capbtabboxtable[][]

# Monitoring the Evolution of Behavioural Embeddings in Social Media
Recommendation

Srijan Saket ShareChat, India 22email<EMAIL_ADDRESS>
11 0009-0006-9460-1203

###### Abstract

Short video applications pose unique challenges for recommender systems due to
the constant influx of new content and the absence of historical user
interactions for quality assessment of uploaded content. This research
characterizes the evolution of embeddings in short video recommendation
systems, comparing batch and real-time updates to content embeddings. The
analysis investigates embedding maturity, the learning peak during view
accumulation, popularity bias, $l2$-norm distribution of learned embeddings,
and their impact on user engagement metrics. The study unveils the contrast in
the number of interactions needed to achieve mature embeddings in both
learning modes, identifies the ideal learning point, and explores the
distribution of $l2$-norm across various update methods. Utilizing a
production system deployed on a large-scale short video app with over 180
million users, the findings offer insights into designing effective
recommendation systems and enhancing user satisfaction and engagement in short
video applications.

###### Keywords:

embeddings evolution; monitoring; short video

##  1 Introduction

Short video applications have experienced a significant surge in demand, with
users seeking short-form engaging content experiences. This has led to the
adoption of embedding-based recommender systems for effective content
recommendations. These systems utilize models like Field-aware factorization
machines, wide-and-deep neural networks, and two-tower models to learn user
and content embeddings, as cited in [3, 8, 4]. However, the unique nature of
short video content presents challenges. With constant new content uploads and
vast content space, recommending relevant content becomes complex, especially
for new uploads without historical user interactions. Over time, the system
can develop behavioral embeddings to capture user preferences. Yet, evaluating
content and recommendations remains challenging due to limited view share, as
well as the inherent challenges of short video content, such as diversity,
varying shelf-life, and cold start problems, as mentioned in [1, 5, 2, 6].

To address this issue, it becomes essential to gain a comprehensive
understanding of how embeddings evolve with user interactions over time. By
studying the evolution of embeddings, we can uncover valuable insights into
content dynamics and improve the evaluation and effectiveness of
recommendation algorithms. In this work, we focus on characterizing the
evolution of learned embeddings of short video content and propose metrics
that enable us to gauge both the quality of content embeddings and the
recommendations provided. To understand how content embeddings evolve, we
consider two forms of embedding updates: (i) batch embedding updates where
user interactions are accumulated and embeddings are updated in batches every
x hours, and (ii) realtime-embeddings, where each content’s embedding is
updated in realtime after each user interaction.

Figure 1: System comparison of realtime vs batch setup of embedding updation

Using both these methods for comparison 1, we characterize the evolution of
embeddings along a number of aspects. First, we focus on embedding maturity
and consider the question: How many user interactions does content require to
obtain ”mature” embedding? We find that realtime embeddings mature a lot
quicker, taking only ${1/5}$-th views compared to views taken by batch-trained
embeddings to mature.

Second, we investigate the change in cosine similarity of each content
embedding per additional view, i.e. How the embeddings evolve with additional
views, and use this estimate to quantify the learning of embedding update
happening with each new user interaction. We note that peak learning happens
notably faster in realtime embeddings compared to batch embeddings.
Consequently, real-time training leads to a quicker convergence of embeddings
towards their final vectors compared to batch training. Furthermore, we cross-
validate it with user engagement metrics including video click rate and
successful video plays across view buckets which support the peak learning
observation.

Third, noting that most embedding-based recommenders rely on the $l2$-norm of
embeddings, we investigate how the $l2$-norm is distributed across view
buckets for both realtime and batch embeddings and observe that batch-trained
embeddings suffer from significantly higher norm, with the norm of high view
posts being 5x higher than posts with fewer views, thereby contributing
towards increasing the popularity bias in the content recommended on the
platform.

We present a detailed analysis using batch-trained and realtime-trained
embedding systems deployed at scale on a short-video app serving
recommendations to over 180 million users. We contend that the analysis and
findings presented from our production systems at scale inform the design of
content recommendation systems, especially at the early stage of new content.

Figure 2: Prevalence bias among various view buckets across batch and real-
time training methods

ffm type | signal type | # posts | # updates
---|---|---|---
batch | click | 42409 | 42409
batch | share | 53664 | 76144
batch | play | 100903 | 100903
batch | skip | 108259 | 108259
batch | like | 119516 | 177126
realtime | click | 144922 | 34352180
realtime | share | 144913 | 34297979
realtime | play | 139823 | 18269337
realtime | skip | 139823 | 18269330
realtime | like | 144903 | 34304760

Figure 3: Number of post and embedding updates using the FFM model for the
dataset used in the paper.

##  2 Evolution of Content Embeddings

In feed recommendation models, a common method to prioritize content for a
user in a recommender system is by assessing the dot product between the
user’s embeddings and the content’s embeddings. Hence, the norm and the angle
of embeddings in Euclidean space play a major role in deciding its ranking
order in the user’s feed. We begin by describing the dataset collected and
then proceed to characterize the embeddings in subsequent subsections.

###  2.1 Dataset & Embedding Methods

We gathered a dataset of video posts created in the Hindi language over a
period of one week on the ShareChat application, capturing both implicit
signals (such as video play, and skip) and explicit signals (including click,
like, share). For each signal, we utilized Field-aware Factorization Machines
(FFM) [7] to learn 32-dimensional embeddings from user interactions. The
dataset consists of time-series data, where each post is associated with an
embedding learned at different points in time.

We focus on content embeddings for exposition and consider distance measures
such as $l2$-norm and cosine distance of content embeddings from different
reference points (like initial value or running difference). We compute the
above-mentioned metrics for two modes of learning behavioral embeddings
namely, batch and real-time. The batch setup updates the embeddings at a
specified frequency by collecting data over a period of six hours whereas the
real-time method dynamically updates them based on every interaction data
point.

In Table 3, we provide the number of posts and embedding updates associated
with the dataset for each signal type. Note that the ratio of embedding
updates with the number posts is much smaller for batch updates. This is
because in the batch case, updates are sporadic and not done after every
interaction.

For simplicity, we focus our analysis on the ”view” signal, although we expect
similar trends for other signals since the learning method remains consistent.
To ensure a sufficiently large number of interactions for capturing evolution,
we retained posts with views equal to or exceeding 100k. Throughout this
paper, the terms ”views” and ”interactions” are used interchangeably,
indicating user engagement with the video content.

(a) Comparison of maturity curves for batch & realtime. For batch, saturation
happens at $\approx 10k$ views.

(b) Real-time embedding updates: Peak learning happens at 1.5k views and
saturation happens at 3.5k views.

Figure 4: Maturity curve and Peak learning for realtime and batch embeddings
averaged across all content, plotted against views.

###  2.2 Embedding Maturity with Views

Fig. 4(a) illustrates the cosine distance between the content embedding at a
given time ’t’ and embedding at time ’t-1’ of the content, plotted against the
number of views ’x’ the content has received on the platform.

Suppose we consider a threshold of 0.5 for the cosine distance as a criterion
to assess the maturity of the learning process for a particular content. Our
analysis reveals that batch embeddings surpass this threshold at approximately
10k views, whereas realtime embeddings achieve it at around 2k views. This
suggests that utilizing realtime updates leads to considerably faster learning
of embeddings compared to the batch mode.

Figure 5: Video click rate and successful video play from experiments on the
described dataset.

However, utilizing a fixed threshold as a means of quantifying our findings
mathematically is not the most optimal approach, as this threshold is heavily
influenced by various factors such as the data, model, and initialization
strategy of the embeddings. Consequently, we turn our attention to examining
the variation in cosine distance with each additional view of the content,
averaging this change across all content embeddings. By plotting this
information, we can identify the point at which maximum learning occurs and
determine the number of views or interactions required beyond that point to
achieve convergence for both realtime and batch learning strategies. This
approach allows for a more nuanced understanding of the learning process and
facilitates the comparison of different learning strategies.

For this purpose, let us first define checkpoints on views as
$V_{1},V_{2},\cdots,V_{k}$. Further, let us represent the embedding vectors of
content at the number of views = $V_{i}$ as
${V_{i}}^{1},{V_{i}}^{2},\cdots,{V_{i}}^{N_{i}}\leavevmode\nobreak\
\forall\leavevmode\nobreak\ i\in[1,k]$, where $N_{i}$ is the number of posts
on the social media platform that reached at least $V_{i}$ views. Then, the
amount of learning for embeddings at views $=V_{i}$ can be defined as

$L(V_{i})=\frac{1}{(V_{i}-V_{i-1})}\sum_{j=1}^{N_{i}}Dist({V_{i}}^{j},{V_{i-1}}^{j})\leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\
\forall\leavevmode\nobreak\ i\in[1,k],$ (1)

where $Dist(x,y)$ can be any distance metric. In this paper, we use cosine
distance as the metric, that is, $Dist(x,y)=1-\frac{<x,y>}{|x|_{2}|y|_{2}}$
Since we are looking at the average across thousands of content posts, the
statistics, such as threshold, are more stable.

Figure 4(b) illustrates the learning progression of the model at various view
checkpoints. It is observed that in the realtime mode, the content embeddings
reach their peak learning point twice as fast compared to the batch mode.
Additionally, the saturation point, where further updates have minimal impact,
is reached three times faster in the realtime mode (at 1.5k views) compared to
the batch mode (at 3.5k views). These findings highlight the efficiency and
accelerated learning capabilities of updating embeddings in realtime compared
to the batch approach.

(a) Realtime embedding updates

(b) Batch embedding updates

Figure 6: For batched updates, the norm ratio is higher for converged
embeddings w.r.t. initial embeddings.

Validation from user engagement metrics: To validate the above insights, we go
back and look at the business metrics, such as video click rates and
successful video play percentage, for both realtime and batched updates and
plot them in Fig. 5. We see that the realtime model has a much better
performance in terms of video click rate and successful video play percentage
in the lower views bucket (especially at $\leq 5k$ views). This is because it
is able to figure out the optimal content embedding much faster than batch (3x
faster saturation cutoff as shown in Fig. 4). This, in turn, results in better
content targeting and higher user engagement on the platform.

###  2.3 Embedding Norm and Popularity Bias

Since most ranking approaches use dot product of user and content embeddings,
content embeddings with a higher norm would result in a higher ranked order
for that content, thereby recommending it more. Keeping this in mind, we
investigate how the $l2$-norm is distributed across content of different view
buckets once the embedding matures. In figures 6(a) and 6(b), we plot the
histogram of the $l2$-norm distance of content embeddings (comparing the
view$\equiv 0$ embedding with the mature embedding at views$\equiv 100k$ for
both realtime and batched trained embeddings, respectively.

We observe that the $l2$-norm of the embeddings grows drastically with more
views for batched updates. This implies that the model in this case ranks
content with more views higher, resulting in higher popularity bias, thereby
resulting in the serving of content that is generic and not catering to users’
specific interests leading to loss in user engagement.

Validation from user engagement metrics: To validate the above hypothesis, we
plot the business metrics in Fig. 3 that relate to the percentage of views in
low (and high) view ranges. We note that the batch model suffers from severe
popularity bias with popular posts garnering more than 60% of the views.

##  3 Conclusion & Future Work

This paper delves into the intricacies of machine learning production
pipelines, explicitly focusing on large-scale recommendation systems. By
addressing the complexity and challenges associated with quantitatively
monitoring recommendation quality, we have made significant progress in
understanding the evolution of embeddings on Sharechat, a social media
platform with a substantial user base. Further, we analyzed the business
metrics such as successful video views and popularity bias, and show that the
proposed metrics for monitoring embeddings highly correlate with the business
outcomes. While the analysis is closely linked to the specific algorithm used,
the techniques for updating behavioral embeddings remain the same, suggesting
generalizability across different recommendation systems.

For future work, we propose several avenues for further exploration. One area
of interest is determining the minimum number of views necessary to comprehend
the complexity levels associated with video or image content on social media.
Additionally, we can explore techniques to reduce the frequency of updates
based on improvements in maturity to bring down server costs and propose
initialization schemes to expedite the maturity process. Finally, the question
of whether all user interactions contribute equally to learning is worth
looking into, prompting the need to investigate optimal strategies for
exposing content to specific user groups to maximize learning outcomes.

## References

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# Extended Analysis of the Effects of the Sumatra’s Topography on Downstream
Low-level Vortex Development over the Indian Ocean

###### Abstract

Fine et al. (2016, hereafter F16) investigated the potential role of Sumatra
Island, as well as the Malay Peninsula and Java, in creating terrain-induced
circulations over the Indian Ocean (IO) that subsequently develop into
tropical cyclones (TCs). Applying sophisticated vortex tracking software to
2.5 yrs of model analyses, F16 found four regions downstream of topographic
features in the Maritime Continent to be prolific generators of low-level
cyclonic vortices (123/yr). Vortices shed from these “hotspot” regions
contributed to 25% of all TCs occurring in the IO basin during that period.
This present study extends the limited analyses of F16 by applying a similar
approach to 10 yrs (2008-2017) of ERA5 analyses. While the 2.5-yr period which
F16 studied was slightly ($\sim$8%) more active in terms of vortex production
than the 10-yr period, in general F16’s findings are representative of the
longer-term record with $\sim$70% ($\sim$80%) of all vortices (shed vortices)
occurring with easterly low-level (925 hPa) flow over the “hotspot” regions.
Additional analysis of the 10-yr record found that vortex counts are highest
near MJO phase 1 when low-level easterlies are strongest over the maritime
continent region. A secondary peak in vortex (and shed vortex) counts occurs
during MJO phase 4 when low-level westerlies were present near the equator
west of Sumatra. This suggests that low-level westerly surges on the equator
impinging on Sumatra associated with the MJO contribute to an increase in wake
vortex development. While the frequency of vortex genesis over the four
“hotspot” regions is strongly tied to the annual cycle of winds, periods with
anomalous zonal flow are shown to impact vortex counts. This is most apparent
in the region off the southern tip of Sumatra (SS) where vortex counts were 4
times higher during periods of anomalous easterlies compared to periods with
anomalous westerlies. While positive (negative) El-Nino-Southern Oscillation
(ENSO) and Indian-Ocean Dipole (IOD) conditions drive anomalous easterlies
(westerlies), the relationship between vortex count and these large-scale
indices is weak (r ¡ 0.1) in most regions. Only in region SS did the large-
scale conditions associated with these indices appear to impact vortex
formation frequency in the sense that positive ENSO and IOD conditions drive
anomalous easterlies which result in higher vortex formation rates.

##  1 Introduction

Under certain atmospheric conditions, stratified flow can be blocked by
topographic features resulting in downstream formation of wake vortices
(Smolarkiewicz and Rotunno, 1989; Rotunno and Smolarkiewicz, 1991). Kuettner
(1967, 1989) was the first to propose that Sumatra may serve as a generator of
wake vortices that subsequently develop into tropical cyclones (TCs). Easterly
flow blocked by Sumatra’s narrow mountain range, which exceeds 3000m in places
and straddles the equator from 6∘N to 6∘S, can result in the formation of wake
cyclonic vortices over the India Ocean (IO). Due to the paucity of
observations over the IO, Kuettner’s observations of these wake vortices have
received little attention until recently.

As a result of limitations in our basic understanding of, and ability to
predict the intraseasonal oscillation, particularly its initiation, a field
campaign known as the Dynamics of the Madden-Julian Oscillation (DYNAMO) was
conducted in the Indian Ocean (IO) region during the period October 2011–March
2012 (Yoneyama et al., 2013). This experiment provided researchers with
unprecedented atmospheric and oceanic datasets over a data-sparse region of
our planet including observations from upper-air soundings from ships and
islands (Ciesielski et al., 2014), radars, aircraft, and satellites. During
DYNAMO a wake vortex initiated off the northern tip of Sumatra in November
2011 as low-level easterlies associated with an approaching MJO convective
envelope (Johnson and Ciesielski, 2013; Gottschalck et al., 2013) flow
impinged upon the island. This vortex drifted slowly westward for four days
developing into a TC which caused significant damage and deaths in Sri Lanka
(http:// www.webcitation.org/63Vnhm01u). This storm and other TCs, which
formed from wake vortices during DYNAMO, resulted in a renewed an interest in
this topic.

Fine et al. (2016) (hereafter F16) investigated the potential role of Sumatra
Island, as well as the adjacent topography of the Malay Peninsula and Java
(Fig. 1), in producing terrain-induced circulations over the Indian Ocean that
subsequently develop into TCs. Applying sophisticated vortex tracking software
(Hodges 1995, 1999) to high-resolution (0.25°) model analyses, F16 found that
these topographic features are prolific generators of low-level cyclonic
vortices which contributed to 25% of the TCs occurring in the IO basin during
their study period. F16’s findings were based on a limited period (2.5 yr) in
which high-resolution ECMWF analyses were available (YOTC analyses from May
2008 to April 2010) and 6 months of a special DYNAMO operational analyses
(from October 2011 to March 2012).

With the recent availability of the ECMWF Reanalysis 5th Generation (or ERA5)
high-resolution dataset for the years 1979 to present, the opportunity to
extend the F16 analyses to additional years became possible. The goal of this
study is to determine the representativeness of F16’s findings compared to a
longer period (2008-2017) and a different, and presumably improved, reanalysis
dataset. Utilizing this longer analysis period, we investigate variability of
vortex formation and its relationship to various large-scale signals such as
the MJO, IOD, and ENSO signals. Finally, we consider some long-term IO TC
statistics to examine the relationship of TCs to wind regimes and large-scale
indices.

Figure 1: Analysis domain for study and topography of the region (elevation
scale to right in km). Blue lines at: 3∘-7∘N,100∘E, 2∘N-2∘S, 97∘E, and 3∘-7∘S,
105∘E represent averaging areas for zonal winds corresponding to these line
segments ($U_{N}$, $U_{E},$ and $U_{S}$, respectively) to delineate the
various flow regimes in the area which affect lee vortex production.

##  2 Data and Methodology

###  2.1 Datasets

ECMWF Reanalysis 5th Generation (or ERA5), which replaces the ERA-Interim
reanalysis, is based on 4D-Var data assimilation using Cycle 41r2 of the
Integrated Forecasting System (IFS), which was operational at ECMWF in 2016. A
detailed description of the ERA5 configuration, which benefits from a decade
of developments in model physics, core dynamics, and data assimilation
relative to ERA-Interim, can be found in Hersbach et al. (2020). For this
study we used both vorticity and zonal winds from ERA5.

The Madden-Julian Oscillation (MJO) is the major fluctuation in tropical
weather on weekly to monthly timescales (Madden and Julian, 1971). The MJO can
be characterized as an eastward moving ’pulse’ of cloud and rainfall near the
equator that typically recurs every 30 to 60 days. The location and strength
of the MJO are given by the Real-time Multivariate MJO (RMM) index developed
by Wheeler and Hendon (2004). This index is based on a pair of empirical
orthogonal functions (EOFs) of the combined fields of near-equatorially
averaged 850-hPa zonal wind, 200-hPa zonal wind, and satellite-observed
outgoing longwave radiation (OLR) data. Daily values of the RMM index provide
the amplitude and phase of the MJO. For this study, classification of the
vortices by MJO phase was only done when the MJO signal had a significantly
robust amplitude defined here as when the RMM amplitude was ¿ 1.

To represent the variability of the El Niño/Southern Oscillation (ENSO) we use
the Multivariate ENSO Index Version 2 (MEI.v2) which combines both oceanic and
atmospheric variables into a single assessment of the state of ENSO (Wolter
and Timlin, 2011; Zhang et al., 2019). Positive (negative) values of this
index imply warm, El Niño (cool, La Niña) conditions across the east-central
equatorial Pacific. The MEI.v2 is available on a monthly basis.

Variability in the IO region is often characterized by changes in the east-
west sea surface gradient across the IO basin referred as the Indian Ocean
Dipole (IOD) mode (Saji et al., 1999). The IOD is commonly measured by the
Dipole Mode Index (DMI), that is, the difference between sea surface
temperature (SST) anomalies between the western (50∘-70∘E) and eastern
(90∘-110∘E) tropical (10∘S-10∘N) IO. A positive (negative) IOD period is
characterized by cooler (warmer) than average water in the tropical eastern
Indian Ocean and warmer (cooler) than average water in the tropical western
Indian Ocean.

Information on IO tropical cyclone tracks and intensity was obtained from the
Joint Typhoon Warning Center (JTWC) best-track archive which goes back to 1945
(Chu et al., 2002). For this study TC data were used from 1980 to 2017,
although Chu et al. (2002) state that the years after 1984 have the best data
quality. The best-track data contains the storm center locations and
intensities (i.e., the maximum 1-minute mean sustained 10-meter wind speed) at
six-hour intervals. Storms are only considered here that (1) reach TC
intensity (i.e., maximum sustained winds of 35 knots or 39 mph) and (2) formed
over the IO (i.e., extending from Africa to 105∘E). Storms with missing wind
speeds, which are most prevalent in the earlier years of the archive, were not
considered.

###  2.2 Vortex tracking

As in F16, identification and tracking of low-level lee vortices was carried
out based on the relative vorticity field using the objective feature tracking
code of Hodges (1995, 1999). To facilitate the use of this software, relative
vorticity at 6 h and 0.25∘ horizontal resolution from ERA5 analyses were
vertically averaged using data at 850, 875, 900, 925 hPa from 50∘-110∘E,
20∘N-20∘S. The F16 analyses had only three vertical levels in the 850 to 925
hPa layer. After smoothing the vorticity field to retain spatial scales
greater than 450 km, cyclonic vortex features were tracked if they maintained
an amplitude greater than 1.0 $\times$ 10-5 s-1 for longer than 2 days.

To focus on wake vortices with the potential to develop into TCs, we restrict
our analyses to cases where the vortex moved westward over the Indian Ocean.
As in F16 these shed vortices are defined as those with 1) a final location
over the Indian Ocean that is ¿ 500 km from Sumatra, and either 2) a final
minus initial displacement from Sumatra ¿ 250 km, or 3) their average speed
away from Sumatra is ¿ 0.5 ms-1. The first condition ensures that the shed
vortex at the end of its track is some critical distance from Sumatra while
conditions 2 or 3 guarantee that the vortex is moving away from its generating
landmass.

Application of the tracking code to ten years of ERA5 data yields information
on both the tracks and locations of cyclonic lee vortices. Because of seasonal
changes in the flow regime, genesis locations are shown in Fig. 2 for the
boreal cold season (November to April) and the boreal warm season (May to
October). Overall, these analyses based on 10 years of statistics are
remarkably similar to those shown in F16. For example, during the boreal
winter season (Fig. 2a), northeasterly flow across the Malay Peninsula and
northern tip of Sumatra result in a high frequency of lee vortices being
formed downstream of these topographic features. Two boxes shown in this
figure (covering the same areas as in F16) are defined to help quantify the
relationship between the winds and vortex generation over these regions in
subsequent analyses. These two regions are referred to a SN (Sumatra North)
and MP (Malay Peninsula). Other hotspots for lee vortex generation are also
seen over Sri Lanka and the west coast of India but are not considered further
in this study. Between the equator and 10∘S, westerly flow predominates such
that production of lee vortices over the IO west of the any topographic
features is much less common in this area.

During the boreal summer monsoon (Fig. 2b), southeasterly flow prevails across
the southern tip of Sumatra and Java resulting in a high frequency of vortex
production in the lee of these topographical features. As in F16, analysis
boxes are defined as SS (Sumatra South) and JV (Java) to highlight these lee
vortex hotspots for further analysis. Westerly flow dominates the NH IO region
during this period resulting in several lee vortex hotspots. However, these
areas are not considered further as any vortices shed from these areas would
move eastward and likely not contribute to any TCs.

To better understand the relationship of different flow regimes on the
production of lee vortices, three computational lines shown in Fig. 1 are
defined: (1) 3∘-7∘N, 100∘E, (2) 2∘N-2∘S, 97∘E, and (3) 3∘-7∘S, 105∘E. Averages
of zonal winds in these 3 areas, referred to as $U_{N}$, $U_{E}$, and $U_{S}$,
respectively, are considered representative of the flow in the adjacent
analysis boxes and over the equator west of Sumatra. In regressing relative
vorticity in the analysis boxes onto zonal winds, $U_{N}$ and $U_{S}$, F16
found that correlations maximize around 0.8 in the 950-850 hPa layer in the
north and around 0.6 in the 950-1000 hPa layer to the south. Such correlations
are expected considering flow blocking effects of topography and the average
height of 1-2 km in northern Sumatra and slightly lower in the south. Thus,
for future analyses involving the winds in this study, data from the 925 hPa
level are used.

Table 1: Vortex formation and shedding statistics for four regions (SN, MP, SS, and JV) and based on different analyses (YOTC/DYNAMO used in F16 and ERA5) and analysis periods (2.5 yr period examined in F16 and 2008-2017 period). Numbers in parentheses represent annual rates.  Region (Analysis, Years) | Total Vortices | # Shed Vortices | Percent Shed
---|---|---|---
SN (YOTC/DYN, 2.5 yr) | 73 (29.2) | 43 (17.2) | 59%
SN (ERA5, 2.5 yr) | 69 (27.6) | 40 (16.0) | 58%
SN (ERA5, 10 yr) | 248 (24.8) | 143 (14.3) | 58%
MP (YOTC/DYN, 2.5 yr) | 85 (34.0) | 15 (6.0) | 18%
MP (ERA5, 2.5 yr) | 75 (30.0) | 21 (8.4) | 28%
MP (ERA5, 10 yr) | 295 (29.5) | 90 (9.0) | 31%
SS (YOTC/DYN, 2.5 yr) | 74 (29.6) | 25 (10.0) | 34%
SS (ERA5, 2.5 yr) | 69 (27.6) | 20 (8.0) | 29%
SS (ERA5, 10 yr) | 272 (27.2) | 80 (8.0) | 29%
JV (YOTC/DYN, 2.5 yr) | 77 (30.8) | 20 (8.0) | 26%
JV (ERA5, 2.5 yr) | 96 (38.4) | 49 (19.6) | 51%
JV (ERA5, 10 yr) | 326 (32.6) | 185 (18.5) | 57%

##  3 Results

###  3.1 Comparison to Fine et al. 2016

Vortex statistics for the four vortex production hotspots identified in Fig. 2
are listed in Table 1 for the YOTC/DYN (YD) period. For each region, we
compare the number of total and shed vortices from F16 to that from ERA5
(referred hereafter as EYD). In general, the statistics for F16 and EYD agree
reasonably well except for the JV region in which EYD has 25% more total
vortices and more than double the number of shed vortices. Considering all
four hotspot regions, Table 2 show that the total the number of vortices
formed is identical between these analyses (i.e., 309) but the percentage shed
is higher in EYD (42% versus 33%) primarily due to the JV region with its high
shed frequency.

Figure 2: Cyclonic vortex genesis locations on a 1∘ grid for (a) November to
April and (b) May to October periods based on 10-yr (2008-2017) analyses of
ERA5 data. Streamlines depict the 925- 850 hPa layer flows. Boxes highlight
vortex production hotspots which are used for further analyses in this study.

F16 showed a strong relationship between the winds in the vicinity of the
topographic features and the production of lee vortices. In their study they
found that about 80% (85%) of vortices (shed vortices) occurred in the
presence of low-level easterly flow (F16 Table 1). Similar statistics are
present for the EYD (not shown). Comparison of low-level winds between the F16
and the EYD analysis show little difference (Fig. 3). For example, the
temporal correlation of daily-averaged $U_{S}$ winds between these analyses is
0.99 and a difference in means is less than 0.2 m s-1, with F16 having
slightly stronger easterlies (or weaker westerlies) throughout the year. With
this similarity in winds between the two analyses, it difficult to understand
why the percentage of shed vortices in the JV region is nearly double in EYD.

F16 identified 13 TCs which developed from shed lee vortices in their 2.5 yr
analyses. These TCs were tracked primarily by using the vorticity field but in
4 cases the shed vortex amplitude fell below the threshold limit of 1.0
$\times$ 10-5 s-1 such that continuity of the tracked vortex into a TC was
established by also tracking the vortex as a depression in the height field.
Using ERA5 we were able to identify these 13 TCs with similar tracking issues
as in F16.

Overall, the good agreement between F16 and that from the ERA5 for the YD
period gives us confidence that the ERA5 has reproduced the salient feature of
vortex formation, shedding, and development into TCs found in F16. Since ERA5
has improved model physics and data assimilation over the analysis used in
F16, it seems reasonable to assume that the notable differences we did find
(e.g., higher vortex production and shedding over JV region using ERA5) are
likely better represented in ERA5. We now present statistics for the longer
10-yr record to determine if the findings of F16 are representative of this
longer-term period.

Table 2:  Vortex formation and shedding statistics for four regions (SN, MP, SS, and JV) combined based on different analyses (YOTC/DYAMO used in F16 and ERA5) and analysis periods (2.5 yr period examined in F16 and 2008-2017 period). Numbers in parentheses represent the annual rate (i.e., vortices/year).  Analysis, Years | Total Vortices | # Shed Vortices | Percent Shed
---|---|---|---
F16, 2.5 yr | 309 (123.6) | 103 (41.2) | 33%
EYD, 2.5 yr | 309 (123.6) | 130 (52.0) | 42%
ERA5 10yr | 1141 (114.1) | 498 (49.8) | 44%
Table 3:  Tropical cyclone counts over the NH and SH of the Indian Ocean for the YD, 2008-17, and 1980-2017 periods. Numbers in parentheses represent the annual rates (i.e., TCs/year).  Period | NH IO | # SH IO | NH+SH IO
---|---|---|---
YD (2.5 yr) | 15 (6.0) | 34 (13.6) | 49 (19.6)
2008-17 (10 yr) | 51 (5.1) | 105 (10.5) | 156 (15.6)
1980-2017 (38 yrs) | 181 (4.8) | 434 (11.4) | 615 (16.2)

###  3.2 Vortex statistics based on 10 years of ERA5

To place the F16 analyses in the context of a longer period, Tables 1 and 2
include the vortex formation and shed statistics for the 2008-2017 period. To
facilitate this comparison between periods of different length, the numbers in
parentheses list the annual rate (i.e., vortex count divided by the number of
years). Comparing the ERA5 results for the two periods shows that YD-period
was characterized with a higher frequency of vortex formation in all four
regions (Table 1). Considering the regions collectively (Table 2), the YD-
period showed an 8% rate increase in vortex formation and an $\sim$4% increase
in shed vortex numbers compared to the 10-yr mean. Further examination of
fields at 925 hPa over these regions revealed that the YD-period had slightly
stronger (0.3 m s-1) easterly winds and higher cyclonic relative vorticity
(6$\times$10-7s-1) compared to the 10-yr period. It’s worth noting that the TC
frequency over the IO was 20% higher in YD-period compared to 10-yr mean
(Table 3). In summary, the YD-period was slightly more active than the 10-yr
mean in terms of vortex formation, occurrence of shed vortices, and TCs, a
likely consequence of an enhanced easterly component of the flow during the YD
period. Having established a context for the YD-period, we now consider some
additional characteristics of lee vortex production in the 10-yr period.

Figure 3:  a) Time series of daily-averaged winds over southern Sumatra
($U_{S}$) for the YOTC period (May 2008 to April 2009) from F16 (black) and
ERA5 (red), b) similar to a) expect annual cycle of monthly averaged $U_{S}$
winds.

Figure 4:  Monthly frequency of terrain-induced cyclonic vortices (top of
black bar) and those which shed (top of red bar) for (a) SN region and (b) MP
region. (c) Monthly mean zonal winds (m s-1, scale to left) at 925 hPa along
100∘E ($U_{N}$ line segment shown in Fig. 1), and mean monthly vorticity
(10-5s-1, scale to right) at 925 hPa over SN (cyan) and MP (red). The numbers
in the parentheses indicate the total number of vortices formed and those that
shed, respectively, over each region. Numbers in upper-right side of panels
represent the correlation between the monthly vortex frequency and the
monthly-averaged zonal winds over $U_{N}$.

Figure 5:  Monthly frequency of terrain-induced cyclonic vortices (top of
black bar) and those which shed (top of red bar) for (a) SS region and (b) JV
region. (c) Monthly mean zonal winds (m s-1, scale to left) at 925 hPa along
105∘E ($U_{S}$ line segment shown in Fig. 1), and mean monthly vorticity
(10-5s-1, scale to right) at 925 hPa over SS (cyan) and JV (red). Numbers in
parentheses indicate the total number of vortices formed and those that shed,
respectively, over each region. Numbers in upper-right side of panels
represent the correlation between the monthly vortex frequency and the
monthly-averaged zonal winds over $U_{S}$.

Figure 6:  Vortex count as a function of zonal wind (m s-1) for non-shed (green) and shed vortex (red) cases for the four regions of interest in this study. Numbers in parentheses in top labels represent the number of non-shed and shed vortex cases, respectively. Within each panel the numbers give the percentage of cases in which the vortex was initialized under easterly flow conditions (non-shed – green, shed – red).  Table 4:  Zonal wind (m s-1) statistics for regions of interest. From left to right: Mean zonal wind for region ($\bar{U}$) based on 2008-17 period, average zonal wind associated with vortex formation ($U\\!V\\!F$), difference between $U\\!V\\!F$ and $\bar{U}$, $U\\!V\\!F$ for non-shed vortices, $U\\!V\\!F$ for shed vortices.  Region | $\bar{U}$ | Average $U$ for |  $U\\!V\\!F$ \- $\bar{U}$ | $U\\!V\\!F$ | $U\\!V\\!F$
---|---|---|---|---|---
|  | vortex formation |  | (non- | (shed)
|  | $U\\!V\\!F$ |  | shed) |
SN | 1.5 | -1.3 | -2.8 | -0.8 | -1.7
MP | 0.0 | -2.7 | -2.7 | -2.2 | -3.7
SS | -0.3 | -3.1 | -2.8 | -3.1 | -2.9
JV | -1.1 | -3.8 | -2.7 | -2.3 | -4.8

The annual cycle of monthly vortex count for vortices originating from
terrain-induced circulations in regions SN and MP are shown in Fig. 4. As seen
here, vortex counts maximize in the months with the strongest mean easterlies
with a peak in January over SN and in February in MP. During the boreal summer
months, prevailing westerlies over these regions result in the production of
few lee vortices. In contrast over the SS and JV regions, the vortex count
peaks in the boreal summer months when easterlies prevail over these southern
regions (Fig. 5). Also, while the northern regions have only a single peak in
production numbers, the annual cycles over the southern regions appear more
complex with multiple peaks. For example, over SS there is a gradual ramp up
to a peak in August when easterlies ($U_{S}$) are strongest, but then the
highest peak occurs in October when mean easterlies are reduced from the late
summer maximum. Likewise, over JV multiple peaks occur with the highest number
in July and a secondary peak in November. And while the mean winds have
transitioned to weak westerlies by November, the mean low-level vorticity
remains negative (i.e., cyclonic). Also, listed in Figs. 4 and 5 are the
correlation between the monthly-averaged vortex frequency and monthly-averaged
zonal winds. Correlations are near or above $-0.9$ in all the regions except
SS indicating that the annual cycle of zonal winds in the former regions
explain $\sim$80% of the variance in monthly vortex counts. On the hand, the
lower correlation in region SS ($-0.67$) suggests that zonal wind variability
outside the annual cycle (i.e., intraseasonal or interannual time scales) is
more influential on the monthly vortex count in this region.

Figure 7:  Vortex count as a function of relative vorticity (10-5 s-1) for non-shed (green) and shed vortex (red) cases for the four regions of interest in this study. Numbers in parentheses in top labels represent the number of non-shed and shed vortex cases, respectively.  Table 5:  Relative vorticity (10-5 s-1) statistics for regions of interest. From left to right: Mean zonal vorticity for region ($\bar{\zeta}$) based on 2008-17 period, average $\zeta$ associated with vortex formation ($V\\!V\\!F$), difference between $V\\!V\\!F$ and $\bar{\zeta}$, $V\\!V\\!F$ for non-shed vortices, $V\\!V\\!F$ for shed vortices.  Region | $\bar{\zeta}$ | Average $\zeta$ for |  $V\\!V\\!F$ \- $\bar{\zeta}$ | $V\\!V\\!F$ | $V\\!V\\!F$
---|---|---|---|---|---
|  | vortex formation |  | (non- | (shed)
|  | $V\\!V\\!F$ |  | shed) |
SN | -0.07 | 1.2 | 1.27 | 1.1 | 1.3
MP | -0.05 | 1.0 | 1.05 | 0.8 | 1.3
SS | -0.68 | -1.2 | -0.52 | -1.2 | -1.3
JV | -0.56 | -1.1 | -0.54 | -0.9 | -1.2

To further explore the relationship of vortex formation and shedding to winds
and vorticity, Figs. 6 and 7 examine the distribution of the zonal winds and
vorticity for shed and non-shed cases over the four regions of interest,
respectively. In these figures the wind speed and vorticity represent their
values at the time the vortex was first identified in the regions of interest.
Included in Fig. 6 are percentage of non-shed and shed vortices occurring
with easterly flow. In addition, Tables 4 and 5 summarize the zonal wind and
vorticity statistics for vortex formation in these regions. Clearly the
presence of easterly flow is a dominant factor in determining vortex formation
and shedding. JV, which had the highest number of vortices during this 10-yr
period (326), also had the strongest easterlies during times of vortex
formation. In contrast, SN had the fewest vortices (248) and the weakest
easterlies. The increase in the easterly component of the wind from its mean
state and that observed with vortex formation is remarkably consistent among
the regions being 2.75 m s${}^{-1}\pm$ 0.05 m s-1 (Table 4,
$U\\!V\\!F-\bar{U}$). This consistency is likely coincidental, as the
analogous cyclonic vorticity increase (Table 5, $V\\!V\\!F-\bar{\zeta}$)
varies considerably among the regions being nearly double for the NH
locations. In general, shed cases are associated with stronger easterlies and
higher cyclonic vorticity (Tables 4 and 5). While non-shed cases occur with
easterly flow 61-81% of the time, the presence of easterly flow for shed
cases, as one might expect, is even higher (76% to 94%). As seen in Table 1
the shed frequency, i.e., percentage of vortices which shed and move westerly
after forming, varies among the regions ranging from $\sim$30% in ML and SS to
greater than 50% in SN and JV. While SN has the highest shed frequency at 57%,
it also has the weakest easterly winds, such that factors the other than zonal
wind speed (e.g., vertical shear, large-scale thermodynamical environment)
must be contributing to the frequency at which vortices stay intact and shed
once they form.

###  3.3 Relationship of vortex production to large-scale signals (MJO, IOD,
ENSO)

The 10-yr time series of monthly vortex counts for the four regions of
interest are shown in Fig. 8. Beyond the seasonal variability, as depicted in
the Figs. 4 and 5, these time series contain fluctuations on intraseasonal
and interannual time scales as well. Leveraging this longer analysis period,
we now consider variability of vortex formation and its relationship to
various large-scale signals such as the MJO, IOD, and ENSO signals.

Figure 8:  Time series of monthly vortex count for four regions of interest
(black bars show total count, red bars show shed-vortex count). Numbers in
parentheses give the total and shed vortex count for 2008-17 period. Blue
(red) shading represent periods in region SS that experienced prolonged
periods of anomalous negative (positive) monthly zonal wind anomaly
$U^{\prime}$.

Figure 9 examines the vortex and zonal wind statistics based on the phase of
the MJO. Here vortex counts and winds are only considered if the MJO signal
was reasonably strong, defined here as the RMM index amplitude being $\geq 1$.
In general, vortex counts are highest when easterlies are strongest (i.e.
phases 7, 8, and 1). The modulation of vortex count by MJO phase is most
prominent in the southern regions (SS and JV) where the zonal wind speed
variations by the MJO are more pronounced. For example, the wind speed change
over the course of the MJO over the southern regions is about 4-5 m s-1
compared to 2-3 m s-1 over SN and MP. Consistent with the findings above, the
right panels of Fig. 9 show that shed vortices are generally associated with
stronger easterly winds.

Figure 9:  Statistics for vortex count (left panels) and winds (right panels)
for four regions of interest (black curves are for all vortices, red curves
are for shed vortices) as function of MJO phase.

A common feature associated with the MJO over the IO is a region of strong
near-equatorial westerlies which follows the period of strongest convection.
This feature, referred to as a westerly wind burst (WWB) and examined
extensively in previous literature (Rui and Wang, 1990; Hendon and Salby,
1994; Kiladis et al., 1994) has a prominent low-level signature peaking near
700 hPa (Kiladis et al., 2005). Since F16 examined a case where vortex
formation in both hemispheres appeared to be assisted by blocking of strong
low-level equatorial westerlies by central Sumatra, Fig. 10 considers the
statistics of vortex formation and low-level equatorial winds based on the MJO
phase. Here the statistics for all the regions are considered together and the
low-level equatorial flow $U_{E}$ is taken from the region (2∘N-2∘S, 97∘E)
shown in Fig. 1, that is centered on the equator and a few hundred kms to the
west of Sumatra. As seen here the vortex counts are highest during MJO phase 1
when equatorial westerlies are weak and off equatorial winds are easterly (as
seen in Fig. 9). However, a secondary peak occurs in vortex count during
phase 4 when the equatorial westerlies are strongest. This peak in westerlies
over $U_{E}$ during MJO phase 4 is consistent with the canonical structure of
the MJO described in Kiladis et al. (2005) which places the low-level
westerlies during this phase to the west the MJO convective center located
over the Maritime continent. This suggests that westerly surges on the equator
associated with MJO convection may be contributing to the uptick in vortex
formation during MJO phase 4. This uptick during MJO phase 4 is seen in all
regions but is most prominent in SS and is weakest in JV (Fig. 9). The
mechanism for vortex formation in this situation is most likely a combination
or superposition of two effects: (1) the generation of equatorial Rossby waves
to the west of the MJO convective envelope (Gill, 1980) and (2) blocking and
splitting of the flow as it encounters the steep terrain of Sumatra, which can
serve to enhance counter-rotating circulations at opposite ends of the island
(Smith, 1989).

Figure 10:  Statistics for vortex count (left panels) and $U_{E}$ winds (right
panels) for all regions collectively (black curves are for all vortices, red
curves are for shed vortices) as function of MJO phase.

Figure 11:  Time series for period 2008-17 of monthly-averaged zonal wind
(black curve) and monthly anomaly of zonal wind from its annual cycle
($U^{\prime}$, red curve) for regions of interest from top to bottom: SN, MP,
SS, and JV. Blue (red) shading represent periods in region SS that experienced
prolonged periods of anomalous negative (positive) $U^{\prime}$.

To further examine the temporal variability in the vortex count depicted in
Fig. 8, we show in Fig. 11 the time series of monthly-averaged zonal wind
and its anomaly from the annual cycle (depicted in Figs. 4 and 5) for the
four regions of interest. The large, negative correlations of these monthly-
averaged winds to vortex count (Table 6, middle column) reflect the strong
relationship that exists between vortex formation and the presence of easterly
winds. The variance explained by this relationship is smallest in region SS
consistent with its behavior over the annual cycle discussed earlier. However,
when vortex count is regressed against the anomaly of the zonal winds from its
annual cycle, this relationship is strongest in region SS (Table 6, rightmost
column). This suggests that perturbations to the annual cycle of winds caused
by signals other the annual cycle are influencing vortex formation in region
SS. For whatever reason, periods of persistent anomalous winds are more
prevalent in the southern regions and largest in SS. Four such periods (two
with negative wind anomalies and two with positive anomalies) have been
highlighted in Figs. 8 and 11 to show how anomalous zonal winds are impacting
vortex formation in region SS. For these two periods with anomalous easterlies
(-2.1 m s-1) the SS vortex count averaged 4/month (76 vortices in 19 months);
for the two periods with anomalous westerlies (+2.6 m s-1), the SS vortex
count averaged 1.1/month (23 vortices in 22 months). This fourfold increase in
vortex formation between anomalous wind periods highlights the sensitivity of
vortex development to anomalies in the large-scale wind field.

Table 6:  (middle) Correlation (r) between monthly vortex count and monthly-averaged zonal wind ($\bar{U}$ ), and (right) correlation between monthly vortex count and monthly-zonal wind anomaly from its mean annual cycle ($U^{\prime}$). For these correlations winds averaged over each region of interest were used based on data for 2008-2017 period.  Region | r (vortex count, $\bar{U}$) | r (vortex count, $U^{\prime}$)
---|---|---
SN | -0.77 | -0.15
MP | -0.79 | -0.20
SS | -0.59 | -0.41
JV | -0.70 | -0.27

Having established the strong dependence of vortex formation on the large-
scale wind field, we now consider how the wind field is impacted by
circulation changes related to the IOD and ENSO signals. Figure 12 shows the
time series of the ENSO MEI.v2 and IOD indices for the 10-yr period of this
study. These two indices show a weak temporal correlation (0.23) during this
period. Detailed discussions of their interaction and influence on each other
can be found in other studies (Behera et al., 2006; Cai et al., 2011). The
2008-17 time frame contained two prominent ENSO warm events near the end of
2009 and 2015 into early 2016 and two cool events in 2008 and the latter half
of 2010 into 2011. In general, the warm (cool) events are associated with
suppressed (enhanced) convection over the Maritime Continent and enhanced low-
level easterlies (westerlies) over the IO (Ramage, 1968; Chang et al., 2004).
The negative phase of the IOD as depicted in the schematic in Fig. 13 is
associated with warm SSTs in the eastern IO, increased convection over the
maritime continent, and enhanced low-level westerlies over the equatorial IO.
The positive phase of the IOD would have opposite impacts, namely suppressed
convection over the maritime continent and enhanced low-level easterlies over
the equatorial IO.

Figure 12:  Times series for period 2008-17 of: (a) ENSO index, (b) IOD index,
(c) $U^{\prime}$ over SS, (d) vortex count over SS. Blue (red) shading
represent periods in region SS that experienced prolonged periods of anomalous
negative (positive) $U^{\prime}$.

Figure 13:  Schematic of positive phase of Indian Ocean Dipole (from NOAA
Climate.gov).

Table 7 lists the correlations between monthly zonal wind anomaly
($U^{\prime}$) and the ENSO and IOD indices. In all the regions a small
negative correlation is observed, which suggests that positive (negative) ENSO
and IOD conditions are driving anomalous easterlies (westerlies). Correlations
are slightly larger between $U^{\prime}$ and the IOD index in all regions
except JV, possibly because the IOD is a more regional index for the areas
considered here. Having identified the importance of the wind field on vortex
formation and the relationship, albeit weak, between these large-scale indices
and the winds, we now consider whether vortex formation is related to the
large-scale circulation changes associated with ENSO and the IOD signals. The
right-most two columns in Table 7 list the correlations between vortex count
and these large-scale indices. Only in region SS are correlations significant,
which is consistent with the stronger relationship between $U^{\prime}$ and
vortex count seen in Table 6 and the higher correlations between $U^{\prime}$
and indices in Table 7 for this region. The positive correlations seen in
region SS suggest that positive (negative) ENSO and IOD conditions are
associated with enhanced easterly (westerlies) and thus a higher (lower) rate
of vortex formation. The bottom two panels of Fig. 12 show the $U^{\prime}$
and vortex count for region SS to help illustrate the relationship between
these fields. It is worth noting that when the ENSO and IOD indices are of the
same sign as in the 2015-16 period, the anomalous winds and impact on the
vortex formation seem most dramatic. Vortex formation in region SS typically
peaks in the months from May to October (Fig. 5) when the mean flow has an
easterly component. For these months, Fig. 14a depicts the total flow field
during 2015 when enhanced easterlies were present over SS and 30 vortices
formed. In contrast, anomalous westerlies during the 2016 period (Fig. 14b)
resulted in weak flow from the northwest over SS and the formation of only 12
vortices. The reason that this relationship is significant only in region SS
during this period is unclear at this time.

Table 7:  (from left to right) Correlation (r) between monthly-zonal wind anomaly ($U^{\prime}$) and ENSO index, correlation between $U^{\prime}$ and IOD index, correlation between number of vortices formed and ENSO index, and correlation between number of vortices formed and IOD. All correlation were computed using data for the 2008-2017 period.  Region | r ($U^{\prime}$, ENSO) | r ($U^{\prime}$, IOD) | r(# vor, | r(# vor,
---|---|---|---|---
|  |  | ENSO) | IOD)
SN | -0.35 | -0.41 | 0.10 | 0.13
MP | -0.25 | -0.33 | 0.11 | ¡0.10
SS | -0.45 | -0.50 | 0.36 | 0.21
JV | -0.46 | -0.35 | ¡0.10 | ¡0.10

Figure 14: a) 925 hPa flow field for May – October 2015, b) 925 hPa flow field
for May – October 2016. Reference vector and scale for wind vectors (m s-1)
shown at bottom. Red box outlines region SS. Created using NCEP reanalysis II
and NOAA/PSL visualization tools.

###  3.4 Characteristic of the long-term TC record over the IO

One of the key findings of F16 is that 25% of the TCs in the IO basin during
the YD period had their origins in vortices that shed from topographic
features in the western maritime continent. A cursory examination of remaining
7.5 years in the 2008-17 period found an additional 15 TCs that had their
origins in shed vortices. Most likely this number is an undercount since
vortices can weaken below the vorticity tracking threshold (1$\times$10-5s-1)
before reintensifying. While identification of these more subtle cases is
beyond the scope of this study, it is instructive to examine some of the
characteristics of the long-term TC record over the IO.

Figure 15:  (a) Monthly frequency of tropical cyclones over the NH IO (black)
and impacting India and Sri Lanka (cyan) for the period 2008-2017. (b) Monthly
mean zonal wind (m s-1) over northern Sumatra ($U_{N}$, black curve), zonal
wind speed $U_{N}$ at 5 days prior to a storm initialization (one x-symbol for
each TC), the red circle shows the mean of winds represented by the x- symbols
in that month.

Figure 16:  (a) Monthly frequency of tropical cyclones over the SH IO (black)
for the period 2008-2017. (b) Monthly mean zonal wind (m s-1) over northern
Sumatra ($U_{S}$, black curve), zonal wind speed $U_{S}$ at 5 days prior to a
storm initialization (one x-symbol for each TC), the red circle shows the mean
of winds represented by the x- symbols in that month.

Figs. 15 and 16 show the annual cycle of TC count over the IO for the NH and
SH regions for 2008-17, respectively. During this 10-yr period, 51 TCs were
identified over the NH and 105 over the SH. Of the NH cases, 22 made landfall
in India or Sri Lanka with TC intensity or as decaying TCs. Over the NH IO, TC
numbers peak in November with a secondary maximum in May. While the NH May
peak occurs during a period of mean westerlies over ($U_{N}$), the November
maximum occurs during a period of climatological easterlies (Fig. 15b). Also
plotted in this figure are the winds over the northern region ($U_{N}$) five
days prior111Winds over the regions of interest ($U_{N}$ and $U_{S}$) at 5
days prior to time $t_{0}$ were used here because over the period from $t_{0}$
to $t_{0}-$15 days they had the strongest easterly component. to the time
($t_{0}$) when the cyclone was first identified by JTWC. It worth noting that
while in some months the $U_{N}$ winds are mean westerly, there are a number
of cases in which the winds were easterly at $t_{0}$ such that the potential
for the TC to have initialized from a lee vortex existed. Over the SH IO, TC
numbers peak in February during which $U_{S}$ is mean westerly (Fig. 16).
During the months with mean easterlies in $U_{S}$ (May through October) the TC
count is generally low. Similar to the NH, there are number of TC cases in
months with mean westerlies in which $U_{S}$ winds were easterlies at $t_{0}$.

Figure 17:  Time series for period 2008-17 of: a) monthly count for NH IO TCs
(black), TCs impacting India and Sri-Lanka (cyan), b) monthly count for SH IO
TCs (black), c) ENSO index, d) IOD index. Numbers in parentheses indicate the
number of TCs in each category for this 10-yr period.

The time series of monthly TC count over the NH and SH IO regions is shown in
Fig. 17, along with the ENSO and IOD indices for the 2007-2008 period. No
significant correlations (¡0.1) exist between the TC count time series and
these indices. However, if we consider only TCs that originated east of 90∘E,
a small negative correlation ($-0.2$) is found between NH TCs and the IOD.
This suggests that the warmer waters over the eastern IO (negative phase of
IOD) contribute to higher TC numbers.

Since other ocean basins have shown a sensitivity of TC formation to the phase
of the MJO (Maloney and Hartmann, 2000; Zhang, 2013), we now composite the IO
TC count by the MJO phase based on their initialization time $t_{0}$. We note
that time from $t_{0}$ to TC formation is on average 36 hours over the NH and
45 hours over the SH. Using these criteria, Fig. 18 shows that in both
hemispheres cyclone initiation occurs most frequently in MJO phase 3. These
findings are consistent with Bessafi and Wheeler (2006) who found that TC
numbers over the southern IO increase by a factor of 2.6 between MJO
convectively active phases (2 and 3) compared to convectively suppressed
phases (8 and 1). Recalling that easterlies and vortex formation peak around
phase 1 (Fig. 10) or about 8 to 12 days prior to MJO phase 3, and that the
average gestation period from vortex formation to TC genesis is 10.1 days
(F16), then shed vortices conceivably are contributing to the storm
initialization peak in MJO phase 3. For TCs impacting India and Sri Lanka
(Fig. 18b), the storm initialization peak occurs slightly later around MJO
phase 4 in agreement with the findings of Hall et al. (2001). This slightly
later peak over the northern IO is due to the poleward drift with time of the
convectively active regions of the intraseasonal signal in this region of the
world.

Figure 18:  Statistics for TC count as function MJO phase based on period
2008-17 for (top) NH IO TCs, (middle) TCs impacting India and Sri-Lanka and
(bottom) SH IO TCs. Time that storm was first identified by JTWC was used to
categorize TC by MJO phase. Only cases where the MJO amplitude was ¿ 1 are
considered here.

Figure 19:  Time series for period 1980-2017 of: a) monthly count for NH IO
TCs (black), TCs impacting India and Sri-Lanka (cyan), b) monthly count for SH
IO TCs (black), c) ENSO index, d) IOD index. Numbers in parentheses indicate
the number of TCs in each category for this 38-yr period.

Figure 20:  Statistics for TC count as function MJO phase based on period
1980-2017 for (top) NH IO TCs, (middle) TCs impacting India and Sri-Lanka and
(bottom) SH IO TCs. Time that storm was first identified by JTWC was used to
categorize TC by MJO phase. Only cases where the MJO amplitude was ¿ 1 are
considered here.

To examine the representativeness of the 10-yr TC record relative to a longer
period, Fig. 19 shows time series of TC count for years 1980-2017. This
period contained several ENSO cycles with significant El Nino (warm) events in
1982-83, 1987-88, 1997-98, and 2015-16. During this 38-yr period the NH IO
basin averaged 4.8 TCs/year while the SH IO basin experienced more than double
this rate at 11.4 TCs/year. These rates are similar to the 2008-17 period but
below that of the YD period investigated by F16 (Table 6). Landfalling or
decaying TCs impacting India and Sri Lanka averaged 2.2 per year during this
period. No long-term trends were detectable in any of these time series. Also,
no significant correlation (¿0.1) of TC numbers to large-scale indices were
observed except for a slight correlation ($-0.2$) between TC numbers for
storms initializing east of 90∘E and the IOD index. As in the 10-yr record
(2008-17), TC initializations for this longer period (Fig. 20) peak in MJO
phase 3 over both NH and SH IO basins and MJO phase 4 for storms impacting
India/Sri Lanka.

##  4 Summary and conclusions

With the recent availability of the ERA5 high-resolution reanalyses for the
years 1979 to present, the opportunity to extend the Fine et al. (2016, F16)
vortex tracking analyses to additional years became available. The goal of
this study is to determine the representativeness of F16’s findings compared
to a longer period (2008-2017) using this improved operational analysis and to
examine the characteristics of vortex formation and shedding and their
relationship to intraseasonal and interannual oscillations for this longer
record.

F16 identified four vortex genesis regions near the northern and southern tips
of Sumatra (see Fig. 2 for their locations). Application of the tracking
software to 10 years of ERA5 analyses in a similar fashion to F16 yielded the
following conclusions based on statistics for these four vortex “hotspots”.

  * •

For the 2.5-yr period, referred herein as the YD-period since F16 used
YOTC/DYNAMO (YD) analyses, terrain-induced production of vortices was similar
between F16 and ERA5 (123/yr) while the vortex shedding rate was slightly
higher in ERA5 (42% versus 33% in F16).

  * •

For the 10-yr period, vortex production in ERA5 was 114/yr; vortex shedding
frequency was 44%.

  * •

The higher rate (8%) of vortex formation during the YD-period compared to the
longer-term mean was likely due to an enhanced easterly component of the flow
during the YD-period.

While the YD-period of F16’s analyses was slightly more active in terms of
vortex production than the 10-yr period, in general F16’s findings are
representative of the longer-term record. The following represents conclusions
based on additional analysis of the 10-yr record of vortex production and
shedding in the ERA5 dataset:

  * •

$\sim$70% ($\sim$80%) of all vortices (shed vortices) occur with easterly low-
level (925 hPa) flow over the regions of interest.

  * •

Vortices which shed (i.e., move westward over the IO) are typically associated
with stronger low-level easterlies and higher cyclonic vorticity. However, it
is unclear why the SN region (the area off the northern tip of Sumatra) has
the highest shed frequency yet is characterized with the weakest easterlies.

  * •

Vortex counts are highest near MJO phase 1 when stronger low-level easterlies
are present over the maritime continent region.

  * •

The annual cycle of zonal winds largely controls vortex formation rates in the
regions of interest. For reasons unclear at this time, this relationship is
less apparent for region SS (the area off the southern tip of Sumatra) where
zonal wind variability outside the annual cycle plays a more impactful role in
determining vortex formation.

  * •

Low-level equatorial westerlies west of Sumatra, which peak during MJO phase
4, are coincident with a secondary peak in vortex (and shed vortex) counts.
This suggest that low-level westerly surges on the equator impinging on
Sumatra associated with the MJO contribute to an increase in wake vortex
development.

  * •

Periods with anomalous low-level easterlies (westerlies) have higher (lower)
than average vortex counts.

  * •

For reasons unclear at this time, anomalous low-level winds were most
pronounced in region SS. For example, during periods of anomalous easterlies
(19 months), the vortex count averaged 4/month. In contrast during periods of
anomalous westerlies (22 months), the vortex count averaged 1.1/month. This
fourfold increase in vortex formation between periods of anomalous low-level
zonal winds highlights the sensitivity of vortex development to anomalies in
the large-scale wind field.

  * •

While positive (negative) El-Nino-Southern Oscillation (ENSO) and Indian-Ocean
Dipole (IOD) conditions drive anomalous easterlies (westerlies), the
relationship between vortex count and these large-scale indices is generally
weak (r ¡ 0.1). Only in region SS do the large-scale conditions reflected in
these indices appear to impact vortex formation numbers (r=0.36 with ENSO and
0.21 with IOD). These positive correlations imply that the positive ENSO and
IOD conditions drive anomalous easterlies which result in higher vortex
formation rates.

While identifying which Indian Ocean (IO) tropical cyclones (TCs) were
associated with low-level topographically forced shed vortices was beyond the
scope of this study, the following TC statistics were examined:

  * •

Based on the Joint Typhoon Warning Center (JTWC) database, 51 (105) TCs were
identified over NH (SH) IO during 2008-17 period. This TC frequency (15.6/yr)
was somewhat less than that observed during the F16 period (19.6/yr).
Determining the percentage of TCs in the long-term record which originated
from shed vortices is left for a future study.

  * •

TC initialization is most frequent over the IO during MJO phase 3 when
convective anomalies are largest over the eastern IO. Since shed vortex counts
peak around phase 1 (Fig. 10) or about 8-12 days earlier, it is possible that
shed vortices contribute to the TC initialization peak observed in MJO phase
3.

  * •

Little, if any, correlation exists between TC frequency in the IO and ENSO and
IOD signals. A slight uptick in TCs numbers for storms originating east of
90°E during the negative IOD phase suggest that warm waters in eastern IO may
be contributing to this increase.

Future work in the area of this study could include extending the tracking
analyses to yet additional years to determine whether the relationships
summarized above are robust over yet longer periods. Remaining questions from
this study, which further analysis could help elucidate, include the
following. What factors, other than zonal wind, control the frequency of
vortex shedding? Why do the large-scale signals (such as ENSO and IOD) have a
preferred influence on the zonal winds in region SS resulting in more
prominent zonal wind anomalies and a larger impact on vortex formation in this
region? What percentage of shed vortices in the extended period (2008-2017)
developed into TCs, and in particular, how many of these TCs impacted
vulnerable populations in India and Sri Lanka? Addressing this latter question
may require that the vortex tracking code be run with geopotential height
anomalies and/or a smaller vorticity threshold to track shed vortices which
weaken then subsequently reintensify. And finally, Kuettner’s (1989)
observations of IO twin cyclones could be examined to determine how many of
these cases can be attributed to twin shed vortices (Ferreira et al., 1996).

###### Acknowledgements.

We thank Kevin Hodges from the University of Reading for his assistance in
getting the tracking code working with ERA5 analyses and Rick Taft for his IT
support with this project. This research has been supported by the National
Science Foundation under Grant AGS-1853633. The ERA5 data were obtained from:
https://cds.climate.copernicus.eu, the MJO RMM indices were provided by the
Australian Bureau of Meteorology from: www.bom.gov.au/climate/mjo, the MEI.v2
ENSO index from: https://psl.noaa.gov/enso/mei/, the DMI data from:
https://psl.noaa.gov/gcos wgsp/Timeseries/Data/dmi.had.long.data, and
information on Indian Ocean tropical cyclones from:
https://www.metoc.navy.mil/jtwc/jtwc.html?best-tracks.

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