and the Sahel. While some of the
other teleconnections of the ISM shown in Boers et al. (2019) have been
explained in recent years; for example, the dynamical mechanism linking the
ISM to the circumglobal teleconnection (Beverley et al., 2019, 2021) or to the
Yellow River Basin (Gupta et al., 2022), the reasons for the synchronization
between the ISM and WAM remain unclear. Our study thus aims to identify the
atmospheric processes that drive the synchronization between the ISM and the
WAM.

Previous studies on rainfall variability during boreal summer monsoon have
traditionally used methods such as linear regression, empirical orthogonal
functions (EOFs), and composite analyses (Ding and Wang, 2005, 2007, Wang and
Ding, 2008, Vellore et al., 2014, Walker et al., 2015). These are not suitable
to capture the spatial characteristics of EREs. Additionally, the
identification of specific and possibly varying time lags associated with
particular interaction patterns of different atmospheric processes is
challenging. Therefore, in this study, we examine the spatial patterns
associated with EREs that occur concurrently in the tropics and subtropics by
employing a climate network approach (Tsonis and Swanson, 2008, Malik et al.,
2010, Boers et al., 2014, 2019, Strnad et al., 2022, 2023). Climate networks
are networks where links reflect a strong statistical correlation between
corresponding nodes, typically representing time series from different spatial
locations. Here, the correlation is accessed by quantifying the synchronicity
of EREs using the event synchronization algorithm (Quian Quiroga et al.,
2002). We adopt the methodology introduced in Strnad et al. (2023) to identify
groups of densely connected nodes in the network, referred to as communities.
These can be understood as spatial regions where EREs occur significantly
synchronously.

Our method uncovers a community of synchronous EREs comprising North India,
China, and the Sahel region. We then investigate the mechanisms responsible
for the synchronization by building upon the method from Schlör et al. (2023),
clustering the propagation of EREs in a multivariate latent space. Our
approach reveals a robust time-lagged connection between the ISM and WAM
monsoon regions, prompting a subsequent exploration using traditional
meteorological analysis tools. We can show that the aforementioned large-scale
modes of variability, namely the BSISO, the TEJ, and ENSO interact to foster
the synchronization between the ISM and the WAM.

##  2 Data and Methods

###  2.1 Datasets used

#### Precipitation data

We use the $0.25^{\circ}$ daily resolved precipitation data from the Multi-
Source Weighted-Ensemble Precipitation (MSWEP) dataset (Beck et al., 2019b)
for the period of 1980–2022. The MSWEP dataset is chosen for its longer time
range compared to other available multi-satellite precipitation products,
improving statistical robustness. It has been shown to represent high rainfall
quantiles well on global scales (Beck et al., 2019a). We restrict our analysis
to the tropics and the subtropics of the Northern Hemisphere
($180^{\circ}\,\mathrm{W}$ – $180^{\circ}\,\mathrm{E}$,
$30^{\circ}\,\mathrm{S}$ – $70^{\circ}\,\mathrm{N}$, see Fig. 1 a).

#### Reanalysis data

To analyze large-scale patterns associated with the synchronization we use the
following variables from the ERA5 Global Reanalysis dataset (Hersbach et al.,
2020): Daily outgoing longwave radiation (OLR), sea surface temperature (SST),
and on pressure levels from $50$–$1000$ hPa horizontal $(u,v)$-wind fields,
vertical velocity $w$, specific humidity $q$ and temperature $T$. The datasets
used for the multivariate PCA analysis are interpolated onto a
$1^{\circ}\times 1^{\circ}$ grid, and all remaining datasets are interpolated
onto a $2.5^{\circ}\times 2.5^{\circ}$ grid. To ensure the robustness of our
analysis and to avoid confounding effects from long-term climate change, we
apply a linear detrending to all reanalysis datasets.

#### ENSO index

The ENSO state is obtained using the Multivariate ENSO index version 2 (MEIv2)
(Wolter and Timlin, 2011). The MEIv2 is a multivariate index that combines six
observed variables over the tropical Pacific Ocean to provide a comprehensive
measure of the ENSO state. The MEIv2 is available from the NOAA Physical
Sciences Laboratory (PSL) at https://psl.noaa.gov/enso/mei/ (Last Accessed:
10th April 2024).

#### BSISO index

The daily resolved BSISO index by Kikuchi et al. (2012) is taken from
https://iprc.soest.hawaii.edu/users/kazuyosh/Bimodal_ISO.html (Last Accessed:
10th May 2023). The first two leading principal components (PCs) are used to
define the state of the BSISO by the amplitude
$A=\sqrt{PC_{1}^{2}+PC_{2}^{2}}$, where $A\geq 1$ ($A<1$) is regarded as
active (inactive) (Wheeler and Hendon, 2004). The two-dimensional phase space
spanned by $PC_{1}$ and $PC_{2}$ is subdivided into eight equally sized
sections that denote the phase of the BSISO.

#### Tropical Easterly Jet index

We employ the index definition of Huang et al. (2019) to describe the
characteristics in terms of amplitude and variability of the TEJ for the
period from June through September. This index, denoted as Tropical Easterly
Jet Index (TEJI), is mathematically formalized as the mean anomaly time series
of the zonal winds ($u$) at the $200$ hPa pressure level, of locations in the
box within the interval [$0^{\circ}\,\mathrm{E},70^{\circ}\,\mathrm{E}$],
[$0^{\circ}\,\mathrm{N},15^{\circ}\,\mathrm{N}$] (magenta boxes in SI Fig.
S6). The metric of TEJI is computed by spatially averaging the $u$-wind
anomalies enclosed within these boxes. We define positive and negative phases
of the TEJI as events exceeding one standard deviation from the mean (below
for negative, above for positive; see SI Fig. S6).

#### PDO index

The Pacific Decadal Oscillation (PDO) is a long-term climate pattern that is
characterized by a positive and negative phase (Fig. S9). The PDO is known to
be connected with ENSO and influences the climate in the Indo-Pacific domain
and the North American continent (Di Lorenzo et al., 2023). The PDO index is
defined as the first EOF of the monthly SST anomalies in the North Pacific
Ocean. It is obtained from the NOAA Physical Sciences Laboratory (PSL) at
https://psl.noaa.gov/data/climateindices/list/ (Last Accessed: 26th April
2024).

###  2.2 Communities of Synchronous Extreme Rainfall Events

Figure 1: Schematic of the Community Detection approach. a The climate network
is constructed by mapping the data to a spatial grid of $N$ approximately
uniformly distributed points using the Fekete algorithm (Bendito et al.,
2007). For visualization purposes, only every $10$th grid point is plotted.
Dashed lines indicate the latitudinal range of the analysis
$[20^{\circ}\,\mathrm{S},60^{\circ}\,\mathrm{N}]$. b Every grid point is
associated with a precipitation time series. By thresholding locally at the
90th percentile ($Q_{0.9}$), we obtain binary event series ($Evs$). c The
Event Synchronization algorithm (Quian Quiroga et al., 2002) is employed to
evaluate the statistical dependencies between all pairs of time series (i.e. a
total of $N\times N$ comparisons). The time series and event series in b and c
are just for illustrative purposes. d The adjacency matrix $\mathbf{A}$ of the
network characterizes the linkages between nodes, delineating the network’s
underlying topology. Each black dot represents a statistically significant
synchronization between two nodes. Again, this matrix is for illustrative
purposes. e Communities within the climate network represent groups of nodes
characterized by stronger internal connectivity compared to their connections
with nodes outside the community. The communities are determined by
identifying blocks in the adjacency matrix $\mathbf{A}$ by using a
probabilistic community detection algorithm. f Multiple runs of the community
detection algorithm are performed to ensure the stability of the community
pattern. The membership likelihood of each node to a community is determined
by the number of times it is assigned to a specific community. Here it is
plotted for the community comprising North India (NI) and the Sahel Zone (SZ).
The hatched areas in e and f indicate regions with only few wet days, which
are excluded from the analysis.

The community detection approach is schematically visualized in Fig. 1. On a
regular (rectangular) grid, grid points are spatially closer together the
closer they are to the poles and therefore also more likely correlated. This
could cause biases in the community detection algorithm later (see Sec. 2.2).
To avoid these confounding correlation effects, we first map the data to a
grid of spatially approximately uniformly distributed points using nearest-
neighbor interpolation (Fig. 1 a) by employing the Fekete algorithm (Bendito
et al., 2007). For computational reasons, the distance between two points of
the new grid is set to around $111$ km, which corresponds to the spatial
distance between two points at the equator of a regular Gaussian $1^{\circ}$
grid, resulting in a total of approximately $9600$ grid points. We only
consider “wet days”, i.e., days with rainfall sum of at least 1 mm. To capture
the most intense rainfall events and analyze their characteristics, we
determine ERE days per location as those where the daily precipitation sum
exceeds the $0.9$th quantile ($Q_{0.9}(\cdot))$ of all wet days at that
specific location (Fig. 1 b).

We use climate networks to determine regions of significantly synchronously
occurring EREs. The climate network is constructed as follows: Let a
spatiotemporal dataset of rainfall time series be denoted as
$\mathbf{X}\in\mathbb{R}^{N\times T}$, where $N$ represents the spatial
locations and $T$ is the number of time points. The climate network is then
defined as $\mathcal{G}=(V,E)$, where each geographical location $i\in
1,\dots,N$ corresponds to a node $n_{i}\in V$, and is associated with the
rainfall time series $\vec{x}_{i}=x_{i,0},\dots,x_{i,T}\in\mathbf{X}$. $E$
represents the set of edges within the network. An edge between two nodes
$n_{i}$ and $n_{j}$ encodes a robust statistical dependence between the time
series $\vec{x}_{i}$ and $\vec{x}_{j}(t)$ labeled as edge $e_{ij}\in E$.

The Event Synchronization algorithm (Quian Quiroga et al., 2002) is employed
to evaluate the statistical dependencies as a measure of the synchronization
between all pairs of time series in the network Fig. 1 c). This method
involves counting concurrently occurring events within event sequences from
different locations, allowing a temporal gap – the so-called dynamical delay
$\tau$ – between events in these sequences to account for time deviations of
at most $10$ days (see SI Sec. SI 1). The synchronization strength between
locations is assessed by summing up synchronous time points across all event
pairs and their statistical significance is estimated using a null-model test.
The adjacency matrix $\mathbf{A}$ of a network characterizes the linkages
between nodes, delineating the network’s underlying topology. It is a
mathematical representation of these connections and captures the presence or
absence of links between nodes expressed as a $N\times N$ matrix, where
$A_{i,j}=1$ indicates that events at location $i$ are statistically
significantly followed by events at location $j$, implying that we place an
edge from node $n_{i}$ to $n_{j}$ and set $A_{i,j}=1$. For details, we refer
the reader to Sec. SI 1 or to the detailed descriptions in Malik et al.
(2010), Boers et al. (2014, 2019), Strnad et al. (2023).

Communities within the climate network represent groups of nodes characterized
by stronger internal connectivity compared to their connections with nodes
outside the community. Keeping in mind that the network is constructed based
on pairs of event series exhibiting significant synchronicity in the
occurrence of EREs, these communities correspond to spatial regions that can
span considerable geographical distances (Fig.1 e) and where the occurrence of
EREs in such cases is likely attributable to one (or even multiple) shared
underlying physical mechanism(s) (Strnad et al., 2023). Mathematically,
communities are determined by identifying blocks in the adjacency matrix
$\mathbf{A}$. Very common is an approach that uses a stochastic block model
(SBM). The SBM serves as a generative model for random graphs, generating
community structures - specifically, subsets of nodes referred to as “blocks”.
These exhibit distinct connectivity patterns, being connected with one another
at particular densities. The model implementation used in this work is the
network analysis package graph_tool (Peixoto, 2014b) favored for its
computational efficiency and its probabilistic output. Additionally, this
implementation can identify the optimal number of communities in the data
based on the principle of parsimony. For more in-depth details, we refer the
reader to Peixoto (2014a, 2019). As the community detection algorithm is
inherently probabilistic, we repeat it $100$ times and use the distribution of
different community detection outputs to quantify the membership likelihood of
spatial locations (Fig. 1 f). We define the membership likelihood as the
number of times a node is assigned to a specific community. For more details
on the community detection algorithm for climate networks, we refer the reader
to Strnad et al. (2023).

###  2.3 Lagged Synchronous Rainfall Index

We generalize the concept of the community-specific synchronous ERE index,
denoted as $SRI(t)$, introduced by Strnad et al. (2023), to assess for a
community its degree of synchronization over time for a specified delay
$\tau_{\text{lag}}$. The index is computed for a particular set of locations
$A$, describing one community within the network. For each time step $t$, we
count the number of EREs that occur in all event series $e_{n}$ in $A$ and are
followed by events in all event series $e_{m}$ in $B$ at a lag
$\tau_{\text{lag}}$:

$SRI_{\tau_{\text{lag}}}(t)=\sum_{n\in A}\sum_{n\in B}e_{n}(t)\cdot
e_{m}(t-\tau_{\text{lag}})\;.$ (1)

We further observe that the lag between synchronous events in $A$ and $B$ can
vary. Thus, we also count all synchronizations between $A$ and $B$ within a
certain range $[\tau_{\text{min}},\tau_{\text{max}}]$, by using eq. 1. The
synchronous rainfall index $SRI$ is estimated as:

$SRI(t)=\sum_{\tau=\tau_{\text{min}}}^{\tau_{\text{max}}}SRI_{\tau}(t)\;.$ (2)

This counting process enables us to quantify the frequency of EREs within a
set of locations $A$ that are followed by events in a set of locations $B$
within a range of possible lags. To further pinpoint the points in time of
exceptionally strong (lagged) synchronization, we identify the local maxima in
the time series $SRI$ that are above the 90th percentile and define these as
the most synchronous days (MSDs).

###  2.4 Latent Space Clustering of Propagation Pathways

Figure 2: Sketch of the latent space clustering. The propagation pathways are
clustered via traces in the latent space $z$. The high-dimensional input field
is transformed to a low-dimensional latent space which is denoted by the
encoder. In our case, the encoder function is based on a Multivariate
Principal Component Analysis (MV-PCA) on 200-hPa $u$ and $v$, 500-hPa vertical
velocity $\omega$ and 400-hPa relative humidity. Input fields,
$x(t_{1}),\dots,x(t_{n})$, for a propagation sample of $n$ consecutive time
steps are encoded to the latent space $z$ (displayed as black dots). These
build a trace in the latent space (visualized by connected lines). These
traces are clustered by a clustering algorithm, the clusters are visualized as
red and blue regions in the latent space. These correspond to the composite
anomaly maps of the input field in the original space.

To obtain meaningful clusters of the propagation pathways, we propose a
variation of latent space clustering, schematically visualized in Fig. 2, as
it was applied in, e.g., (Schlör et al., 2023). We initially employ empirical
orthogonal function (EOF) analysis, also known as principal component analysis
(PCA). This well-established technique is used for reducing the dimensionality
of spatiotemporal data, while retaining the largest possible fraction of its
original variance. A spatiotemporal field $x\in\mathbf{X}$ can consist of
multiple variables. At time $t$ a transformation, $z_{t}=e(x_{t})$, is applied
to map the high-dimensional space ,$\mathbb{R}^{N}$, to a lower-dimensional
space,$\mathbb{R}^{M}$, where $M\ll N$.

To cluster the dynamics of the propagation up to a lag of $+15$ days, we
compute the traces in the latent space $z$, where each sample $s$ concatenates
the steps in the latent space $z$ from day $0$ to day $+15$:
$s=\\{z_{0},z_{1},\ldots,z_{15}\\}$. Therefore, each sample $t$ is a vector of
length $15\times n_{EOFs}$, where $n_{EOFs}$ is the number of EOFs used for
the clustering. To select the EOFs that best represent the propagation
pathways, we consider the EOFs whose PCs have the highest correlation
coefficient with the lagged synchronous index $SRI(t)$ (eq. 2).

We employed the $k$-means clustering algorithm to cluster the traces in the
latent space $z$. To determine the optimal number of clusters, we utilized the
silhouette score (Rousseeuw, 1987).It measures the similarity of an object to
its own cluster compared to other clusters, ranging from -1 to 1. A high value
indicates a strong match to its cluster and a poor match to neighboring
clusters. A high average silhouette score across all samples indicates an
appropriate clustering configuration. We performed a grid search over the
number of clusters and EOFs, ranging from $2$ to $10$ clusters and $1$ to $10$
EOFs, in order to identify the optimal clustering configuration (see Sec. SI
4). Here, the best clustering is obtained for $2$ clusters and a single EOF
(SI Fig. S5).

###  2.5 Estimation of Conditional Probabilities

The probability for the occurrence of synchronous rainfall days within a set
of locations (denoted as $s=1$) under a condition, $a$, is calculated as
follows. Define the set of MSDs (i.e. days where we observe a high number of
synchronizations between North India and the Sahel, see Sec. 2.3) as $S$ and
the set of days that fulfill the condition $a$ as $A$. Then

$P(s=1|a)=\frac{P(s=1,a)}{P(a)}=\frac{||S\cap A||}{||A||}$

describes the conditional probability for synchronous events under condition
$a$. Here, $||\cdot||$ denotes the set cardinality and $S\cap A$ the
intersection of $S$ and $A$. Accordingly, the conditional probability for a
second condition $b$ with a set of days $B$ is computed as:

$P(s=1|a,b)=\frac{P(s=1,a,b)}{P(a,b)}=\frac{||S\cap A\cap B||}{||A\cap
B||}~{}.$ (3)

A corresponding null model is estimated by counting the days of maximum
synchronization $||S||$ divided by the total number of days. Therefore, by
construction, the null model is $\leq 0.1$ (as our threshold for defining the
MSDs was on the 0.9 quantile), and thus, the upper limit for the null model is
$P_{\mathrm{nullmodel}}(s=1)=0.1$.

##  3 Results

###  3.1 Lagged extreme rainfall synchronization between North India and the
Sahel

Figure 3: Synchronization pattern of extreme rainfalls between North India and
the Sahel. a Regions of statistically significant synchronization between
spatial locations are plotted according to their membership likelihood of
being in the community comprising NI (red contour) and SZ (green contour). The
communities are determined using a probabilistic hierarchical community
detection algorithm based on the Stochastic Block Model and overlaps of $100$
independent runs. Hatched areas indicate regions with few wet days, which are
excluded from the analysis. We find a community that comprises the regions of
North India (NI), East Asia (EA), and the Sahel Zone (SZ). The connection
between NI (red contours), SZ (green contours), and EA (magenta contours) is
investigated. b Lead-lag correlations in steps of days between time series
obtained from counting the number of extreme events of locations in the NI and
the SZ (green line) and NI and EA (magenta line). The dashed line indicates
the 95% confidence interval for a statistically significant correlation. The
maximum correlation occurs at a lag of $+12$ days (vertical solid line), i.e.
EREs in NI are followed by EREs in SZ by around 12 days, while the EREs in NI
and EA typically occur synchronously. c Interannual variability of the
synchronization between NI and SZ is investigated. The most synchronous days
(MSDs) are counted per year. The 75th (25th) percentile of years with the
highest (lowest) number of days identified as MSD are labeled as synchronous
(dry) years, marked by red (green) markers. d For the MSDs, we estimate the
distribution over the week of the year in the observation period from June to
September.

#### Pattern of the synchronization

We identify a distinct synchronization pattern encompassing North Asia; in
particular, North China, North India (NI) including the Indo-Gangetic Plain,
the Himalayan foothills, delineated by the Himalayan mountain chain, and the
Sahel Zone (SZ) bounded between the tropical rainforest and the Sahara desert
(Fig. 3 a). Our investigation focuses on exploring why the EREs manifest
synchronously (within a certain time range) over this large spatial region.
The regions are part of a “community” within the climate network constructed
by estimating patterns of simultaneously occurring extreme rainfall events of
a domain restricted to the tropics and boreal subtropics (see Sec. 2.2). The
high spatial coherence indicates that the community is a stable manifestation
of the synchronization pattern associated with synchronous EREs (Fig. S3). It
can be partly attributed to the Eurasian Wave Train associated with the Silk
Road pattern (Gupta et al., 2022). In the following, we thus focus on the
synchronization between North India (red contour in Fig. 3 a) and the Sahel
Zone (green contour in Fig. 3a).

#### Time lags of the synchronization

Synchronizations were observed to peak in strength at a time lag of around
$12$ days, on average, throughout boreal summer (June, July, August,
September) (Fig. 3 b). This typical time delay between EREs within the NI
region and the SZ locations is estimated by lead-lag correlation analysis. The
number of occurrences of synchronization patterns between NI and SZ is not
constant but varies substantially between different years (Fig. 3 c). We
obtain this yearly fluctuation by counting the number of MSDs per year. For
later reference, we define the top $25~{}\%$ as the synchronous years (red
markers in Fig. 3 c) and the lowest $25~{}\%$ as the least synchronous years
(green markers in Fig. 3 c). We also observe that the synchronization occurs
mainly during the core monsoon season from July through mid-August (Fig. 3 d).
The distribution over the JJAS period is estimated by the week of the year for
all identified MSDs. Therefore, hereafter we focus on synchronization events
in July and August, which we consider to be the background state under which
most synchronization happens. While the occurrence of synchronous events is
high mainly during July and August, coinciding with the period of highest
daily rainfall sums in India, there is still strong interannual variability
within these months.

#### Anomalous convection in the northwest of India

Figure 4: Convective anomalies in North India. Panel a shows composites of the
MSDs for the Outgoing Longwave Radiation (OLR) superimposed by the vertical
velocities $\omega$ at $400~{}$hPa (measured in Pa/s) by colored contours.
Orange solid (purple dashed) contours denote anomalously rising conditions for
regions with anomalies larger (smaller) than $3\,$Pa/s. Grey shading
represents the Himalayan mountains. Panel b (d) visualizes the zonal
(meridional) circulation averaged between
$20^{\circ}\,\mathrm{N}-30^{\circ}\,\mathrm{N}$
($70^{\circ}\,\mathrm{E}-80^{\circ}\,\mathrm{E}$), visualized by dashed
rectangles in a. All composites are computed for the conditions on Day 0.
Panels b,d are split into two parts: on top the meridionally (zonally)
averaged precipitation anomalies are displayed; on the bottom, the vertical
circulation is shown by composites of relative humidity anomalies (shading)
and wind fields (arrows). In a, b, d colored contours denote statistical
significance at a $95\%$ confidence level using a two-sided $t$-test. Grey
contours show the highest $10\%$ orography. The wind fields in the zonal
(meridional) circulation plots are estimated using the meridionally (zonally)
averaged $u$ ($v$) anomalies, measured in m s-1, and the vertical velocity
$\omega$ in the horizontal direction, measured in hPa s-1. Only statistically
significant arrows at a $95\%$ confidence level using a two-sided $t$-test are
shown. Panel c shows the condition probabilities (Sec. 2.5) of the most
synchronous days (MSDs) conditioned on active (inactive) BSISO phases marked
by blue (red) bars. The grey bars denote the likelihood of a respective null
model that randomly distributes the MSDs over the BSISO phases with respect to
the relative occurrence of each phase.

The synchronization is initiated by anomalously strong convection in northwest
India (Fig. 4 a). We observe two characteristics. Firstly, the anomalously
strong convection (Fig. 4) in the northwest also coincides with the locations
where the strongest rainfall occurs (Fig. 4 b,d) as is usually expected in the
tropics. Secondly, we also note a deepening of the monsoon trough for the band
of enhanced negative OLR anomalies at around $15^{\circ}\,\mathrm{N}$ (Fig. 4
a). We further observe a strong anomalous moistening of the upper atmosphere
in Fig. 4 b and d, as well as anomalous easterly zonal winds in the upper
atmosphere around $200~{}$hPa.

The anomalously strong convection in northwest India already suggests the
presence of the BSISO. An analysis based on conditional probabilities (see
Sec. 2.5) supports this impression and shows a substantially increased
likelihood for MSDs when the BSISO is in phases 6 and 7 (Fig. 4 c, SI Fig. S14
e). The convective band is thus likely to be associated with the active phase
of the BSISO, which is characterized by heavy rainfall (see e.g., Kikuchi et
al. (2012), Kiladis et al. (2014), Kikuchi (2021)).

Further, during the MSDs for both clusters, we observe an increased inflow of
moist air from the Arabian Sea via the cross-equatorial Somali Jet (Fig. S10
a, b). The Somali Jet is a major source of moisture during the ISM (Rai et
al., 2018). It is therefore consistent that the synchronization pattern is
mainly established during the core monsoon season (Fig. 3 c) when the Somali
Jet is most active. For dry years (green markers in Fig. 3 c), the
synchronization is less pronounced, and the enhanced Somali-Jet inflow
vanishes (Fig. S10 c), indicating that the moisture flux from the Arabian Sea
is crucial for the initiation of the synchronization. When this moisture flux
hits the western Himalayan mountains, it leads to forced deep convection (Fig.
4 a, b, d). The convection that initiates the synchronization is thus – at
least partially – forced by the orography.

###  3.2 Propagation pathways of the synchronization

Figure 5: Propagation for OLR and vertical velocity. We cluster the
propagation pathways based on the most synchronous days using the lagged
synchronous index (compare Fig. 3 b). The first column (panels a,c,e,f) shows
the first cluster of propagation pathways using OLR. The second column (panels
b,d,f,h) shows the second cluster. We create composite anomaly maps (estimated
with respect to the month of the year) for days 0 to +12 after initialization
of outgoing longwave radiation (OLR) in shading, overlapped by vertical
velocity $\omega$ at $400\,$hPa (measured in Pa/s) in black line contours.
Black solid (dashed) contours denote anomalously rising (sinking) air with
$\omega$ anomalies larger (smaller) than $2\,$Pa/s. For visual reasons,
composites are only shown in steps of $+4$ days, starting from day $0$.
Colored areas denote statistically significant values at $95~{}\%$ confidence
level.

The synchronization between North India and the Sahel Zone is not
instantaneous but lags by almost two weeks (Fig. 3 b). However, when
investigating individual years, we observe that the mean lag is not constant
but varies across years (SI Fig. S4). We thus investigate potential variations
in the diversity of the synchronization propagation pathways. From the
observation of the convective initiation and the vertical circulation plots
(Fig. 4), we expect that the propagation pathways are somehow driven by the
convective activity, the subsequent moistening of the upper atmosphere and
anomalous processes in the upper troposphere (around $200~{}$hPa). This
motivates the choice of the following variables for a multivariate PCA (MV-
PCA). We use vertical velocity $\omega$ at $500~{}$hPa as a proxy for
convective activity, relative humidity at $400$ hPa to account for the
moistening of the mid and upper troposphere and horizontal ($u$) and
horizontal ($v$) winds at $200~{}$hPa for the propagation. Where clusters of
consecutive days occur in the set of MSDs, we remove all but the first to
avoid including the same event more than once in our composite. The MV-PCA
helps to substantially reduce the dimensionality of the fields and to identify
the PCs of the OLR field that are associated with the synchronization (see
Sec. 2.4 for details).

We create a trace in the latent space of $15$ consecutive days for each time
point that is identified as an MSD. We use these traces as input features for
a $k$-means clustering algorithm. The clustering with the highest silhouette
score is obtained for $k=2$ clusters and $1$ EOF (Fig. 5). We thus find two
distinct clusters, and consistently, the years in which these clusters occur
are largely distinct from each other in terms of timing (Fig. 6 d). We observe
that the propagation of the negative OLR anomalies is accompanied by a strong
rising motion of the air in the mid-troposphere (Fig. 5 a-h). Composite
anomaly maps are computed for each cluster and each day in steps of $+3$ days
(Fig. 5) revealing two different propagation clusters:

  * •

Strong Propagation The first column in Fig. 5, demonstrates the propagation of
anomalous OLR in steps of 4 days, from day 0 to day 12. Note that negative OLR
anomalies often coincide with intense rainfall. We see a region of negative
OLR anomalies propagating from North India (NI) toward the Sahel Zone (SZ).
These are largely confined to NI and re-emerge later in the SZ. Strongly
anomalous OLR values over the full range of the SZ are observed from around
day $+8$ on (Fig. 5 e). The associated rainfall lags the rainfall in North
India by around $10-12$ days.

  * •

Weak Propagation The second column of Fig. 5 does not show a clear propagation
pattern and the anomalies over SZ are of reduced intensity. Substantially
different from the first cluster is not only the intensity but also the speed
of the propagation. This is reflected by strongly anomalous OLR values are
observed from around day $+10$ on (Fig. 5 g). The rainfall here lags the
rainfall in North India by around $+12-15$ days.

The clusters also exhibit different background conditions in the Indian Ocean
and the Western Pacific. While the first cluster shows persistent convective
anomalies over NI and parts of the Maritime Continent, the second cluster
reveals a developing pattern of reduced convection at NI, parts of the Arabian
Sea and around the equatorial Western Pacific (Fig. 5 h–l). However, as the
first cluster shows a more intense propagation and the number of samples in
cluster 0 is twice the number of samples in cluster 1, we suggest that the
first cluster is the main manifestation of the mechanism resulting in the
synchronization between NI and SZ, while the second cluster is a weaker
variation of the main mechanism. Further, given the smaller cluster size, we
cannot rule out that some reasonable fraction of events are not causally
connected but arise by chance. Therefore, in the following, we will focus on
the first cluster.

###  3.3 Background conditions favoring the ISM–WAM synchronization

Figure 6: Background SST states for latent cluster. a–c shows the sea surface
temperature (SST) background state conditions for the Strong Propagation (a)
and Weak Propagation (b). For comparison, conditions for years with few/no
synchronizations are also shown (c). Dotted areas indicate statistical
significance at $95~{}\%$ confidence level using Student’s $t$-test. Panel d
shows the distribution of days classified as Strong and Weak Propagation
alongside the PDO index (magenta line). The dotted vertical line indicates the
year 1986 after which the clustered propagation pathways match the PDO phases
quite well.

#### SST background state enhancing synchronization likelihood

We find that the background SST state shows distinct patterns for the two
clusters. The Strong Propagation cluster shows an anomalous cooling in the
central Pacific (Fig. 6 a) – a La Niña like pattern – and a band of
anomalously warm SSTs in the northwest Pacific at around
$40^{\circ}\,\mathrm{N}$, which is known as the Kuroshio-Oyashio extension (Di
Lorenzo et al., 2023, Joh et al., 2023). Together, these patterns in the
Pacific Ocean resemble the patterns of a negative phase of the Pacific Decadal
Oscillation (PDO) in JJAS (see Fig. S9). We find that starting from around
1986, the occurrences of samples that are clustered as Strong Propagation
(Weak Propagation) are well aligned with the negative (positive) phase of the
PDO (Fig. 6 d) even though the match is not perfect. The negative phase of the
PDO favors the occurrence of La Niña events (Di Lorenzo et al., 2023). La
Niña-like conditions lead to an anomalously wet monsoon season in North India
through modulating the Walker circulation (Xavier et al., 2007) and by
assisting the northward propagation of the BSISO towards the north of India
(Strnad et al., 2023). We additionally observe associated cool SSTs over the
Arabian Sea and the Bay of Bengal, which are probably due to the enhanced
convection over the region, i.e. cooling the surface through increased
insolation and precipitation. However, this might also be associated with a
negative Indian Ocean Dipole which is often dynamically linked to La Niña
events (Meyers et al., 2007, Cherchi and Navarra, 2013).

The second cluster does not show a strong SST pattern in the tropical Pacific
Ocean (Fig. 6 b). We identify a weak warming pattern in the Eastern Pacific
represented by anomalously warm SSTs in the Pacific Ocean (Fig. 6 b). However,
this pattern is less pronounced than the La Niña-like one, suggesting that the
La Niña background state provides an important intensification of the
synchronization, even if the synchronization can also occur without a La Niña
event. For years with only a few synchronizations, which we call dry years, we
identify a more pronounced El Niño-like pattern represented by anomalously
warm SSTs in the central equatorial Pacific Ocean (Fig. 6 c). This is
consistent with the observation that central Pacific El Niño events are more
often associated with a weakening of the Indian monsoon (Fan et al., 2017) and
thus also weakening the synchronization between North India and the Sahel.

#### Synchronization is guided by the Tropical Easterly Jet

Figure 7: Background states for propagation clusters. We visualize different
conditions for the samples of the days classified as most synchronous days
that were clustered by multivariate PCA (Fig. 5) into Strong Propagation
(first column) and Weak Propagation (second column). For comparison,
conditions for years with few/no synchronizations (see Fig. 3 c) are also
shown (third column). The first row (a–c) shows the composited zonal wind
anomalies at 200 hPa. The second row (g–i) is as the first row but for
meridional wind anomalies at 200 hPa. The third row (j–l) is also as the first
row but for geopotential height (GPH) anomalies with arrows representing the
horizontal wind anomalies at 200 hPa. All composited anomalies are computed
with respect to the month of the year. In all panels, colored areas imply
statistical significance at $95~{}\%$ confidence level using the Student’s
$t$-test and only statistically significant wind arrows are shown.

The composite wind field at $200$ hPa for the Strong Propagation cluster shows
an established corridor that zonally connects the area around the Yellow River
Basin with North India and SZ (Fig. 7 a). The flow is guided by the orography
of the Tibetan Plateau and the pattern is especially prominent to the south of
the Tibetan Plateau. These patterns resemble the characteristics of an
enhanced TEJ (Fig. S6). The enhancement is likely a result of the La Niña-like
conditions (Fig. 6 a) and the associated Walker circulation response. Induced
by La Niña, there is anomalous heating over the Tibetan Plateau (Duan et al.,
2012). The subsequent anomalous meridional temperature gradient leads to a
strengthening of the TEJ core position over the Indian Ocean (Fig 7 a; also
Nithya et al., 2017). Further evidence is provided by the spatial correlation
patterns obtained by correlating the 200-hPa zonal wind, 200-hPa meridional
wind, and 500-hPa vertical velocity respectively with the lagged synchronous
index (see eq.1). The correlation pattern resembles the structure of the
tropical easterly jet (Nicholson and Klotter, 2021) (see also SI Fig. S6). The
pattern of an enhanced TEJ is not visible for the Weak Propagation cluster
(Fig. 7 b). Here, the zonal winds are only moderately enhanced over the
equatorial Indian Ocean. In dry years, the zonal wind field is not enhanced
over the Indian Ocean and the Bay of Bengal (Fig. 7 c). On the contrary, the
pattern resembles a weakened TEJ (Fig. S6 b), which can be explained by the El
Niño-like SST pattern (Fig. 6 c).

The 200-hPa meridional wind anomalies for composited time points of the Strong
Propagation cluster (Fig. 7 d) show a large-scale wave train pattern (Fig. 7
g) ranging from Japan to North India. The ridge in Fig. 7 d is guided by an
anticyclone-cyclone-anticyclone (A-C-A) circulation pattern. We observe these
as a subtropical anticyclone near Japan (Fig. 7 j) occurring together with an
anomalous high known as the Bonin high, a cyclone-like structure over the
South of China and anticyclone over the Himalayans, suggesting a relationship
with the Silk Road Pattern (Enomoto et al., 2003). The positive CGT drives
southwesterlies into the northwest and north of India (Fig. 7 g), which brings
additional moisture from the Arabian Sea. At the local-synoptic level, this is
similar to the Western disturbances (WD)-tropical storm interactions (Hunt et
al., 2021). This wave train pattern reduces to weak northerly anomalies in the
second cluster (Fig. 7 e) and vanishes altogether for dry years (Fig. 7 f).

#### Combination of processes initiating the synchronization

Figure 8: Probabilities for the occurrence of synchronization conditioned on
BSISO phases, ENSO and TEJ. a-f Most synchronous days (MSDs) are defined using
the $0.9$ quantile to ensure a robust sample size of possible events (Fig. 3
b) when using the lagged synchronous index (compare Fig. 3 d). Their
probability of occurrence is conditioned on the state of the Boreal Summer
Intraseasonal Oscillation (BSISO), the Tropical easterly jet (TEJ), and the
respective phase of the El Niño Southern Oscillation (ENSO) for the respective
time points computed as in eq: 3. Blue (red) bars indicate an active
(inactive) BSISO state conditioned on the state of ENSO and the TEJ. Grey bars
denote the respective null model, i.e. MSDs are assigned randomly to days in
the JJAS season and assigned to the distribution of BSISO phases.

Taken together, the initiation of the synchronization mechanism can be
attributed to a threefold process: Firstly, a negative PDO phase favors La
Niña conditions (Fig.6a), promoting deep convection over peninsular India,
facilitated by the anomalous Walker circulation response (Fig.4b). Secondly,
this response supports the progression of the BSISO towards northwest India
(Fig. 4 a), substantially enhancing the frequency of deep convection there.
Thirdly, La Niña-like conditions also enhance the TEJ (Fig. 7 d, SI Fig. S7).
We can provide strong statistical evidence for the importance of these three
factors coming together. By estimating conditional probabilities (eq. 3) for
the occurrence of MSDs, conditioned on the three impacting factors BSISO, ENSO
and the TEJ (see Sec. 2.1), we observe that the conditional probabilities for
a day in JJAS being a MSD conditioned on La Niña, TEJ, as well as an active
BSISO phase is substantially enhanced (Fig. 8). For a reduced TEJ we observe
hardly any synchronizations, even if the BSISO is active and La Niña
conditions are present (Fig. 8 b,d,f) emphasizing the necessary rolethe TEJ
play in the propagation.

This is further supported by the observation that the pattern of anomalously
negative OLR in Fig. 4 a occurs further north than in the full composites for
BSISO phases 6 and 7 (SI Fig. S14), whereas the subset of points in La Niña
years together with enhanced TEJ in BSISO phases 6 and 7 (Fig. S15 e,f) shows
greater similarity to the composite MSD map (Fig. 4 a).

The combination of these factors results in an increased presence of upper-
level moisture and a stronger TEJ. The enhanced BSISO pushes moisture further
north and northwest towards Pakistan. In this region, the dry static stability
is very low, and anomalous moisture readily triggers convection. In
consequence, we observe a significantly increased moistening of the middle to
upper atmosphere from $500~{}$hPa to $200~{}$hPa (Fig. 4 b).

###  3.4 Mechanism driving precipitation in the Sahel Zone

Figure 9: Composite thermodynamic structure for synchronized EREs over the
Sahel. Conditions for the MSDs of the Strong propagation cluster are shown.
The first column shows the zonal circulation averaged over
$10^{\circ}\,\mathrm{N}-18^{\circ}\,\mathrm{N}$, while the second column shows
the meridional circulation, averaged over
$10^{\circ}\,\mathrm{E}-20^{\circ}\,\mathrm{E}$. The first row shows the
conditions on Day 0 and the second row shows the average for days 10–12, which
are the days of the strongest synchronizations (see Fig. S3 b). Each subplot
consists of two panels. The top panel shows the meridionally (zonally)
averaged precipitation anomalies (with respect to the month). The bottom panel
shows the vertical structure of the circulation in arrows and the filled
contours show relative humidity anomalies. Grey contours show the orography.
The wind fields in the zonal (meridional) circulation plots are estimated
using the meridionally (zonally) averaged $u$ ($v$) anomalies, measured in m
s-1, and the vertical velocity $\omega$ in the horizontal direction, measured
in Pa s-1. Only statistically significant wind arrows at a $95\,\%$ confidence
level using a two-sided $t$-test are shown.

Our results indicate that the anomalous deep convection over NI (Fig. 4 b,c)
leads to anomalous moistening of the mid- and upper-troposphere, centered at
around $400~{}$hPa, that is then transported towards SZ via the TEJ. The TEJ
is also enhanced further southwest of NI such that the propagation over the
Arabian Sea and the Sahel Zone is guided by an anomalously strong flow of
easterly winds (Fig. 7 d,j). We applied a Lagrangian trajectory analysis
(Sprenger and Wernli, 2015) to investigate the number of days it takes to
transport the moist anomalies from NI to SZ (see SI Sec. SI 12, Fig. S17). The
analysis confirmed that the moist anomaly takes around 6–9 days to arrive over
SZ, consistent with the propagation pathways in Fig. 5 a-e.

For timepoints around day 0, we observe a weak orographic forcing over the
Ethiopian Highlands and the western coast (Fig. 9). We also see an enhancement
of the TEJ over the Sahel (Fig. S12 a) but there is no substantial increase in
moisture at around $400~{}$hPa (Fig. 9 a,b). These patterns change around 1–2
days after the arrival of the anomalous moisture in the upper troposphere. We
now observe anomalous heavy rainfall over the Sahel (Fig. 9 c,d). The rainfall
extends over the full zonal and meridional range of the Sahel from
$-5^{\circ}\,\mathrm{E}-40^{\circ}\,\mathrm{E}$;
$5^{\circ}\,\mathrm{N}-15^{\circ}\,\mathrm{N}$ with two peaks in intensity,
one is over the Ethiopian Highlands, one over the Northwest African coast
(Fig. 9 c). Composites of Strong Propagation MSDs show only marginally
enhanced intensity at the region of the upper-level TEJ at $200\,$hPa (compare
the zonal circulation at day 0, Fig. 9 a, with day +12, Fig. 9 c). The upper-
level westerlies do not vary substantially with respect to the climatology,
consistent with (Lemburg et al., 2019). Instead, anomalous moistening happens
from near the surface up to about $400~{}$hPa (Fig. 9 c,d). Hence, it is not
the local variability of the TEJ on weekly to subseasonal timescales that
modulates the Sahel rainfall; rather its variability on interannual
timescales. The strength of the teleconnection also, therefore, does not
depend on the local strength but the positioning of the TEJ.

Already at day 0, we find weak anomalous orographic forcing over the Ethiopian
Highlands but further moisture incursion is restricted by the Simien Mountains
(around $40^{\circ}\,\mathrm{E}$ in Fig. 9 a). However, as we see on day +12,
the upper-tropospheric moisture anomalies can readily pass over this mountain
chain barrier, carried by the TEJ (Fig. 9 c). The anomalous moisture in the
east ($>45^{\circ}\,\mathrm{E}$) is transported towards the west and the north
of the Sahel Zone (Fig. 9 c,d). At this stage the center of the composite deep
convection is around $20^{\circ}\,\mathrm{E}$ and $15^{\circ}\,\mathrm{N}$
(Fig. 5 e, SI Fig. S12).

The meridional cross-section on day 12 (Fig. 9 d) shows an overturning
circulation, where convection occurs slightly off the equator at around
$10^{\circ}\,\mathrm{N}$ and is extremely deep, extending to the tropopause.
This circulation overturns and leads to subsidence at both
$5^{\circ}\,\mathrm{N}$ and $15^{\circ}\,\mathrm{N}$. The anomalous moisture
brought to the mid- and upper-troposphere above the SZ by the TEJ leads to
deep instability in a region already characterized by widespread convection
during this time of year. Further, the anomalous upper-level moisture supports
sustained deep convection by reducing dry entrainment, ultimately leading to
heavier widespread precipitation. There is also a positive feedback, with the
overturning circulation facilitating convergence in the lower levels, leading
to the observed increase in near-surface humidity. In particular, we observe
enhanced integrated vapor transport (IVT) influx driven by the increased
convective activity (Fig. S10), which brings additional moisture from the
Atlantic Ocean into the continent at levels around $900~{}$hPa (Fig. 9 c, Fig.
S11).

##  4 Discussion

We have identified and explained a teleconnection pattern linking extreme
rainfall events (EREs) on a continental scale between North India as part of
the ISM and the Sahel Zone as part of the WAM. We first demonstrated that the
synchronization pattern of EREs between North India and the Sahel Zone is a
robust feature of the boreal summer monsoon system. The synchronization
pattern is not a statistical artifact but is rather driven by anomalous large-
scale atmospheric circulation, supported by the background state of the
climate system. Our work provides a physical explanation for the
teleconnection between the Asian and the African Monsoon domains.

We find that the synchronization is initiated by anomalously strong convection
in the northwest of India, which is associated with an enhanced active phase
of the BSISO. During La Niña conditions there is typically a stronger South
Asian monsoon (via the Walker circulation) and, driven by the BSISO, it is
more likely for EREs to arise in northwest India (Strnad et al., 2023).
Importantly, these EREs substantially moisten the upper troposphere over NI
via detrainment associated with deep convection. Subsequently, the anomalous
upper-level moisture is advected over the Arabian Sea and Sahel by the TEJ –
itself strengthened by La Niña conditions. Moist air aloft over the Sahel
provides conditions that are then favorable for supporting and sustaining deep
convection (and hence EREs) there. Hence, the strength of this teleconnection
depends on the positioning of the TEJ and not on its regional intensity over
SZ.

While prior investigations have provided detailed insights into intraseasonal
precipitation variability at a regional level in North India (Malik et al.,
2010, Stolbova et al., 2014, Boers et al., 2019, Hunt et al., 2021, Hunt and
Turner, 2022) and parts of the Sahel (Gleixner et al., 2017, Lemburg et al.,
2019, Vashisht et al., 2021), our study integrates and consolidates these
findings into a broader context. This synthesis enhances our comprehension of
the underlying physical mechanisms, thereby holding the potential to enhance
seasonal and sub-seasonal forecasts using windows of opportunities (Mariotti
et al., 2020) during boreal summer in the tropical monsoon domain.

Still, some open questions remain. Firstly, the propagation pathway shown in
this study was uncovered by using OLR as a proxy for intense rainfall. OLR has
the advantage of being directly measurable and therefore a reliable variable.
However, it is not a direct measure of precipitation. Secondly, the local
causes of the enhanced rainfall in the Sahel Zone remain unclear. Deep
convective precipitation over the SZ relies on the interaction of several
complex processes, including interactions of mesoscale convective systems with
the East African Jet at around $600~{}$hPa and the TEJ. Thirdly, the role of
the CGT in the synchronization between North India and the Sahel Zone is not
fully understood. We find some patterns indicating a partial modulation by the
CGT, but its effect seems to be minor. Further, future research could better
investigate the Weak Propagation propagation cluster. As the previous analysis
suggests that the Strong Propagation is the dominant process, the Weak
Propagation could be a combination of multiple and presumably more local
interactions.

There are multiple ways to extend this work. One first step would be to test
the occurrence of the synchronization pattern in current general circulation
models (GCMs). On the one hand, an analysis of the teleconnection pattern in
GCMs could provide insights into the robustness of the synchronization
pattern. On the other hand, as precipitation dynamics and teleconnections are
not always well reproduced in the current GCMs (Boyle and Klein, 2010, Hess et
al., 2022, Douville et al., 2023), the comparison could help to identify
potential biases in the models. Another next step could be to integrate the
knowledge about the uncovered teleconnection in current operational forecast
systems. Of particular interest will be the representation of these
synchronizations in deep learning global forecasts (Lam et al., 2023, Bi et
al., 2023, Lessig et al., 2023), which are better capable of capturing complex
non-linear relationships in the data.

## Data Availability

Precipitation data was taken from the MSWEP dataset
(https://www.gloh2o.org/mswep)Beck et al. (2019b). Datasets for the composite
analysis from 1979 till date were taken from Copernicus Climate Change Service
(C3S) (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-
era5-pressure-levels?tab=overview) Hersbach et al. (2018). Plots were
generated using the Cartopy library Met Office (2010 - 2015).

## Code Availability

The code for generating and analyzing the networks is made publicly available
under Strnad and Schlör (2023). The analysis uses the geoutils package
(Strnad, 2023). The code for reproducing the analysis of the network
communities and the data analysis in this paper is publicly available under
Strnad (2024). Plots were generated using the Cartopy (Met Office, 2010 -
2015) and the Metpy v1.6 libraries (May et al., 2022).

## Acknowledgements

F.S. and B.G. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy - EXC number
2064/1 - Project number 390727645. F.S. thanks the International Max Planck
Research School for Intelligent Systems (IMPRS-IS) for supporting his PhD
program. N.B. acknowledges funding by the Volkswagen Foundation, the European
Union’s Horizon 2020 research and innovation program under the Marie
Sklodowska-Curie grant agreement No. 956170, as well as from the European
Union’s Horizon Europe research and innovation program under grant agreement
No. 101137601. K.M.R.H. is supported by a NERC Independent Research Fellowship
(MITRE; NE/W007924/1).

## Author’s contribution

F.S. and B.G. conceived and designed the study. F.S. conducted the analysis.
F.S. and B.G. prepared the manuscript. F.S., K.M.R.H., N.B., and B.G.
discussed the results and edited the manuscript.

## Competing Interests

The authors declare that they have no competing interests.

## References

  * Beck et al. (2019a) H. E. Beck, M. Pan, T. Roy, G. P. Weedon, F. Pappenberger, A. I. J. M. van Dijk, G. J. Huffman, R. F. Adler, and E. F. Wood.  Daily evaluation of 26 precipitation datasets using Stage-IV gauge-radar data for the CONUS.  _Hydrol. Earth Syst. Sci._ , 23(1):207–224, Jan. 2019a.  ISSN 1027-5606.  doi:10.5194/hess-23-207-2019.
  * Beck et al. (2019b) H. E. Beck, E. F. Wood, M. Pan, C. K. Fisher, D. G. Miralles, A. I. J. M. van Dijk, T. R. McVicar, and R. F. Adler.  MSWEP V2 Global 3-Hourly 0.1° Precipitation: Methodology and Quantitative Assessment.  _Bull. Am. Meteorol. Soc._ , 100(3):473–500, Mar 2019b.  ISSN 0003-0007.  doi:10.1175/BAMS-D-17-0138.1.
  * Bendito et al. (2007) E. Bendito, A. Carmona, A. M. Encinas, and J. M. Gesto.  Estimation of Fekete points.  _J. Comput. Phys._ , 225(2):2354–2376, Aug 2007.  ISSN 0021-9991.  doi:10.1016/j.jcp.2007.03.017.
  * Beverley et al. (2019) J. D. Beverley, S. J. Woolnough, L. H. Baker, S. J. Johnson, and A. Weisheimer.  The northern hemisphere circumglobal teleconnection in a seasonal forecast model and its relationship to European summer forecast skill.  _Clim. Dyn._ , 52(5):3759–3771, Mar. 2019.  ISSN 1432-0894.  doi:10.1007/s00382-018-4371-4.
  * Beverley et al. (2021) J. D. Beverley, S. J. Woolnough, L. H. Baker, S. J. Johnson, A. Weisheimer, and C. H. O’Reilly.  Dynamical mechanisms linking Indian monsoon precipitation and the circumglobal teleconnection.  _Clim. Dyn._ , 57(9):2615–2636, Nov. 2021.  ISSN 1432-0894.  doi:10.1007/s00382-021-05825-6.
  * Bi et al. (2023) K. Bi, L. Xie, H. Zhang, X. Chen, X. Gu, and Q. Tian.  Accurate medium-range global weather forecasting with 3D neural networks.  _Nature_ , 619:533–538, July 2023.  ISSN 1476-4687.  doi:10.1038/s41586-023-06185-3.
  * Boers et al. (2014) N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths, and J. A. Marengo.  Prediction of extreme floods in the eastern Central Andes based on a complex networks approach.  _Nat. Commun._ , 5(5199):1–7, Oct 2014.  ISSN 2041-1723.  doi:10.1038/ncomms6199.
  * Boers et al. (2019) N. Boers, B. Goswami, A. Rheinwalt, B. Bookhagen, B. Hoskins, and J. Kurths.  Complex networks reveal global pattern of extreme-rainfall teleconnections.  _Nature_ , 566(7744):373–377, feb 2019.  ISSN 0028-0836.  doi:10.1038/s41586-018-0872-x.  URL http://www.nature.com/articles/s41586-018-0872-x.
  * Bordoni and Schneider (2008) S. Bordoni and T. Schneider.  Monsoons as eddy-mediated regime transitions of the tropical overturning circulation.  _Nat. Geosci._ , 1:515–519, Aug. 2008.  ISSN 1752-0908.  doi:10.1038/ngeo248.
  * Boyle and Klein (2010) J. Boyle and S. A. Klein.  Impact of horizontal resolution on climate model forecasts of tropical precipitation and diabatic heating for the TWP-ICE period.  _J. Geophys. Res. Atmos._ , 115(D23), Dec. 2010.  ISSN 0148-0227.  doi:10.1029/2010JD014262.
  * Cherchi and Navarra (2013) A. Cherchi and A. Navarra.  Influence of ENSO and of the Indian Ocean Dipole on the Indian summer monsoon variability.  _Clim. Dyn._ , 41(1):81–103, July 2013.  ISSN 1432-0894.  doi:10.1007/s00382-012-1602-y.
  * Di Capua et al. (2020) G. Di Capua, M. Kretschmer, R. V. Donner, B. van den Hurk, R. Vellore, R. Krishnan, and D. Coumou.  Tropical and mid-latitude teleconnections interacting with the Indian summer monsoon rainfall: a theory-guided causal effect network approach.  _Earth Syst. Dyn._ , 11(1):17–34, Jan. 2020.  ISSN 2190-4979.  doi:10.5194/esd-11-17-2020.
  * Di Lorenzo et al. (2023) E. Di Lorenzo, T. Xu, Y. Zhao, M. Newman, A. Capotondi, S. Stevenson, D. J. Amaya, B. T. Anderson, R. Ding, J. C. Furtado, Y. Joh, G. Liguori, J. Lou, A. J. Miller, G. Navarra, N. Schneider, D. J. Vimont, S. Wu, and H. Zhang.  Modes and Mechanisms of Pacific Decadal-Scale Variability.  _Annu. Rev. Mar. Sci._ , (Volume 15, 2023):249–275, Jan. 2023.  doi:10.1146/annurev-marine-040422-084555.
  * Dijkstra et al. (2019) H. A. Dijkstra, E. Hernández-García, C. Masoller, and M. Barreiro.  _Networks in Climate_.  Cambridge University Press, Cambridge, England, UK, Feb. 2019.  ISBN 978-1-31627575-7.  doi:10.1017/9781316275757.
  * Ding and Wang (2005) Q. Ding and B. Wang.  Circumglobal Teleconnection in the Northern Hemisphere Summer.  _J. Clim._ , 18(17):3483–3505, Sept. 2005.  ISSN 0894-8755.  doi:10.1175/JCLI3473.1.
  * Ding and Wang (2007) Q. Ding and B. Wang.  Intraseasonal Teleconnection between the Summer Eurasian Wave Train and the Indian Monsoon.  _J. Clim._ , 20(15):3751–3767, Aug. 2007.  ISSN 0894-8755.  doi:10.1175/JCLI4221.1.
  * Douville et al. (2023) H. Douville, K. Raghavan, J. Renwick, R. Allan, P. Arias, M. Barlow, R. Cerezo-Mota, A. Cherchi, T. Gan, J. Gergis, D. Jiang, A. Khan, W. P. Mba, D. Rosenfeld, J. Tierney, , O. Zolina, and . W. C. Changes.  _Water Cycle Changes_ , pages 1055–1210.  Cambridge University Press, 2023.  doi:10.1017/9781009157896.010.
  * Duan et al. (2012) A. Duan, G. Wu, Y. Liu, Y. Ma, and P. Zhao.  Weather and climate effects of the Tibetan Plateau.  _Adv. Atmos. Sci._ , 29(5):978–992, Sept. 2012.  ISSN 1861-9533.  doi:10.1007/s00376-012-1220-y.
  * Enomoto et al. (2003) T. Enomoto, B. J. Hoskins, and Y. Matsuda.  The formation mechanism of the Bonin high in August.  _Q. J. R. Meteorolog. Soc._ , 129(587):157–178, Jan. 2003.  ISSN 0035-9009.  doi:10.1256/qj.01.211.
  * Fan et al. (2017) F. Fan, X. Dong, X. Fang, F. Xue, F. Zheng, and J. Zhu.  Revisiting the relationship between the South Asian summer monsoon drought and El Niño warming pattern.  _Atmos. Sci. Lett._ , 18(4):175–182, Apr. 2017.  ISSN 1530-261X.  doi:10.1002/asl.740.
  * Findlater (1969) J. Findlater.  A major low-level air current near the Indian Ocean during the northern summer.  _Q. J. R. Meteorolog. Soc._ , 95(404):362–380, Apr. 1969.  ISSN 0035-9009.  doi:10.1002/qj.49709540409.
  * Geen et al. (2020) R. Geen, S. Bordoni, D. S. Battisti, and K. Hui.  Monsoons, ITCZs, and the Concept of the Global Monsoon.  _Rev. Geophys._ , 58(4):e2020RG000700, Dec. 2020.  ISSN 8755-1209.  doi:10.1029/2020RG000700.
  * Gleixner et al. (2017) S. Gleixner, N. Keenlyside, E. Viste, and D. Korecha.  The El Niño effect on Ethiopian summer rainfall.  _Clim. Dyn._ , 49(5):1865–1883, Sept. 2017.  ISSN 1432-0894.  doi:10.1007/s00382-016-3421-z.
  * Gupta et al. (2022) S. Gupta, Z. Su, N. Boers, J. Kurths, N. Marwan, and F. Pappenberger.  Interconnection between the Indian and the East Asian Summer Monsoon: spatial synchronization patterns of extreme rainfall events.  _Int. J. Climatol._ , n/a(n/a), Sept. 2022.  ISSN 0899-8418.  doi:10.1002/joc.7861.
  * Halpern and Woiceshyn (2001) D. Halpern and P. M. Woiceshyn.  Somali Jet in the Arabian Sea, El Niño, and India Rainfall.  _J. Clim._ , 14(3):434–441, Feb. 2001.  ISSN 0894-8755.  doi:10.1175/1520-0442(2001)014<0434:SJITAS>2.0.CO;2.
  * Hersbach et al. (2018) H. Hersbach, B. Bell, P. Berrisford, G. Biavati, A. Horányi, J. Muñoz Sabater, J. Nicolas, C. Peubey, R. Radu, I. Rozum, D. Schepers, A. Simmons, C. Soci, D. Dee, and J.-N. Thépaut.  Era5 hourly data on single levels from 1979 to present, 2018.  Accessed on 02-03-2022.
  * Hersbach et al. (2020) H. Hersbach, B. Bell, P. Berrisford, S. Hirahara, A. Horányi, J. Muñoz-Sabater, J. Nicolas, C. Peubey, R. Radu, D. Schepers, A. Simmons, C. Soci, S. Abdalla, X. Abellan, G. Balsamo, P. Bechtold, G. Biavati, J. Bidlot, M. Bonavita, G. De Chiara, P. Dahlgren, D. Dee, M. Diamantakis, R. Dragani, J. Flemming, R. Forbes, M. Fuentes, A. Geer, L. Haimberger, S. Healy, R. J. Hogan, E. Hólm, M. Janisková, S. Keeley, P. Laloyaux, P. Lopez, C. Lupu, G. Radnoti, P. de Rosnay, I. Rozum, F. Vamborg, S. Villaume, and J. N. Thépaut.  The ERA5 global reanalysis.  _Quarterly Journal of the Royal Meteorological Society_ , 146(730):1999–2049, 2020.  ISSN 1477870X.  doi:10.1002/qj.3803.
  * Hess et al. (2022) P. Hess, M. Drüke, S. Petri, F. M. Strnad, and N. Boers.  Physically constrained generative adversarial networks for improving precipitation fields from Earth system models.  _Nat. Mach. Intell._ , 4:828–839, Oct. 2022.  ISSN 2522-5839.  doi:10.1038/s42256-022-00540-1.
  * Huang et al. (2019) S. Huang, Z. Wen, Z. Chen, X. Li, R. Chen, and Y. Guo.  Interdecadal change in the relationship between the tropical easterly jet and tropical sea surface temperature anomalies in boreal summer.  _Clim. Dyn._ , 53(3):2119–2131, Aug. 2019.  ISSN 1432-0894.  doi:10.1007/s00382-019-04801-5.
  * Huang et al. (2021) S. Huang, B. Wang, Z. Wen, and Z. Chen.  Enhanced Tropical Eastern Indian Ocean Rainfall Breaks Down the Tropical Easterly Jet–Indian Rainfall Relationship.  _J. Clim._ , 34(8):3039–3048, Apr. 2021.  ISSN 0894-8755.  doi:10.1175/JCLI-D-20-0631.1.
  * Hunt and Turner (2022) K. M. R. Hunt and A. G. Turner.  Nonlinear intensification of monsoon low pressure systems by the BSISO.  _Weather and Climate Dynamics Discussions_ , pages 1–28, June 2022.  doi:10.5194/wcd-2022-31.
  * Hunt et al. (2021) K. M. R. Hunt, A. G. Turner, and R. K. H. Schiemann.  How Interactions between Tropical Depressions and Western Disturbances Affect Heavy Precipitation in South Asia.  _Mon. Weather Rev._ , 149(6):1801–1825, June 2021.  ISSN 1520-0493.  doi:10.1175/MWR-D-20-0373.1.
  * Joh et al. (2023) Y. Joh, T. L. Delworth, A. T. Wittenberg, X. Yang, A. Rosati, N. C. Johnson, and L. Jia.  The role of upper-ocean variations of the Kuroshio-Oyashio Extension in seasonal-to-decadal air-sea heat flux variability.  _npj Clim. Atmos. Sci._ , 6(123):1–11, Aug. 2023.  ISSN 2397-3722.  doi:10.1038/s41612-023-00453-9.
  * Kikuchi (2021) K. Kikuchi.  The Boreal Summer Intraseasonal Oscillation (BSISO): A Review.  _Journal of the Meteorological Society of Japan. Ser. II_ , pages 2021–045, Mar. 2021.  ISSN 0026-1165.  doi:10.2151/jmsj.2021-045.
  * Kikuchi et al. (2012) K. Kikuchi, B. Wang, and Y. Kajikawa.  Bimodal representation of the tropical intraseasonal oscillation.  _Clim. Dyn._ , 38(9):1989–2000, May 2012.  ISSN 1432-0894.  doi:10.1007/s00382-011-1159-1.
  * Kiladis et al. (2014) G. N. Kiladis, J. Dias, K. H. Straub, M. C. Wheeler, S. N. Tulich, K. Kikuchi, K. M. Weickmann, and M. J. Ventrice.  A Comparison of OLR and Circulation-Based Indices for Tracking the MJO.  _Mon. Weather Rev._ , 142(5):1697–1715, May 2014.  ISSN 1520-0493.  doi:10.1175/MWR-D-13-00301.1.
  * Koteswaram (1958) P. Koteswaram.  The Easterly Jet Stream in the Tropics$\ast$.  _Tellus_ , Jan. 1958.  ISSN 1180-5694.  URL https://www.tandfonline.com/doi/abs/10.3402/tellusa.v10i1.9220.
  * Kotz et al. (2022) M. Kotz, A. Levermann, and L. Wenz.  The effect of rainfall changes on economic production.  _Nature_ , 601:223–227, Jan. 2022.  ISSN 1476-4687.  doi:10.1038/s41586-021-04283-8.
  * Kumar et al. (2006) K. K. Kumar, B. Rajagopalan, M. Hoerling, G. Bates, and M. Cane.  Unraveling the Mystery of Indian Monsoon Failure During El Niño.  _Science_ , 314(5796):115–119, Oct. 2006.  ISSN 0036-8075.  doi:10.1126/science.1131152.
  * Lam et al. (2023) R. Lam, A. Sanchez-Gonzalez, M. Willson, P. Wirnsberger, M. Fortunato, F. Alet, S. Ravuri, T. Ewalds, Z. Eaton-Rosen, W. Hu, A. Merose, S. Hoyer, G. Holland, O. Vinyals, J. Stott, A. Pritzel, S. Mohamed, and P. Battaglia.  Learning skillful medium-range global weather forecasting.  _Science_ , 382(6677):1416–1421, Dec. 2023.  ISSN 0036-8075.  doi:10.1126/science.adi2336.
  * Lee et al. (2013) J.-Y. Lee, B. Wang, M. C. Wheeler, X. Fu, D. E. Waliser, and I.-S. Kang.  Real-time multivariate indices for the boreal summer intraseasonal oscillation over the Asian summer monsoon region.  _Clim. Dyn._ , 40(1):493–509, Jan. 2013.  ISSN 1432-0894.  doi:10.1007/s00382-012-1544-4.
  * Lemburg et al. (2019) A. Lemburg, J. Bader, and M. Claussen.  Sahel Rainfall–Tropical Easterly Jet Relationship on Synoptic to Intraseasonal Time Scales.  _Mon. Weather Rev._ , 147(5):1733–1752, May 2019.  ISSN 1520-0493.  doi:10.1175/MWR-D-18-0254.1.
  * Lessig et al. (2023) C. Lessig, I. Luise, B. Gong, M. Langguth, S. Stadtler, and M. Schultz.  AtmoRep: A stochastic model of atmosphere dynamics using large scale representation learning.  _arXiv_ , Aug. 2023.  doi:10.48550/arXiv.2308.13280.
  * Madhu (2014) V. Madhu.  Variation of Zonal Winds in the Upper Troposphere and Lower Stratosphere in Association with Deficient and Excess Indian Summer Monsoon Scenario.  _Atmospheric and Climate Sciences_ , 4(4):685–695, Aug. 2014.  doi:10.4236/acs.2014.44062.
  * Malik et al. (2010) N. Malik, N. Marwan, and J. Kurths.  Spatial structures and directionalities in Monsoonal precipitation over South Asia.  _Nonlinear Processes Geophys._ , 17(5):371–381, Sep 2010.  ISSN 1023-5809.  doi:10.5194/npg-17-371-2010.
  * Mariotti et al. (2020) A. Mariotti, C. Baggett, E. A. Barnes, E. Becker, A. Butler, D. C. Collins, P. A. Dirmeyer, L. Ferranti, N. C. Johnson, J. Jones, B. P. Kirtman, A. L. Lang, A. Molod, M. Newman, A. W. Robertson, S. Schubert, D. E. Waliser, and J. Albers.  Windows of Opportunity for Skillful Forecasts Subseasonal to Seasonal and Beyond.  _Bull. Am. Meteorol. Soc._ , 101(5):E608–E625, May 2020.  ISSN 0003-0007.  doi:10.1175/BAMS-D-18-0326.1.
  * Masiwal et al. (2023) R. Masiwal, V. Dixit, and A. K. Seshadri.  Explaining Dynamics and Rapid Onset of the Somali Jet through Its Kinetic Energy Budget.  _J. Atmos. Sci._ , 80(3):833–847, Feb. 2023.  ISSN 0022-4928.  doi:10.1175/JAS-D-22-0160.1.
  * May et al. (2022) R. M. May, K. H. Goebbert, J. E. Thielen, J. R. Leeman, M. D. Camron, Z. Bruick, E. C. Bruning, R. P. Manser, S. C. Arms, and P. T. Marsh.  Metpy: A meteorological python library for data analysis and visualization.  _Bulletin of the American Meteorological Society_ , 103(10):E2273 – E2284, 2022.  doi:10.1175/BAMS-D-21-0125.1.  URL https://journals.ametsoc.org/view/journals/bams/103/10/BAMS-D-21-0125.1.xml.
  * Met Office (2010 - 2015) Met Office.  _Cartopy: a cartographic python library with a Matplotlib interface_.  Exeter, Devon, 2010 - 2015.  URL http://scitools.org.uk/cartopy.
  * Meyers et al. (2007) G. Meyers, P. McIntosh, L. Pigot, and M. Pook.  The Years of El Niño, La Niña, and Interactions with the Tropical Indian Ocean.  _J. Clim._ , 20(13):2872–2880, July 2007.  ISSN 0894-8755.  doi:10.1175/JCLI4152.1.
  * Nicholson and Klotter (2021) S. E. Nicholson and D. Klotter.  The Tropical Easterly Jet over Africa, its representation in six reanalysis products, and its association with Sahel rainfall.  _Int. J. Climatol._ , 41(1):328–347, Jan. 2021.  ISSN 0899-8418.  doi:10.1002/joc.6623.
  * Nithya et al. (2017) K. Nithya, M. G. Manoj, and K. Mohankumar.  Effect of El Niño/La Niña on tropical easterly jet stream during Asian summer monsoon season.  _Int. J. Climatol._ , 37(15):4994–5004, Dec. 2017.  ISSN 0899-8418.  doi:10.1002/joc.5137.
  * Pattanaik and Satyan (2000) D. R. Pattanaik and V. Satyan.  Fluctuations of Tropical Easterly Jet during contrasting monsoons over India: A GCM study.  _Meteorol. Atmos. Phys._ , 75(1):51–60, Nov. 2000.  ISSN 1436-5065.  doi:10.1007/s007030070015.
  * Peixoto (2014a) T. P. Peixoto.  Hierarchical block structures and high-resolution model selection in large networks.  _Physical Review X_ , 4(1):1–18, 2014a.  ISSN 21603308.  doi:10.1103/PhysRevX.4.011047.
  * Peixoto (2014b) T. P. Peixoto.  The graph-tool python library.  _figshare_ , 2014b.  doi:10.6084/m9.figshare.1164194.  URL http://figshare.com/articles/graph_tool/1164194.
  * Peixoto (2019) T. P. Peixoto.  Bayesian Stochastic Blockmodeling.  In _Advances in Network Clustering and Blockmodeling_ , pages 289–332. John Wiley & Sons, Ltd, Chichester, England, UK, Nov. 2019.  ISBN 978-1-11948329-8.  doi:10.1002/9781119483298.ch11.
  * Quian Quiroga et al. (2002) R. Quian Quiroga, T. Kreuz, and P. Grassberger.  Event synchronization: A simple and fast method to measure synchronicity and time delay patterns.  _Phys. Rev. E_ , 66(4):041904, Oct. 2002.  ISSN 2470-0053.  doi:10.1103/PhysRevE.66.041904.
  * Rai et al. (2018) P. Rai, M. Joshi, A. P. Dimri, and A. G. Turner.  The role of potential vorticity anomalies in the Somali Jet on Indian Summer Monsoon Intraseasonal Variability.  _Clim. Dyn._ , 50(11):4149–4169, June 2018.  ISSN 1432-0894.  doi:10.1007/s00382-017-3865-9.
  * Rao and Srinivasan (2016) S. Rao and J. Srinivasan.  The impact of latent heating on the location and strength of the tropical easterly jet.  _Meteorol. Atmos. Phys._ , 128(2):247–261, Apr. 2016.  ISSN 1436-5065.  doi:10.1007/s00703-015-0407-z.
  * Rousseeuw (1987) P. J. Rousseeuw.  Silhouettes: A graphical aid to the interpretation and validation of cluster analysis.  _J. Comput. Appl. Math._ , 20:53–65, Nov. 1987.  ISSN 0377-0427.  doi:10.1016/0377-0427(87)90125-7.
  * Sathiyamoorthy et al. (2007) V. Sathiyamoorthy, P. K. Pal, and P. C. Joshi.  Intraseasonal variability of the Tropical Easterly Jet.  _Meteorol. Atmos. Phys._ , 96(3):305–316, June 2007.  ISSN 1436-5065.  doi:10.1007/s00703-006-0214-7.
  * Schlör et al. (2023) J. Schlör, F. Strnad, A. Capotondi, and B. Goswami.  A multi-modal representation of El Ni\~no Southern Oscillation Diversity.  _arXiv_ , July 2023.  doi:10.48550/arXiv.2307.11552.
  * Sprenger and Wernli (2015) M. Sprenger and H. Wernli.  The LAGRANTO Lagrangian analysis tool – version 2.0.  _Geosci. Model Dev._ , 8(8):2569–2586, Aug. 2015.  ISSN 1991-959X.  doi:10.5194/gmd-8-2569-2015.
  * Stolbova et al. (2014) V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, and J. Kurths.  Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka.  _Nonlinear Processes Geophys._ , 21(4):901–917, Aug 2014.  ISSN 1023-5809.  doi:10.5194/npg-21-901-2014.
  * Strnad (2023) F. Strnad.  fstrnad/geoutils: geoutils, Sept. 2023.  URL https://doi.org/10.5281/zenodo.8354788.
  * Strnad (2024) F. Strnad.  monsoon synchronization, 2024.  URL https://github.com/fstrnad/monsoon_synchronization.
  * Strnad and Schlör (2023) F. Strnad and J. Schlör.  climnet v.2.2.0, 2023.
  * Strnad et al. (2022) F. M. Strnad, J. Schlör, C. Fröhlich, and B. Goswami.  Teleconnection Patterns of Different El Niño Types Revealed by Climate Network Curvature.  _Geophys. Res. Lett._ , 49(17):e2022GL098571, Sept. 2022.  ISSN 0094-8276.  doi:10.1029/2022GL098571.
  * Strnad et al. (2023) F. M. Strnad, J. Schlör, R. Geen, N. Boers, and B. Goswami.  Propagation pathways of Indo-Pacific rainfall extremes are modulated by Pacific sea surface temperatures.  _Nat. Commun._ , 14(5708):1–16, Sept. 2023.  ISSN 2041-1723.  doi:10.1038/s41467-023-41400-9.
  * Tsonis and Swanson (2008) A. A. Tsonis and K. L. Swanson.  Topology and Predictability of El Ni\~no and La Ni\~na Networks.  _Phys. Rev. Lett._ , 100(22):228502, Jun 2008.  ISSN 1079-7114.  doi:10.1103/PhysRevLett.100.228502.
  * Vashisht et al. (2021) A. Vashisht, B. Zaitchik, and A. Gnanadesikan.  ENSO Teleconnection to Eastern African Summer Rainfall in Global Climate Models: Role of the Tropical Easterly Jet.  _J. Clim._ , 34(1):293–312, Jan. 2021.  ISSN 0894-8755.  doi:10.1175/JCLI-D-20-0222.1.
  * Vellore et al. (2014) R. K. Vellore, R. Krishnan, J. Pendharkar, A. D. Choudhury, and T. P. Sabin.  On the anomalous precipitation enhancement over the Himalayan foothills during monsoon breaks.  _Clim. Dyn._ , 43(7):2009–2031, Oct. 2014.  ISSN 1432-0894.  doi:10.1007/s00382-013-2024-1.
  * Walker et al. (2015) J. M. Walker, S. Bordoni, and T. Schneider.  Interannual Variability in the Large-Scale Dynamics of the South Asian Summer Monsoon.  _J. Clim._ , 28(9):3731–3750, May 2015.  ISSN 0894-8755.  doi:10.1175/JCLI-D-14-00612.1.
  * Wang and Ding (2008) B. Wang and Q. Ding.  Global monsoon: Dominant mode of annual variation in the tropics.  _Dyn. Atmos. Oceans_ , 44(3):165–183, Mar. 2008.  ISSN 0377-0265.  doi:10.1016/j.dynatmoce.2007.05.002.
  * Wheeler and Hendon (2004) M. C. Wheeler and H. H. Hendon.  An All-Season Real-Time Multivariate MJO Index: Development of an Index for Monitoring and Prediction.  _Mon. Weather Rev._ , 132(8):1917–1932, Aug 2004.  ISSN 1520-0493.  doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2.
  * Wolter and Timlin (2011) K. Wolter and M. S. Timlin.  El Niño/Southern Oscillation behaviour since 1871 as diagnosed in an extended multivariate ENSO index (MEI.ext).  _Int. J. Climatol._ , 31(7):1074–1087, June 2011.  ISSN 0899-8418.  doi:10.1002/joc.2336.
  * Xavier et al. (2007) P. K. Xavier, C. Marzin, and B. N. Goswami.  An objective definition of the Indian summer monsoon season and a new perspective on the ENSO–monsoon relationship.  _Q. J. R. Meteorolog. Soc._ , 133(624):749–764, Apr. 2007.  ISSN 0035-9009.  doi:10.1002/qj.45.

## Supplementary Information

In this Supplementary Information, we provide additional information on the
data and methods used in this study. We also provide additional figures that
support the main text. The Supplementary Information is organized as follows:
In Sec. SI 1, we provide additional information on the climate network used in
this study. In Sec. SI 2, we provide additional information on the basic
pattern of the synchronization between North India and the Sahel Zone. In Sec.
SI 3 we provide additional information on the yearly fluctuations of the
synchronization between North India and the Sahel. In Sec. SI 4 we outline the
grid search for the optimal parameters of the multivariate PCA. In Sec. SI 5,
we give additional information on the Tropical Easterly Jet (TEJ) and its
characteristics. In Sec. SI 6, we outline additional information on the
Circumglobal Teleconnection (CGT) and its characteristics. SI 7 provides
additional information on the Pacific Decadal Oscillation (PDO) and its
characteristics. The characteristics of the Somali Jet are shown in Sec. SI 8.
We show the characteristics of the convective situation in the Sahel during
day +12 in Sec. SI 9. In Sec. SI 10, we provide additional information on the
Boreal Summer Intraseasonal Oscillation (BSISO) and its characteristics. A
quasi-geostrophic (QG) analysis of the days of the synchronization is shown in
Sec. SI 11. In section SI 12, we provide additional information on the
propagation pathways of the synchronization between North India and the Sahel
Zone as they are estimated by a Lagrangian trajectory model.

##  Appendix SI 1 Climate Network of Synchronous Rainfall Events

#### Event Synchronization

Figure S1: Scheme of time-delayed Event Synchronization. The blue (green) bars
denote events that happen at the locations in $i$ ($j$) at the time points
$t_{i}^{m}$ ($t_{j}^{n}$). $m$ ($n$) denotes the event number at location $i$
($j$). The point in time $t_{i}^{m}$ is identified as synchronous to
$t_{j}^{n}$ since the time difference between $t_{i}^{m}$ and $t_{j}^{n}$ is
within the allowed range given by $\tau_{ij}^{m,n}$ according to the
definition expressed in equation 5. Not shown here is the maximum delay
$\tau_{\text{max}}$.

To quantify the level of synchronization between pairs of time series, we
employ the Event Synchronization algorithm Quian Quiroga et al. (2002). This
algorithm counts the number of events that occur at the same time between
pairs of event sequences ${e^{m}_{i}}{m=1}^{s_{i}}$ and
${e^{n}_{j}}{n=1}^{s_{j}}$, where $s_{i}$ ($s_{j}$) represents the total
number of events at location $i$ ($j$), and $e^{m}_{i}$ ($e^{n}_{j}$) denotes
the timing of an event in location $i$ ($j$). The delay between an event
$e^{m}_{i}$ in location $i$ and an event $e^{n}_{j}$ in location $j$ is
denoted as $d_{ij}^{m,n}=e_{i}^{m}-e_{j}^{n}$. The set
$D_{ij}(e^{m}_{i},e^{n}_{j})$ is defined as the set that contains the four
neighboring events of $e^{m}_{i}$ and $e^{n}_{j}$:

$D_{i,j}^{m,n}=\left\\{d_{i,i}^{m,m-1},d_{i,i}^{m,m+1},d_{j,j}^{n,n-1},d_{j,j}^{n,n+1},2{\tau_{\text{max}}}\right\\},$
(4)

The dynamical delay, denoted as $\tau_{i,j}^{m,n}$, is calculated as half of
the minimum time difference between subsequent events in both time series
around event $e_{i}^{m}$ and $e_{j}^{n}$. It captures a small time delay
between events and is limited to a maximum value of $\tau_{\text{max}}$:

$\tau_{ij}^{m,n}=\frac{1}{2}\min_{\forall d\in D_{ij}^{m,n}}d\;.$ (5)

The parameter $\tau_{\text{max}}$ represents the maximum allowable time delay
between two events, capturing both short and long-spatial range interactions.
In this study, we set $\tau_{\text{max}}$ to 10 days. The event
synchronization strength $R_{i,j}$ between locations $i$ and $j$ is calculated
as the sum of synchronous time points between all pairs of event sequences
${e^{m}_{i}}{m=1}^{s_{i}}$ and ${e^{n}_{j}}{n=1}^{s_{j}}$:

$\displaystyle R_{i,j}$
$\displaystyle=\sum_{m=1}^{s_{i}}\sum_{n=1}^{s_{j}}S_{i,j}^{m,n}\hskip
28.45274pt\text{where}\hskip 14.22636ptS_{i,j}^{m,n}=\begin{cases}1&\hskip
14.22636pt0<d_{ij}^{m,n}<\tau_{i,j}^{m,n}\;,\\\ 0&\hskip
14.22636pt\text{otherwise}\;.\end{cases}$ (6)

We count blocks of consecutive events as a single event, positioned at the
time of the first event. This avoids a dynamical delay value of $1/2$, which
would lead to a case where two sequentially occurring events are not
considered synchronous. The complete event synchronization scheme is
illustrated in Fig. S1.

#### Constructing the network.

Figure S2: Event Synchronization based network links from North India box. We
investigate the occurrence of rainfall extremes in the core monsoon season
from June — September (JJAS). The network links the occurrence of Extreme
Rainfall Events (EREs) that occur in the box in North India (NI) [70-85°E;
28-33°N] (pink rectangle) to synchronously occurring locations using an event-
synchronization (Quian Quiroga et al., 2002) based climate network (Dijkstra
et al., 2019) approach (compare (Boers et al., 2019, Strnad et al., 2023))
using a dynamical time lag of $\tau_{max}=10~{}$days. Green dots denote
locations in which ERES occur statistically significantly synchronously or
within the time lag $\tau_{max}$ after the occurrence of EREs within the North
India box (pink rectangle). The color bar denotes the number of connections
from a certain location to a location in NI. The hatched lines indicate
regions with only very little rainfall in JJAS and these locations are
excluded from the analysis.

The adjacency matrix $\mathbf{A}$ of a network represents the connections
between nodes and defines the network’s underlying topology. It is an $N\times
N$ matrix, where $A_{i,j}=1$ indicates that events at location $i$ are
statistically significantly followed by events at location $j$. To determine
the statistical significance, we perform a null-model test. The null
hypothesis assumes that the observed $R_{i,j}$ value arises from a pair of
randomly generated event sequences $e_{i}^{\prime},e_{j}^{\prime}$ with the
same number of events $s_{i},s_{j}$ as the observed sequences. We construct
surrogate event sequences by randomly and uniformly distributing events. We
consider $e_{i}$ to be significantly synchronous with $e_{j}$ if their
corresponding $R_{i,j}$ value exceeds the 95th percentile of
$R_{i^{\prime},j^{\prime}}$ values obtained from 2000 pairs of surrogate event
sequences $e_{i}^{\prime},e_{j}^{\prime}$. When a significant $R_{i,j}$ value
is found, we establish an edge from node $n_{i}$ to $n_{j}$ and set
$A_{i,j}=1$.

An example of network links of locations in North India between
$70^{\circ}\,\mathrm{E}$ and $80^{\circ}\,\mathrm{E}$ and
$25^{\circ}\,\mathrm{N}-35^{\circ}\,\mathrm{N}$ is shown in Fig. S2. For this
region, we observe a synchronization of rainfall extremes in North India with
the North-East China region around the Yellow River basin, the Western Pacific
above the Philippines, and the Sahel Zone. The connection towards the Yellow
River basin has been analyzed previously (Gupta et al., 2022), in this work
the focus will be set on the synchronization between the monsoon system in
North India and the Sahel Zone.

##  Appendix SI 2 Community Detection in the tropics and subtropics

Figure S3: Membership Likelihoods for different communities. Using the
heuristic outlined in sec. 3 we find $10$ communities. The color bar shows the
membership likelihood of a respective community. $100$ independent runs of the
community detection algorithm have been used for this analysis. We find that
some communities show a quite stable occurrence, some others are more
fluctuating. However, for this work, we are mainly interested in the North
India - Sahel zone community which is one of the most stable communities of
the algorithm.

##  Appendix SI 3 Yearly Fluctuations of the Synchronization

This section investigates the yearly fluctuations of the synchronization
between North India and the Sahel Zone. The different years are clustered
using a Gaussian Mixture model. This indicates that the lead-lag correlation
is not constant but varies between different years. We find that the
synchronization is not constant but varies between different years (Fig. S4)

Figure S4: Yearly fluctuations of the synchronization. The yearly lead-lag
correlations of extreme rainfall events (EREs) between North India (NI) and
the Sahel Zone (SZ) are displayed. The lead-lag correlation is computed using
the counts of EREs per year in NI (SZ). The individual yearly lead-lag
correlations are clustered using a Gaussian Mixture model. This indicates that
the lead-lag correlation is not constant but varies between different years.

##  Appendix SI 4 Grid search for optimal parameters of the Multivariate PCA

The optimal parameters for the Multivariate PCA are found by a grid search.
The grid search is performed by varying the number of EOFs and the number of
clusters. The optimal parameters are found by maximizing the Silhouette Score
(Fig. S5).

Figure S5: Grid search for optimal parameters of the Multivariate PCA. The
optimal parameters for the Multivariate PCA are found by a grid search. The
grid search is performed by varying the number of EOFs and the number of
clusters. The optimal parameters are found by maximizing the Silhouette Score.

##  Appendix SI 5 Tropical Easterly Jet Index

This section presents the characteristics of the Tropical Easterly Jet (TEJ)
according to the definition by Huang et al. (2019). The TEJ is a prominent
feature of the Asian summer monsoon circulation, driven by the meridional
thermal contrast between the Asian landmass and the Indian Ocean. It is
further intensified by the elevated heating over the Tibetan plateau. The
variability of the TEJ substantially influences climate patterns in the
tropical and subtropical domain over Asia and the Sahel zone and its
surrounding regions.

Figure S6: Illustration of enhanced/reduced TEJ phases. Composites of
different phases of the TEJ are shown. The first row shows the enhanced state,
and the second row the reduced state. The first column (a, d) displays the
U200 anomalies (with respect to month), the second column (b, e) showcases the
V200 anomalies, and third row (c, f) exhibits the Geopotential anomalies at
$200$ hPa overlapped by the wind field anomalies at $200~{}$hPa, as identified
by the TEJI metric described in Sec. 2.1. The magenta rectangle in pannel a
visualizes the box that is used to define the TEJI.

#### Pointwise spatial correlation analysis of wind fields

We uncover that multiple potential drivers come together when the probability
of observing the delayed synchronization between North India and the Sahel
Zone is notably increased (Fig.8). We find a substantially higher frequency of
synchronizations during an active Boreal Summer Intraseasonal Oscillation
(BSISO) in phases 5-8, conditioned on a La Niña background state and an
intensified Tropical Easterly Jet (TEJ) in a westerly direction (Fig. 8 c).
The pronounced role of the TEJ in establishing the synchronization is
underlined by the fact that in its absence there are hardly any
synchronizations observed regardless of the respective ENSO state and the
BSISO phases (Fig. 8 b,d,f). Similarly, El Niño-like conditions substantially
decrease the likelihood of observing synchronizations (Fig. 8 a,b). Further,
synchronizations during inactive BSISO are distributed around the null model
(grey bars in Fig 8) and are not statistically significant. We estimate the
relation between BSISO phases (as defined by Kikuchi et al. (2012)) and
concurrent EREs (Fig.S3 a) utilizing a conditional dependence test constructed
as the conditional probability of synchronous rainfall events contingent upon
(i) phase, (ii) active (inactive) BSISO, (iii) state of the El Ni no Southern
Oscillation (ENSO), and (iv) state of the TEJ. This statistical analysis
suggests the interpretation that La Niña-like conditions establish the
foundational state in which the BSISO is predisposed to propagate poleward
over Northern India, as reported by (Strnad et al., 2023). This convective
cloud over Northern India (NI) is then prone to be advected westwards through
the summer circulation over NI in July and August enforced by an enhanced TEJ.
These three factors are now analyzed in detail.

Figure S7: Correlation of Synchronous Rainfall Index with wind fields. a The
pointwise Spearman correlation of the zonal u-wind anomalies at $200\,$hPa
with the lagged synchronous rainfall index is shown. b Same as for a but for
the meridional v-wind anomalies at $200~{}$hPa. c Same as for a/b but for the
vertical velocity $\omega$ at $500~{}$hPa. Colored areas imply statistically
significant correlations at the 99 % confidence interval using a two-sided
Student’s t-test.

##  Appendix SI 6 Circumglobal Teleconnection (CGT)

This section shows the characteristics of the Circumglobal Teleconnection
Pattern (CGT) as defined by Ding and Wang (2005). The CGT is a wave pattern
that is characterized by a zonal wavenumber of 5. It is a wave pattern that is
known to be associated with the Asian Summer Monsoon and the North Atlantic
Oscillation (NAO). The CGT is known to be associated with the Silk Road
Pattern (SRP) (Enomoto et al., 2003) and the East Asian Wave train pattern
(Ding and Wang, 2007). This characteristic wave pattern over Eurasia is shown
in Fig. S8 which resembles the wave pattern identified by Ding and Wang
(2007).

Figure S8: Illustration of positive/negative CGT phases. Composites of
different phases of the CGT are shown. The first row shows the enhanced state,
and the second row the reduced state. The first column (a, d) displays the
U200 anomalies (with respect to month), the second column (b, e) showcases the
V200 anomalies, and third row (c, f) exhibits the Geopotential anomalies at
$200$ hPa overlapped by the wind field anomalies at $200~{}$hPa, as identified
by the CGTI metric described in Sec. 2.1. The magenta rectangle in pannel a
visualizes the box that is used to define the CGTI.

##  Appendix SI 7 Connection to Pacific Decadal Oscillation (PDO)

We observe that the Pacific Decadal Oscillation (PDO) has a signature in the
SST plots of the Strong Propagation (Fig. 6 a). The PDO is a long-term climate
pattern that is characterized by a positive and negative phase (Fig. S9). The
PDO is known to be connected with ENSO and influences the climate in the Indo-
Pacific domain and the North American continent. We observe that starting from
around 1986, the phases of the PDO roughly align with the phases of the
synchronization (Fig. LABEL:fig:yearly_occurrence_cluster_pdo)

Figure S9: Illustration of positive/negative PDO phases. Composites of
different phases of the PDO in JJAS are shown. Panel a shows the SST anomalies
that are associated with the positive PDO phase, while panel b shows the SST
anomalies that are associated with the negative PDO phase.

##  Appendix SI 8 The Somali Jet

The South Asian monsoon onset is marked by a rapid increase in rainfall over
southwest India and is preceded by a reversal of winds in the lower
troposphere. This occurs analogously to the formation of a low-level zonally
oriented jet over the western Indian Ocean. The jet initially flows across the
equator and then turns eastward near the East African coast into a zonal flow
(Findlater, 1969). This jet is commonly known as the Somali jet. Its low-level
southwesterly flow plays a crucial role in transporting moisture for the
Indian and Asian Summer Monsoon. It precedes the onset of the monsoon over
India and exhibits similar characteristics of rapid intensification and
gradual retreat during the monsoon season (Halpern and Woiceshyn, 2001,
Masiwal et al., 2023). This flow can be visualized using Integrated Vapor
Transport (IVT). We observe that for the MSDs the flow is enhanced over the
Arabian Sea and the Bay of Bengal (Fig. S10 a,b) bringing additional moisture
towards the center and North of India. In dry years, consistently the flow is
reduced (Fig. S10 c).

Figure S10: Vertically integrated water vapor flux (IVT) for days of maximum
synchronization for clustered regions. Vertically integrated water vapor flux
(IVF) in eastward and northward directions is visualized for the different
clusters (a,b) and for the July-August background state for years with only a
few synchronizations, called dry years. Only statistically significant
anomalies at the 95 % confidence level are shown. Day 0 denotes the days of
maximum synchronization. The composite anomalies are computed with respect to
the monthly climatology. Only IVT arrows that are significant at $95~{}\%$
level following the Student’s t-test are plotted.  Figure S11: Geopotential
and horizontal wind fields at 900 hPa. Wind fields and geopotential at $900$
hPa are visualized for the different clusters (a,b) and for the July-August
background state for years with only a few synchronizations, called dry years.
Only statistically significant anomalies at the 95 % confidence level are
shown. Day 0 denotes the days of maximum synchronization. The composite
anomalies are computed with respect to the monthly climatology. Only wind
arrows that are significant at $95~{}\%$ level following the Student’s t-test
are plotted.

##  Appendix SI 9 Convection in SZ

Analogously to the convection visualized in Fig 4 for North India, we show the
convection in the Sahel Zone (Fig. S12) for the day +9 in the Sahel Zone for
MSDs in the Strong Propagation cluster. The convection in the Sahel Zone is
characterized by a strong rising motion in the atmosphere at around
$400~{}$hPa. The centers of convection are around the Ethiopian Highlands at
around $15^{\circ}\,\mathrm{E},12^{\circ}\,\mathrm{N}$ and the Western coast.

Figure S12: Convective anomalies in North India. Panel a shows the Outgoing
Longwave Radiation (OLR) superimposed by the vertical velocities $\omega$ at
$400~{}$hPa (measured in Pa/s) by colored contours. Orange solid (purple
dashed) contours denote anomalously rising conditions for regions with
anomalies larger (smaller) than $3\,$Pa/s. Panel b visualizes the zonal
circulation averaged between $20^{\circ}\,\mathrm{N}-30^{\circ}\,\mathrm{N}$
latitude, while panel c the meridional circulation, averaged between
$75^{\circ}\,\mathrm{E}-85^{\circ}\,\mathrm{E}$ longitude. All composites are
computed for the conditions on Day 12. The panel in b (c) is split into two
parts: On top are displayed the meridionally (zonally) averaged precipitation
anomalies while below the vertical circulation is shown by composites of
relative humidity (RH) anomalies (shading) and wind fields (arrows). In a
colored contours denote statistical significance at $95~{}\%$ confidence level
using a two-sided t-test while grey contours visualize the orography. The wind
fields in the zonal (meridional) circulation plots are estimated using the
meridionally (zonally) averaged u (v) anomalies, measured in m/s, and the
vertical velocity $\omega$ in the horizontal direction, measured in hPa/s.
Only statistically significant arrows at $95\,\%$ confidence level using a
two-sided t-test are shown.

##  Appendix SI 10 Convection through BSISO

The Boreal Summer Intraseasonal Oscillation (BSISO) is a prominent feature of
the Asian Summer Monsoon. It is characterized by a northward propagation of
convection over the Indian Ocean and the Maritime Continent. The BSISO
periodically occurs on time scales of around 30-60 days and is associated with
the active and break events of the Asian Summer Monsoon (Kikuchi, 2021). The
BSISO is characterized by eight phases, which are shown in Fig. S13. It has
been shown that ENSO modulates substantially the propagation pathway of the
BSISO (Strnad et al., 2023). In La Niña years, the BSISO is more likely to
propagate over the Indian subcontinent and the North Indian Ocean. Further, in
La Niña years the TEJ is enhanced. Therefore, also the convection centers and
anomalies change and are more confined to the North and Northwest of India.
This is shown in Fig. S15.

Figure S13: Lagged precipitation occurrence in North India. The first column
visualizes the zonal circulation averaged between
$20^{\circ}\,\mathrm{N}-30^{\circ}\,\mathrm{N}$ latitude, while the second
column the meridional circulation, averaged between
$75^{\circ}\,\mathrm{E}-85^{\circ}\,\mathrm{E}$ longitude. The first row shows
the conditions on Day 0 and the second on Day 12, which is the day of the
strongest correlation (see Fig. S3 b). Each subplot consists of two panels.
The top panel shows the meridionally (zonally) averaged precipitation
anomalies (with respect to the month). The down panel shows the vertical
circulation. Here, the colored contours show statistically significant
composites of V-(U-) wind anomalies at the left (right) column. Grey contours
visualize the orography. The wind fields in the zonal (meridional) circulation
plots are estimated using the meridionally (zonally) averaged u (v) anomalies,
measured in m/s, and the vertical velocity $\omega$ in the horizontal
direction, measured in hPa/s. Only statistically significant arrows at
$95\,\%$ confidence level are shown.  Figure S14: Convection centers for BSISO
phases. For phases 1-8 of the BSISO the convection is shown in terms of OLR
anomalies (color shading) and vertical velocity $\omega$ in contours where
solid red (dashed blue) contours indicate anomalously upward (downward)
motion. Figure S15: Convection centers for BSISO phases. For time points in La
Niña years with enhanced TEJ the phases 1-8 of the BSISO are shown in terms of
OLR anomalies (color shading) and vertical velocity $\omega$ in contours where
solid red (dashed blue) contours indicate anomalously upward (downward)
motion.

##  Appendix SI 11 Quasi-Geostrophic Forcing (QG)

The Quasi-Geostrophic (QG) forcing is visualized for the differences cluster,
for the July and August (JA) mean state for years with many synchronizations
and for the July August background state for years with only a few
synchronizations, called dry years (Fig. S16). The QG forcing is calculated
using the method described in Hunt and Turner (2022) and is based on the
anomalies of the geopotential height at $500~{}$hPa and the wind fields at
$200~{}$hPa. The QG-forcing is computed to break down the changes in vertical
velocity using the (also diagnostic) $\omega$ equation:

$\left(\nabla_{p}^{2}+\frac{f}{\sigma}\frac{\partial^{2}}{\partial
p^{2}}\right)\omega=\underbrace{\frac{f_{0}}{\sigma}\frac{\partial}{\partial
p}\left[v_{g}\nabla_{p}(\xi_{g}+f)\right]+\frac{R}{\sigma
p}\nabla_{p}^{2}\left[v_{g}\cdot\nabla T\right]}_{\textrm{quasi-geostrophic
forcing}}+\underbrace{\frac{R}{\sigma p}\nabla_{p}^{2}Q}_{\text{local diabatic
heating}}\;.$ (7)

The symbols have the following meanings: $\omega$ is the vertical velocity,
$f$ is the Coriolis parameter, $\sigma$ is the static stability, $v_{g}$ is
the geostrophic wind, $\xi_{g}$ is the geostrophic vorticity, $R$ is the gas
constant, $T$ is the temperature, and $Q$ is the diabatic heating. Here, the
left-hand side can be interpreted as a three-dimensional Laplacian of vertical
velocity, acting as a negative operator. On the right-hand side, the first
term represents the forcing caused by differential advection of geostrophic
absolute vorticity, the second term represents the forcing due to temperature
advection, and the third term represents the forcing due to local diabatic
heating. The first two terms together form the quasi-geostrophic forcing,
which explains the presence of an ascent maximum and precipitation maximum in
the southwest quadrant of LPSs. The third term, related to local diabatic
heating, is not considered in this context (Hunt, 2022).

Figure S16: Illustration of QG forcing. Quasi Geostrophic (QG) is visualized
for the differences cluster (a,b), for the July and August (JA) mean state for
years with many synchronizations (c) and for the July August background state
for years with only a few synchronizations, called dry years. Only
statistically significant anomalies at the 95 % confidence level are shown.

##  Appendix SI 12 Lagrangian Trajectories between North India and Sahel Zone

To visualize possible trajectories we use a Lagrangian trajectory model. The
Lagrangian trajectory model is based on the LAGRANTO approach (Sprenger and
Wernli, 2015) and is implemented in the geoutils package (Strnad, 2023). The
trajectories are calculated for the most synchronous days in the wet years.
The time point for the start of the trajectories is set as the days of maximum
synchronization occur and we set the starting pressure level at $500\,$hPa.
The resulting trajectories are clustered using a Gaussian Mixture model
algorithm. We identify 3 different groups of trajectories. The most likely
group is shown in Fig. S17 a. Air is rising at NI and then is deflected South-
and Westward, merging with the Tropical Easterly Jet (TEJ) around the Sahel
Zone. The second group is shown in Fig. S17 b. Air is rising at North India
which then propagates towards SZ but is then transported via the subtropical
jet stream further to North China. We conclude that the propagation of
extremes seems to follow the summer mean flow in the upper atmosphere at
around $200~{}$hPa and the TEJ plays a role in modulating the westward
propagation.

Figure S17: Lagrangian Trajectory analysis for trajectories starting in North
India. For the most synchronous days in the wet years, we apply a Lagrangian
Trajectory analysis in an implementation following the LAGRANTO approach
Sprenger and Wernli (2015) for spatial location in the North India box (here
marked by the rectangle). For visual reasons in every group, only every 10th
trajectory is plotted. The time point for the start of the trajectories is set
as the days of maximum synchronization occur and we set the starting pressure
level at $500\,$hPa. The resulting trajectories (in total there are around
$100$ most synchronous days and 20 starting locations, i.e. $\approx 3000$
trajectories) are clustered using a Gaussian Mixture model algorithm. We
identify 3 different groups of trajectories. a shows the most likely group.
Air is rising at NI and then is deflected South- and Westward, merging with
the Tropical Easterly Jet (TEJ) around the Sahel Zone. b shows similarly the
rising air at North India which then propagates towards SZ but is then
transported via the subtropical jet stream further to North China. We conclude
that the propagation of extremes seems to follow the summer mean flow in the
upper atmosphere at around $200~{}$hPa and the TEJ plays a role in the
westward propagation.