[1]AnanthaAiyyer [1]TerrellWade

1]Department of Marine, Earth and Atmospheric Sciences, North Carolina State
University

A. Aiyyer<EMAIL_ADDRESS>
# Acceleration of Tropical Cyclones As a Proxy For Extratropical Interactions:
Synoptic-Scale Patterns and Long-Term Trends

###### Abstract

It is well known that rapid changes in tropical cyclone motion occur during
interaction with extratropical waves. While the translation speed has received
much attention in the published literature, acceleration has not. Using a
large data sample of Atlantic tropical cyclones, we formally examine the
composite synoptic-scale patterns associated with _tangential_ and _curvature_
components of their acceleration. During periods of rapid tangential
acceleration, the composite tropical cyclone moves poleward between an
upstream trough and downstream ridge of a developing extratropical wavepacket.
The two systems subsequently merge in a manner that is consistent with
extratropical transition. During rapid curvature acceleration, a prominent
downstream ridge promotes recurvature of the tropical cyclone. In contrast,
during rapid tangential or curvature deceleration, a ridge is located directly
poleward of the tropical cyclone. Locally, this arrangement takes the form of
a cyclone-anticyclone vortex pair somewhat akin to a dipole block. On average,
the tangential acceleration peaks 18 hours prior to extratropical transition
while the curvature acceleration peaks at recurvature. These findings confirm
that rapid acceleration of tropical cyclones is mediated by interaction with
extratropical baroclinic waves. Furthermore, The tails of the distribution of
acceleration and translation speed show a robust reduction over the past 5
decades. We speculate that these trends may reflect the poleward shift and
weakening of extratropical Rossby waves.

The track and movement of tropical cyclones are known to be governed by the
background environment (e.g., Hodanish and Gray, 1993). It was recognized
early on that the translation speed of a tropical cyclone can be approximated
by the surrounding wind field (Emanuel, 2018). A tropical cyclone, however, is
not an isolated vortex that is passively carried by the current. The
background environment is comprised of synoptic and large-scale circulation
features, with attendant gradients of potential vorticity, moisture, and
deformation. The tropical cyclone actively responds to these external stimuli.
The large scale environment is also impacted by the interaction. For example,
the generation of $\beta$-_gyres_ – that influence tropical cyclone motion –
is a response to the background potential vorticity gradient (e.g., Chan and
Williams, 1987; Wu and Emanuel, 1993). Similarly, vertical wind shear can
limit the intensification of tropical cyclones by importing low entropy air
(e.g., Tang and Emanuel, 2010). This, in turn, can impact subsequent tropical
cyclone motion. On the other hand, a tropical cyclone can influence the large-
scale flow by exciting waves in the extratropical stormtrack, leading to rapid
downstream development and rearrangement of the flow (e.g., Jones et al.,
2003). It can be contended that a tropical cyclone is always interacting with
its environment, and the interaction is partly manifested in its motion.

Track and translation speed are two aspects of tropical cyclone motion that
are particularly important for operational forecasts. The track garners much
attention for obvious reasons – it informs potential locations that will be
affected by a storm. The translation speed impacts intensity change, storm
surge and local precipitation amount. There is a large body of published
literature and review articles dealing with various research and operational
problems related to tropical cyclone track and speed (e.g., Chan, 2005;
Emanuel, 2018). When tropical cyclones move poleward, they often encroach upon
the extratropical stormtrack. This leads to their interaction with baroclinic
eddies of the stormtrack. The outcome of the interaction is varied. Some
tropical cyclones weaken and dissipate while others strengthen and retain
their tropical nature for an additional period. In the North Atlantic, around
50% of tropical cyclones eventually experience extratropical transition - a
complex process during which the warm-core tropical cyclone evolves into a
extratropical cyclone and becomes part of an extratropical stormtrack (e.g.,
Hart and Evans, 2001). Several recent reviews have extensively documented the
research history and dynamics of extratropical transition (e.g., Evans et al.,
2017; Keller et al., 2019). Forecasters have long known that tropical cyclones
accelerate forward during extratropical transition, but relatively less
attention has been devoted to the details of this acceleration in the research
literature.

This paper has two main themes. The first concerns the synoptic-scale flow
associated with rapid acceleration and deceleration of tropical cyclones. This
is addressed via composites of global reanalysis fields and observed tropical
cyclone tracks from 1980–2016. We consider both tangential and curvature
accelerations. To our knowledge, such formal delineation of extratropical
interaction based on categories of tropical cyclone acceleration has not been
presented in the literature. Of note, however, is the recent work of Riboldi
et al. (2019) that is relevant to this paper. That study examined the
interaction of accelerating and decelerating upper-level troughs and recurving
western North Pacific typhoons. Their key findings are: (a) In the majority of
cases, a recurving tropical cyclone is associated with a decelerating upper-
level trough that remains upstream; (b) The upper-level trough appears to
phase lock with the tropical cyclone; and (c) Recurvatures featuring such
trough deceleration are frequently associated with downstream atmospheric
blocking. As we shown in subsequent sections, many of these results can be
recovered independently when we approach the problem from the perspective of
tropical cyclone motion. As such, part of our work complements the findings of
Riboldi et al. (2019).

The second theme concerns the identification of long-term trends in tropical
cyclone motion. While we focus on acceleration, we begin with translation
speed to place our results within the context of related recent work. Kossin
(2018) reported that the translation speed of tropical cyclones over the
period 1949–2016 has reduced by about 10% over the globe, and about 6% over
the North Atlantic. Without directly attributing it, Kossin (2018) noted that
the trend is consistent with the observed slow-down of the atmospheric
circulation due to anthropogenic climate change. In addition to the
circulation changes, the general warming of the atmosphere is associated with
an increase in water vapor content per the Clausius-Clapeyron scaling (CCS).
This translates to increase in precipitation rates that can locally exceed the
CCS (e.g., Nie et al., 2018). Kossin (2018) made the point that the slowing of
tropical cyclones may compound the problem of heavy precipitation in a warmer
climate. However, Moon et al. (2019) and Lanzante (2019) argued that the
historical record of tropical cyclone track data, particularly prior the
advent of the satellite era around the mid-1960s, is likely incomplete. They
also showed that annual-mean tropical cyclone translation speed exhibits step-
like changes and questioned the existence of a true monotonic trend. They
attributed these discrete changes to natural factors (e.g., regional climate
variability) as well as omissions and errors due to lack of direct observation
prior to the availability of extensive remote sensing tools.

We revisit the issue of trends in tropical cyclone motion, but restrict our
attention to the Atlantic basin and the years since 1966. This year is
considered to be the beginning of the _satellite era_ , at least for the
Atlantic (Landsea, 2007). In contrast, global coverage by geostationary
satellites began much later, in 1981 (e.g., Schreck et al., 2014). Lanzante
(2019) found a change point in 1965 for the timeseries of annual average
tropical cyclone speed for the North Atlantic basin. Lanzante (2019) also
reported that accounting for the change point dramatically reduces the trend
from the value reported by Kossin (2018). In light of the issues raised about
the reliability of tropical cyclone track data prior to the _satellite era_ ,
we use 1966 as our starting point and seek to ascertain whether robust trends
exist in the observed record of tropical cyclone acceleration.

##  1 Data

We use the IBTrACS v4 (Knapp et al., 2010) for tropical cyclone locations. The
information in this database typically spans the tropical depression stage to
extratropical cyclone and/or dissipation. Kossin (2018), used all locations in
the IBTrACs as long as a storm lasted more than 3 days and did not apply a
threshold for maximum sustained winds. We follow the same method with one
major difference. We only consider those instances of the track information
wherein a given storm was still classified as tropical. We recognize the fact
that the nature of a storm is fundamentally altered after it loses its surface
enthalpy flux-driven, warm-core structure. After extratropical transition,
evolution is governed by stormtrack dynamics of baroclinic eddies. We wish to
avoid conflating the motions of two dynamically distinct weather phenomena.
For the same reason, we also omit subtropical storms which are catalogued in
the track database. We argue that, by restricting our track data to only
instances that were deemed to be tropical in nature, we can paint a more
appropriate picture of the composite environment and trends associated with
the rapid acceleration of tropical cyclones.

To ascertain whether a tropical storm underwent extratropical transition, we
use the _nature_ designation in the IBTrACS database that relies on the
judgement of the forecasters from one or more agencies responsible for an
ocean basin. In IBTrACS, the nature flag is set to "ET" after the transition
is complete. Admittedly, there will be some subjectivity in this designation.
An alternative would be to employ a metric such as the cyclone phase space
(Hart, 2003), usually calculated using meteorological fields from global
numerical weather prediction models (e.g., reanalysis). As we wish to remain
independent of modeled products to characterize the storms, we rely on the
forecaster designated storm nature. Furthermore, Bieli et al. (2019) found
that the phase space calculation was sensitive to the choice of the reanalysis
model, which would add another source of uncertainty. Occasionally, the nature
of the storm is not recorded (NR) or, if there is an inconsistency among the
agencies, it is designated as mixed (MX). In the north Atlantic, only a small
fraction of track data ($\approx 0.5\%$) in the IBTrACs is designated as NR or
MX. This fraction is higher in other basins (e.g., $\approx 14\%$ in the
western North Pacific). This is another reason why we restrict our attention
to the Atlantic basin. Henceforth, we will collectively refer to the
designations NR, MX and ET as _non-tropical_ , and unless explicitly stated,
omit the associated track data in our calculations.

For the trends and basic statistics, we focus on the years 1966–2019, within
the ongoing _satellite era_ for the North Atlantic basin (e.g. Landsea, 2007;
Vecchi and Knutson, 2008). Compared to years prior, tropical cyclone data is
deemed more reliable once satellite-based observations became available. For
the composites, we use the European Center for Medium Range Weather
Forecasting (ECMWF) ERA-Interim (ERAi) reanalysis (Dee et al., 2011) for the
period 1981–2016. In subsequent sections, we focus on the region 20–50oN,
wherein tropical cyclones are more likely to interact with extratropical
baroclinic waves.

##  2 Tangential and curvature acceleration

The acceleration of a hypothetical fluid element moving with the center of a
tropical cyclone can be written as:

$\mathbf{a}=\frac{dV}{dt}\mathbf{\hat{s}}+\frac{V^{2}}{R}\mathbf{\hat{n}}$ (1)

where $V$ is the forward speed and $R$ is the radius of curvature of the track
at a given location. Here, $\mathbf{\hat{s}}$ and $\mathbf{\hat{n}}$ are
orthogonal unit vectors in the so-called _natural coordinate_ system. The
former is directed along the tropical cyclone motion. The latter is directed
along the radius of curvature of the track. The first term in eq. 1 is the
tangential acceleration and the second is the curvature or normal
acceleration. The speed $V_{j}$ at any track location (given by index j) is
calculated as:

$V_{j}=\frac{(D_{j,j-1}+D_{j,j+1})}{\delta t}$ (2)

where $D$ refers to the distance between the two consecutive points, indexed
as shown above, along the track. Since we used 3-hourly reports from the
IBTrACS, $\delta t=6$ h. The tangential acceleration was calculated from the
speed using centered differences.

To calculate the curvature acceleration, it is necessary to first determine
the radius of curvature, R. A standard approach to calculating R, given a set
of discrete points along a curve – in our case, a tropical cyclone track – is
to fit a circle through three consecutive points. For a curved line on a
sphere, it can be shown that:

$R=R_{e}sin^{-1}{\left(\sqrt{\frac{2d_{12}d_{13}d_{23}}{(d_{12}+d_{13}+d_{23})^{2}-2(d_{12}^{2}+d_{13}^{2}+d_{23}^{2})}}\right)}$
(.1) where $R$ is the radius of curvature, $R_{e}$ is the radius of the Earth,
and the $d$ terms are expressed as follows: $\displaystyle
d_{12}=1-(\cos{T_{1}}\cos{T_{2}}\cos{(N_{2}-N_{1})}+\sin{T_{1}}\sin{T_{2}})$
(.2) $\displaystyle
d_{13}=1-(\cos{T_{1}}\cos{T_{3}}\cos{(N_{3}-N_{1})}+\sin{T_{1}}\sin{T_{3}})$
(.3) $\displaystyle
d_{23}=1-(\cos{T_{2}}\cos{T_{3}}\cos{(N_{3}-N_{2})}+\sin{T_{2}}\sin{T_{3}})$
(.4)

where, $T_{1}$, $T_{2}$, and $T_{3}$ are the latitudes of the 3 points while
$N_{1}$, $N_{2}$, and $N_{3}$ are the longitudes. The center of the circle is
given by the coordinates:

$\displaystyle\tan{\mathbf{T}}=\pm{\frac{\cos{T_{1}}\cos{T_{2}}\sin{(N_{2}-N_{1})}+\cos{T_{1}}\cos{T_{3}}\sin{(N_{1}-N_{3})}+\cos{T_{2}}\cos{T_{3}}\sin{(N_{3}-N_{2})}}{\sqrt{\alpha^{2}+\beta^{2}}}}$
(.1) $\displaystyle\tan{\mathbf{N}}=-{\frac{\alpha}{\beta}}$ (.2) Where
$\mathbf{T}$ and $\mathbf{N}$ are the latitude and longitude, respectively of
the circle’s center, and $\alpha$ and $\beta$ are obtained using:

$\displaystyle\alpha=\cos{T_{1}}(\sin{T_{2}}-\sin{T_{3}})\cos{N_{1}}+\cos{T_{2}}(\sin{T_{3}}-\sin{T_{1}})\cos{N_{2}}+\cos{T_{3}}(\sin{T_{1}}-\sin{T_{2}})\cos{N_{3}}$
(.3)
$\displaystyle\beta=\cos{T_{1}}(\sin{T_{2}}-\sin{T_{3}})\sin{N_{1}}+\cos{T_{2}}(\sin{T_{3}}-\sin{T_{1}})\sin{N_{2}}+\cos{T_{3}}(\sin{T_{1}}-\sin{T_{2}})\sin{N_{3}}$
(.4)

Figure 1: Illustration of the circle-fit and radius of curvature calculations
at five selected locations along the track of hurricanes Katrina (2005) and
Irma (2017).

While the expressions above were derived independently for this work, we make
no claim of originality since they are based on elementary principles of
geometry. Figure 1 shows some examples of the radius of curvature calculation
for hurricanes Katrina (2005) and Irma (2017).

##  3 Basic Statistics

Over the years 1966–2019, 689 storms in the North Atlantic meet the 3-day
threshold. Figure 2 shows some basic statistics for speed and accelerations as
a function of latitude for Atlantic storms. Tropical cyclone locations are
sorted in $10^{\circ}$-wide latitude bins and all instances classified as non-
tropical were excluded. Table 1 provides the same data. The average speed of
all North Atlantic tropical cyclones (including over-land) is about 21 km/hr.
As expected, tropical cyclone speed clearly varies with latitude. It is lower
in the subtropics as compared to other latitudes. It increases sharply in the
vicinity of $40^{o}$ N. The tangential acceleration, as defined in eq. 1, can
be positive or negative. The mean and median tangential acceleration remains
near-zero equatorward of $30^{\circ}$N. This suggests that tropical cyclones
in this region tend to translate steadily, or are equally likely to accelerate
and decelerate. The tangential acceleration is substantially positive poleward
of $30^{\circ}$N. Tropical cyclones in these latitudes are subject to rapid
acceleration. For example, the mean tangential acceleration in the
$30^{\circ}-40^{\circ}$N latitude band is about 5.0 km/hr day-1. The curvature
acceleration, by our definition, takes only positive values and steadily
increases with latitude. The distributions of tropical cyclone speed and
tangential acceleration are relatively symmetric about the median value as
compared to the curvature acceleration.

Figure 2: Distribution of (a) Speed(km hr-1) ; (b) Tangential acceleration (km hr-1 day-1) and (c) Curvature acceleration (km hr-1 day-1) of Atlantic TCs as a function of latitude. Storm instances classified as ET or NR were excluded. Data from 1966–2019 was binned within 10o-wide overlapping latitude bins. Statistics shown are: median (horizontal line within the box), mean (dot), and 10th, 25th, 75th and 90th percentiles. Table 1: Speed (km hr-1), tangential and curvature acceleration (km hr-1 day-1) of Atlantic TCs in the IBTRaCs database as a function of latitude. Storm instances classified as ET or NR were excluded. N refers to number of 3-hourly track positions in each latitude-bin over the period 1966–2019.  |  | Speed | Tang. Accel | Curv. Accel
---|---|---|---|---
Latitude | N | Mean | Median | Std Dev. | Mean | Median | Std Dev. | Mean | Median | Std Dev.
Full Basin | 38822 | 20.85 | 18.87 | 12.2 | 2.27 | 0.68 | 19.5 | 16.42 | 10.88 | 19.0
5–15 | 5870 | 23.53 | 23.4 | 9.4 | 0.18 | 0.0 | 14.7 | 11.65 | 8.2 | 13.1
10–20 | 13087 | 21.10 | 20.6 | 9.3 | -0.13 | -0.0 | 15.3 | 12.29 | 8.5 | 13.3
15–25 | 13656 | 18.66 | 18.1 | 8.6 | 0.26 | -0.0 | 16.0 | 13.90 | 9.4 | 15.6
20–30 | 13074 | 17.21 | 16.4 | 8.6 | 1.40 | 0.4 | 17.1 | 16.48 | 11.2 | 19.0
25–35 | 13905 | 17.74 | 16.2 | 10.2 | 2.74 | 1.3 | 19.7 | 18.04 | 12.2 | 20.6
30–40 | 10815 | 21.37 | 18.6 | 13.5 | 5.33 | 3.0 | 22.8 | 19.34 | 13.4 | 21.0
35–45 | 5272 | 29.41 | 26.7 | 18.0 | 8.27 | 4.8 | 27.4 | 22.41 | 15.8 | 22.9
40–50 | 1607 | 42.37 | 41.0 | 20.8 | 8.75 | 6.4 | 34.9 | 28.45 | 19.9 | 29.0
45–55 | 329 | 55.69 | 53.9 | 19.4 | 6.81 | 6.3 | 37.8 | 36.50 | 25.9 | 38.9
|  |  |  |  |  |  |  |  |  |

##  4 Ensemble average flow

We now examine the flow pattern associated with rapid tangential and curvature
acceleration of tropical cyclones. For this, storm-relative ensemble average
fields are constructed using ERA-interim reanalysis over the period 1980–2016.
We use the method outlined as follows.

  * •

All tropical cyclone track locations are binned into 10∘ wide latitude strips
(e.g., 10-20∘ N, 20-30∘ N, 30-40∘ N). Instances where storms are classified as
_non-tropical_ (c.f. section 2) are excluded. For brevity, only results for
the 30-40∘ N bin are discussed here. A total of 3515 track points are
identified for this latitude bin. Note that a particular tropical cyclone
could appear more than once in a latitude bin at different times.

  * •

The tangential accelerations in each bin are separated into two categories:
rapid acceleration and rapid deceleration. The rapid acceleration composite is
calculated using all instances of acceleration exceeding a threshold: i.e.,
$a\geq a_{\tau}$, where $\tau$ refers to a specified quantile of the
acceleration distribution within the latitude bin. Similarly, the rapid
tangential deceleration composite is based on all instances where $a\leq
a_{\tau}$. We tried a variety of thresholds for $\tau$ (e.g., $0.80-0.95$ for
rapid tangential acceleration, and $0.05-0.20$ for rapid tangential
deceleration). Our conclusions for the composites are not sensitive to the
exact choice of the threshold values as long as they are sufficiently far from
the median.

  * •

We also use the same method to create categories of curvature accelerations.
For this, since we only have positive values, we interpret these two quantile-
based categories as rapid acceleration and near-zero acceleration
respectively.

  * •

For each category, we compute an ensemble average composite field of the
geopotential field at selected isobaric levels. The composites are calculated
after shifting the grids such that the centers of all storms were coincident.
The centroid position of storms was used for the composite storm center, and
the corresponding time was denoted as Day-0. Lag-composites were created by
shifting the dates backward and forward relative to Day-0.

  * •

For anomaly fields, we subtract the long-term synoptic climatology from the
total field. The climatology is calculated for each day of the year by
averaging data for that day over the years 1980-2015. This is followed by a
7-day running mean smoother. To account for diurnal fluctuations, the daily
climatology is calculated for each available synoptic hour in the ERA-interim
data (00, 06, 12, and 18 UTC).

  * •

For brevity, we only show the results for $\tau=0.9$ for rapid acceleration
and $\tau=0.1$ for rapid deceleration. For reference, within 30–40oN latitude
range, $\tau=0.9$ corresponds to $a=32$ km/hr day-1 and the $\tau=0.1$
corresponds $a=-18$ km/hr day-1. For curvature acceleration, they are,
respectively, 48 and 32 km/hr day-1. The sample size of each composite was 352
($\approx 10\%$ of the total number of track points in this latitude range.
These correspond to 196 and 168 unique storms for rapid acceleration and rapid
deceleration respectively.

  * •

Statistical significance of anomaly fields shown in this section are evaluated
by comparing them against 1000 composites created by randomly drawing 352
dates for each composite from the period July–October, 1980–2015. A two-tailed
significance is evaluated at the 95% confidence level with the null hypothesis
being that the anomalies could have resulted from a random draw.

###  4.1 Tangential Acceleration

####  4.1.1 Day 0 (reference day) composite

Figure 3: Storm-relative composite average geopotential heights (thick orange
lines) and anomalies (color shaded) for all TCs located in the latitude bin
30-40oN over the Atlantic. The composite fields are shown for three levels –
300 hPa, 500 hPa and 850 hPa. In each panel, the composite 1000 hPa anomalous
geopotential is shown using thin black contours. All anomalies are defined
relative to a long-term synoptic climatology. The contour intervals are: 12
dam, 6 dam and 3 dam for the three levels respectively. The shading interval
in dam for the 300 hPa anomaly fields is shown in the label-bar. It is half of
the value for the other two levels. The left column is for rapid tangential
acceleration and the right column is for rapid tangential deceleration.

Figure 3 shows storm-centered composite geopotential heights (thick orange
lines) and their anomalies (color shaded) for all Atlantic tropical cyclones
located within 30-40∘ N. Two categories of tangential acceleration are shown:
rapid acceleration (left column) and rapid deceleration (right column). The
fields are shown at three levels – 300 hPa, 500 hPa and 850 hPa. In each
panel, the anomalous 1000 hPa geopotential is shown using thinner black
contours. It highlights the composite tropical cyclone and the surface
development within the extratropical stormtrack.

The ensemble average for rapid tangential acceleration (left column of Fig. 3)
shows the composite tropical cyclone interacting with a well defined
extratropical wavepacket. The tropical cyclone is straddled by an upstream
trough and a downstream ridge. At 500 hPa, the geopotential anomalies of the
tropical cyclone and the upstream trough are close and, consequently, appear
to be connected. This yields a negative tilt in the horizontal and indicates
the onset of cyclonic wrap-up of the trough around the tropical cyclone. The
1000-hPa geopotential anomaly field is dominated by the composite tropical
cyclone. It also shows the relatively weaker near-surface cyclones and
anticyclones of the extratropical stormtrack. The entire wavepacket shows
upshear tilt of geopotential anomalies with height, indicating baroclinic
growth. This arrangement of the tropical cyclone and the extratropical
wavepacket is consistent with the synoptic-scale flow that is typically
associated with extratropical transition (e.g., Bosart and Lackmann, 1995;
Klein et al., 2000; McTaggart-Cowan et al., 2003; Riemer et al., 2008; Riemer
and Jones, 2014; Keller et al., 2019). At this point, all storms in the
ensemble were still classified as _tropical_. Thus, we interpret this
composite as pre-extratropical transition completion state.

Figure 4: Storm-relative average 500-hPa geopotential heights (thick orange
lines) and anomalies (color shaded) for all TCs located in the latitude bin
30-40oN over the Atlantic. The fields are shown for lags Day-2 to Day+2. In
each panel, the composite 1000 hPa anomalous geopotential is shown using thin
black contours. All anomalies are defined relative to a long-term synoptic
climatology. The contour interval is 6 dam and shading interval in dam is
shown in the label-bar. The plus symbol shows the location of the composite TC
at Day 0 and the hurricane symbol shows the approximate location at each lags.
The left column is for rapid tangential acceleration and the right column is
for rapid tangential deceleration

The ensemble average for rapid tangential deceleration cases (right column of
Fig. 3) shows an entirely different synoptic-scale pattern. The extratropical
wavepacket is substantially poleward, with a ridge immediately north of the
composite tropical cyclone. The geopotential anomalies of the extratropical
wavepacket and the composite tropical cyclone appear to be distinct at all
three levels, with no evidence of merger. The prominent synoptic structure is
the cyclone-anticyclone dipole formed by the tropical cyclone and the
extratropical ridge.

####  4.1.2 Lag Composites

To get a sense of the temporal evolution of the entire system, we show lag
composites for Day-2 to Day+2 in Fig. 4. As in the previous figure, the two
categories of acceleration are arranged in the respective columns. The rows
now show 500-hPa geopotential height (thick contours) and anomalies (color
shaded). In each panel, the corresponding 1000-hPa geopotential height
anomalies are shown by thin black contours.

The ensemble average for rapid tangential acceleration (left column of Fig. 4)
shows a tropical cyclone moving rapidly towards an extratropical wavepacket.
At day-2, the tropical cyclone circulation is relatively symmetric as depicted
by the contours of 1000 hPa geopotential anomalies. The downstream
extratropical ridge is prominent, but the upstream trough is much weaker at
this time. On Day-1, the entire extratropical wavepacket has amplified and the
500 hPa geopotential anomalies of the tropical cyclone and a developing
upstream trough have merged. This process continues through Day 0. By Day+1,
the composite storm has moved further poleward and eastward and is now located
between the upper-level upstream trough and downstream ridge in a position
that is optimal for further baroclinic development. The 1000 hPa geopotential
field is now asymmetric with a characteristic signal of a cold front.

Figure 5: Track of the composite tropical cyclone (blue) and the downstream
500-hPa extratropical ridge (orange) from Day-2 to Day +2 for (a) rapid
tangential acceleration, and (b) rapid tangential deceleration. The composites
are based on all TC tracks locations within 30–40oN. Day 0 is the reference
day for the composites in Fig. 4

The picture that is evident from these 500-hPa composite fields is that, over
the course of the 4 days, downstream ridge-trough couplet amplifies while
simultaneously propagating eastward. The upstream trough cyclonically wraps
around the tropical cyclone and the two have merged by Day 1. The geopotential
gradient poleward of the storm is also enhanced, indicating a strengthening
jet streak. These features are consistent with the process of extratropical
transition (e.g., Keller et al., 2019). The poleward moving tropical cyclone
may either interact with an existing wavepacket or perturb the extratropical
flow and excite a Rossby wavepacket that disperses energy downstream (e.g.,
Riemer and Jones, 2014). The outflow of the tropical cyclone is a source of
low potential vorticity (PV) air that further reinforces the downstream ridge
(e.g., Riemer et al., 2008).

To further illustrate the interaction, the tracks of the tropical cyclone and
the 500-hPa ridge of the extratropical wavepacket are presented in Fig. 5a. It
can be clearly seen that the tropical cyclone merges with the extratropical
stormtrack. Furthermore, the 500 hPa ridge has rapidly moved downstream during
the 4 day period, indicating a very progressive pattern. The eastward phase
speed of the extratropical wavepacket, as inferred from the track of the
ridge, is $\approx 7$ ms-1. The tropical cyclone speed, averaged over the same
4-day period, is $\approx 6$ ms-1. The close correspondence between the two
and the merger of the tracks further supports the notion that the synoptic-
scale evolution during rapid acceleration cases is consistent with the
canonical pattern associated with extratropical transition.

On the other hand, during rapid deceleration (right column Fig. 4), the
composite tropical cyclone remains equatorward of the extratropical wavepacket
and maintains a nearly symmetric structure throughout the period. The
arrangement of the tropical cyclone and the extratropical ridge is akin to a
vortex dipole. The extratropical wavepacket is not as progressive as in the
rapid acceleration case. This is seen clearly from the tracks of the tropical
cyclone and the ridge (Fig. 5b). The phase speed of the extratropical
wavepacket is $\approx 3$ ms-1 while the tropical cyclone speed is $\approx
1.5$ ms-1. The phasing of the tropical cyclone and the extratropical
wavepacket has led to the formation of a cyclone-anticyclone vortex dipole. We
return to this point and relate it to similar findings in Riboldi et al.
(2019) in a later section.

###  4.2 Curvature Acceleration

Figure 6: As in Fig. 3, but for rapid and near-zero curvature acceleration

####  4.2.1 Day 0 (reference day) composite

As in the previous section, Figure 6 shows storm-centered ensemble averages,
but this time for the two categories of curvature acceleration. The composite
for rapid acceleration (left column) shows a tropical cyclone that is
primarily interacting with an extratropical ridge that is poleward and
downstream of it. The upstream trough in the extratropics is weaker and
farther westward as compared to the rapid tangential acceleration composite
(Fig. 6a). Furthermore, instead of the upstream trough wrapping cyclonically,
in this case, we see the downstream ridge wrapping anticyclonically around the
tropical cyclone. This is similar to the composite 500-hPa fields that were
based on recurving tropical cyclones as shown in Fig. 5 of Aiyyer (2015).
Thus, in an ensemble average sense, rapid curvature acceleration appears to
mark the point of the recurvature of tropical cyclones.

The composite for near-zero curvature acceleration (right column) is quite
similar to the composite for rapid tangential deceleration (Fig. 6d–f). The
extratropical wavepacket is poleward and the tropical cyclone-ridge system
appears as a vortex dipole.

Figure 7: As in Fig. 4, except for rapid (left column) and near-zero (right
column) curvature acceleration.

####  4.2.2 Lag Composites

The temporal evolution of the entire system for the two categories of
curvature acceleration is shown in Fig. 7. For rapid curvature acceleration,
we see a tropical cyclone that is moving poleward towards an extratropical
ridge. During the subsequent days, the ridge moves eastward initially and
begins to wrap around the tropical cyclone. This arrangement promotes the
recurving of the tropical cyclone. By Day+2, the anticyclonic wrapping and
thinning has resulted in a significantly weaker ridge as compared to a few
days prior. For the near-zero curvature cases ( Fig. 7f–g), the initial
movement of the tropical cyclone is also directly poleward towards the
extratropical ridge. However, in this case, the ridge remains poleward of the
tropical cyclone. There is also significantly less anticyclonic wrapping of
ridge. The tropical cyclone-ridge system takes the form of a cyclonic-
anticyclonic vortex pair similar to the rapid tangential deceleration
composite.

The tracks in Fig. 8 clearly show how the tropical and extratropical systems
propagate. For rapid curvature acceleration (Fig. 8a), the tropical cyclone
track shows a recurving tropical cyclone. The track of the ridge confirms the
initial eastward motion, followed by a poleward shift after parts of it wrap
around the tropical cyclone as noted from Fig. 7a-e. By Day+2, we do not
observe a merger of the tracks that happens in the case of rapid tangential
acceleration (Fig. 5a).

The tracks for near-zero curvature acceleration (Fig. 8a) are somewhat similar
to the rapid tangential deceleration (Fig. 5b). The key point here is that,
although the tropical cyclone moves poleward, tropical cyclone-ridge system
acts like a vortex dipole and is nearly stationary in the zonal direction.
This arrangement of the tropical cyclone and the extratropical wavepacket is
similar to the composite fields in Fig. 10 of Riboldi et al. (2019), where
they show upper-level potential vorticity (PV), 850-hPa potential temperature
and sea-level pressure. The difference is that their composite was conditioned
on the acceleration of the upstream trough for recurving western Pacific
typhoons. It is, however, not surprising that we can recover a similar pattern
when we condition our composites on the basis of tropical cyclone
acceleration. Since the the extratropical wavepacket and the tropical cyclone
are actively interacting, they influence each other’s motion. Riboldi et al.
(2019) referred to this as a phase-locking of the upstream trough and the
tropical cyclone while we have viewed this as a phase-lock between the ridge
and the tropical cyclone. The two are not mutually exclusive since the trough
and the ridge are part of the same wavepacket.

Figure 8: Track of the composite tropical cyclone (blue) and the downstream
500-hPa extratropical ridge (orange) from Day-2 to Day +2 for (a) rapid
curvature acceleration, and (b) near-zero curvature acceleration. The
composites are based on all TC tracks locations within 30–40oN. Day 0 is the
reference day for the composites in Fig. 7

##  5 Extratropical Transition

In the previous section, we showed that the composite synoptic-scale flow
associated with rapid tangential acceleration resembles a pattern that is
favorable for extratropical transition. However, this does not imply that all
storms in the composite underwent extratropical transition. Some tropical
cyclones may begin the process of extratropical transition but dissipate
before its completion (e.g., Kofron et al., 2010). We now consider tropical
cyclone motion from a different perspective by considering only those storms
that completed the transformation from being tropical to extratropical. Hart
et al. (2006) found that the time taken for extratropical transition
completion can vary considerably. For the storms that they examined, this
ranged from 12–168 hours. To get a sense of the temporal evolution relative to
extratropical transition completion, we examine composite tropical cyclone
speed and acceleration as a function of time. For this, we only considered
those Atlantic storms during 1966–2019 that were classified as _tropical_ at
some time and subsequently underwent extratropical transition. Of the 689
candidate storms that passed the three-day threshold, 18 storms were never
classified as _tropical_. Of the remaining 671 storms, 274 were eventually
classified as _extratropical_. This yields a climatological extratropical
transition fraction of 41%. However, in the data record, a few instances exist
where a storm was flagged as _extratropical_ earlier than _tropical_. If we
remove these instances, the extratropical transition fraction slightly reduces
to $\approx 38\%$. These estimates are lower than the fraction of 44% during
1979–2017 in Bieli et al. (2019), and 46% during 1950-1993 in Hart and Evans
(2001). The mean and median latitude of extratropical transition completion in
our data set were, respectively, 40.5∘N and 41.5∘ N. This is consistent with
Hart and Evans (2001) who found that the highest frequency of extratropical
transition in the Atlantic occurs between the latitudes of 35oN–45oN.

Figure 9: Composite speed and accelerations relative to time of (a)
Extratropical transition; and (b) Recurvature. A single pass of 5-point
running average was applied to the speed and tangential acceleration curves.
Two passes of the same filter were applied to the curvature acceleration.

Fig. 9a shows the composite accelerations and speed relative to the time of
extratropical transition. Hour 0 is defined as the first instance in the
IBTrACS where the storm nature is designated as extratropical transition. We
interpret this as the nearest time after extratropical transition has been
completed. In an ensemble-averaged sense, the forward speed of transitioning
tropical storms is seen to reach its peak around the time of extratropical
transition completion. The tangential acceleration peaks about 18 hours prior
to that. The curvature acceleration appears to steadily increase up to the
time of extratropical transition and stabilizes thereafter. The point here is
that the peak tangential acceleration of tropical cyclones precedes
extratropical transition completion. The rapid increase in the speed prior to
extratropical transition completion time is a direct outcome of the
interaction with the extratropical baroclinic wavepacket.

##  6 Recurvature

In the previous section, we found that the composite synoptic-scale flow
associated with rapid curvature acceleration closely matches the pattern
associated with recurving of tropical cyclones (Aiyyer, 2015). To further
explore this connection, Fig. 9b shows the acceleration and speed composite
timeseries relative to recurvature. We follow the method described in Aiyyer
(2015) to determine the location of recurvature. A total of 653 recurvature
points were found for Atlantic tropical storms over the period 1966–2019. Note
that a given storm could have more than one instance of recurvature. Fig 9b
confirms that, in an ensemble average sense, the time of recurvature is
associated with the highest curvature acceleration. Furthermore, it is also
associated with the lowest forward speed and a period of rapid increase in
tangential acceleration.

##  7 Trends

We first examine the trends in the annual-mean translation speed to place our
results within the context of recent studies of tropical cyclone motion. As
noted in the introduction, Kossin (2018) found a decreasing trend in annual-
mean tropical cyclone speed during 1949–2018 over most of the globe. That
study considered all storms in the IBTrACS dataset as long as they survived at
least three days. We revisit this for the Atlantic and test the sensitivity of
the trend when we exclude non-tropical systems. The rationale for this was
discussed earlier in section 2. Figure 10 shows the annual-mean speed of
tropical cyclones for two categories: All storms (grey) and storms excluding
NR and extratropical transition designations (orange). Panel (a) shows this
for the entire Atlantic and Panel (b) for the 20–40oN band.

Figure 10: Annual-mean speed and linear trend for (a) The entire Atlantic; and (b) 20–50oN latitude band. The grey curve is for all storms in the IBTRaCS dataset while the orange curve excludes instances when the storm was classified as ET or NR. Table 2: Trends in Speed (km hr-1 year-1). _All storms_ refers to all instances of a system recorded in the IBTraCs. ET refers to storm nature designated as extratropical, while NR refers to instances when the storm nature was not recorded.  | 1966–2019 | 1949–2019 | 1949–2016
---|---|---|---
| LR | MK-TS | LR | MK-TS | LR | MK-TS
| Trend | p-value | Trend | p-value | Trend | p-value | Trend | p-value | Trend | p-value | Trend | p-value
Atlantic (All storms)
Full basin | 0.029 | 0.19 | 0.028 | 0.15 | -0.016 | 0.28 | -0.016 | 0.32 | -0.019 | 0.24 | -0.021 | 0.25
20–50 | 0.041 | 0.15 | 0.035 | 0.11 | -0.011 | 0.56 | -0.019 | 0.29 | -0.012 | 0.55 | -0.023 | 0.26
Atlantic (Excluding ET,NR)
Full basin | -0.007 | 0.70 | -0.008 | 0.62 | -0.004 | 0.77 | -0.007 | 0.48 | -0.002 | 0.90 | -0.006 | 0.63
20–50oN | 0.008 | 0.76 | 0.002 | 0.93 | <0.001 | 1.00 | -0.009 | 0.52 | 0.005 | 0.79 | -0.007 | 0.72

Table 2 contains the trends calculated using linear regression and the Thiel-
Sen estimate. We also include the trends for 1949–2016 to compare our
calculations with Kossin (2018). For 1949–2016, when we consider all tropical
cyclones, the linear regression and Thiel-Sen estimates of the trends in
annual-mean speed are $-0.019$ and $-0.021$ km hr-1 year -1. These are
practically identical to the value of $-0.02$ km hr-1 year -1 reported by
Kossin (2018). However, the trend for the satellite era over the entire basin
switches to a positive value of $\approx 0.028$ km hr-1 year -1. The
sensitivity to the choice of the years is consistent with Lanzante (2019) who
showed that the negative trend of the annual-mean speed over the longer period
1949–2016 was reduced in magnitude by accounting for the change points such as
those associated with the advent of satellite-based weather monitoring. When
we remove non-tropical data, the trends for various periods and regions are
generally lower. Furthermore, none of the trends shown in Table 2 can be
deemed significant if we use a p-value of 0.05 as the cut-off. We return to
this point in the following section.

Figure 11: Cumulative distributions of tangential acceleration (km hr-1 day-1
) for July-October, 1966–2019 for (a) The entire Atlantic; (b) 0–20oN; and (c)
20–50oN  Figure 12: Cumulative distributions of curvature acceleration (km
hr-1 day-1 ) for July-October, 1966–2019 for (a) The entire Atlantic; (b)
0–20oN; and (c) 20–50oN

###  7.1 Quantile regression

Figure 11 compares the cumulative probability distribution (CDF) of tangential
accelerations over three 10-year periods: 1966–1975, 1988-1997, and 2010–2019.
The data covers the peak hurricane season: July–October (JASO). Three Atlantic
regions are shown - the entire basin, 0–20oN, and 20–50oN. In all three CDFs,
the lower and upper-tail probability of the distribution appear to show a
shift towards the median. The direction of the shift indicates a reduction in
the frequency of both rapid tangential acceleration ($a\geq 15$ km/hr day-1 )
and rapid tangential deceleration ($a\leq-15$ km/hr day-1 ) from the earlier
to recent decades. This is most pronounced over the 20–50oN latitude band. The
CDFs for curvature acceleration (bottom row of Fig. 12) show a similar shift
towards less frequent rapid acceleration. The CDF over the entire year shows
similar shifts. When we consider a smaller subset of months, we find that the
shifts are more pronounced when we omit October and November (not shown).

In the preceding sections, we showed that rapid acceleration or deceleration
of tropical cyclones are typically associated with interactions with the
extratropical baroclinic stormtrack. The attendant synoptic-scale pattern are
distinct in the phasing of the tropical cyclone and the extratropical
wavepacket. It is of interest to determine if the shift in CDFs of
acceleration (Figs. 11, 12) are related to long-term trends. The motivation
being that it can inform us about potential changes in the nature of tropical
cyclone-baroclinic stormtrack interaction. Given that we are interested in the
long-term trends of rapid acceleration and deceleration – i.e., the tails of
the probability distribution – we use quantile regressions (QR) as developed
by Koenker and Bassett (1978). QR is a useful tool to model the behavior of
the entire probability distribution and has been used in diverse fields and
applications (e.g., Koenker and Hallock, 2001). In atmospheric sciences, QR
has been applied to examine trends in extreme precipitation and temperature
(e.g., Koenker and Schorfheide, 1994; Barbosa et al., 2011; Gao and Franzke,
2017; Lausier and Jain, 2018; Passow and Donner, 2019).

The standard form of the simple linear regression model for a response
variable $Y$ in terms of its predictor $X$ is written as:

$\mu\\{Y|X\\}=\beta_{o}+\beta_{1}X$ (5)

Where, $\mu\\{Y|X\\}$ is the conditional mean of Y given a variable X, and
$\beta_{o}$ and $\beta_{1}$ are, respectively, the intercept and the slope.
This linear model fits the mean of a response variable under the assumption of
constant variance over the entire range of the predictor. However, when the
data is heteroscedastic, and there is interest in characterizing the entire
distribution - and not just the mean - QR is more appropriate and insightful.
The standard form of QR is written as follows (e.g., Lausier and Jain, 2018):

$Y(\tau|X)=\beta_{o}^{(\tau)}+\beta_{1}^{(\tau)}X+\epsilon^{(\tau)}$ (6)

where $Y(\tau|X)$ denotes the conditional estimate of Y at the quantile $\tau$
for a given X. By definition, $0<\tau<1$. In our case, Y is the timeseries
vector of either acceleration or speed, and X is the vector comprised of the
dates of the individual storm positions. Here, $\beta_{o}^{(\tau)}$ and
$\beta_{1}^{(\tau)}$ denote the intercept and slope, while the
$\epsilon^{(\tau)}$ denotes the error. As noted in previous studies cited
above, QR does not make any assumption about the distribution of parameters
and is known to be relatively robust to outliers. To determine the trends, we
fit the quantile regression model for a range of quantiles between .05 and
.95. Instead of calculating annual averages to get one value of acceleration
or speed per year, we retain all of the individual values for the tropical
cyclones. The corresponding time for each data point is assigned as a
fractional year.

Figure 13: Quantile regressions of tangential acceleration for regions and
months shown on the panels: The left columns show the acceleration (light blue
circles) for all TCs (NR and ET excluded) as a function of time. The dotted
magenta lines show the linear fits quantiles ranging from 0.05 to 0.95. The
red line shows the ordinary least square fit for the mean. The right columns
show the estimates of the slope (i.e., the trend in km/hr day-1 year-1) for
each quantile, along with the 95% confidence band (dotted magenta). Also shown
is the ordinary least square estimate of trend (red line) and its 95%
confidence band for each quantile.

Figure 13 shows the results of QR for tangential acceleration. The panels on
the left show the acceleration (light blue circles) at individual track
locations from 1966-2019 (ET and NR excluded). The dashed magenta lines are
the linear fits for the quantiles ranging from 0.5 to 0.95. The panels on the
right show the slope (trend; km/hr day-1 year-1) of the linear line as a
function of the quantile. These figures include the best fit using ordinary
least squares (OLS; red line) that models the mean of the distribution. Also
included are the associated 95% confidence bounds. The top row includes data
from all months over the entire Atlantic. The middle row is for 20–50oN over
the peak tropical cyclone months (July-October), and the bottom row restricts
the data to August-September. The latter two illustrate some of the
sensitivity to the choice of domain and months of analysis. They also focus
our attention on the region where tropical cyclones are most likely to
interact with extratropical systems. The corresponding numerical values are
shown in Table 3. Recall from Table 1 that the median value ($\tau=.5$) of
tangential acceleration is a small positive number. As such, $\tau<0.5$ is
indicative of deceleration, while $\tau\geq 0.5$ is indicative of
acceleration.

Table 3: Quantile trends of tangential acceleration over 1966-2019 (km hr-1 day-1 year-1 ) for months and regions labeled below. Trends of magnitude below $0.01$ are not reported. | Entire Atlantic | 20–50oN | 20–50oN
---|---|---|---
| All Months | Jul-Oct | Aug-Sep
$\tau$ | Trend | Change | p | 95% Conf | Trend | Change | p | 95% conf. | Trend | Change | p | 95% conf.
OLS | 0.01 | – | 0.01 | 0.00, 0.03 | 0.01 | 10 | 0.50 | -0.01, 0.02 | , – | 4 | 0.83 | -0.01, 0.02
0.05 | 0.12 | 23 | <0.01 | 0.09, 0.16 | 0.07 | 13 | <0.01 | 0.02, 0.11 | 0.14 | 25 | <0.01 | 0.09, 0.20
0.10 | 0.06 | 18 | <0.01 | 0.04, 0.08 | 0.03 | 10 | 0.03 | 0.00, 0.07 | 0.07 | 19 | <0.01 | 0.03, 0.10
0.15 | 0.03 | 12 | <0.01 | 0.01, 0.05 | – | 0 | 0.98 | -0.02, 0.02 | 0.01 | 5 | 0.35 | -0.02, 0.04
0.20 | 0.02 | 9 | 0.02 | <0.01, 0.03 | – | -2 | 0.76 | -0.02, 0.02 | – | 2 | 0.70 | -0.02, 0.03
0.30 | 0.01 | 8 | 0.19 | -0.00, 0.02 | — | 4 | 0.60 | -0.01, 0.02 | 0.01 | 6 | 0.53 | -0.01, 0.02
0.50 | 0.03 | – | <0.01 | 0.02, 0.03 | 0.03 | – | <0.01 | 0.02, 0.04 | 0.01 | – | 0.04 | 0.00, 0.03
0.70 | 0.02 | 18 | <0.01 | 0.01, 0.03 | 0.03 | 19 | <0.01 | 0.01, 0.05 | – | 2 | 0.75 | -0.02, 0.02
0.80 | 0.02 | 9 | 0.01 | 0.00, 0.04 | 0.02 | 9 | 0.04 | 0.00, 0.05 | -0.01 | -5 | 0.40 | -0.04, 0.02
0.85 | – | -2 | 0.73 | -0.02, 0.02 | 0.01 | 1 | 0.64 | -0.02, 0.04 | -0.04 | -11 | 0.05 | -0.07, -0.00
0.90 | -0.02 | -5 | 0.13 | -0.04, 0.01 | -0.03 | -7 | 0.09 | -0.07, 0.00 | -0.07 | -15 | <0.01 | -0.12, -0.02
0.95 | -0.11 | -18 | <0.01 | -0.15, -0.07 | -0.14 | -18 | <0.01 | -0.20, -0.07 | -0.17 | -23 | <0.01 | -0.25, -0.10

From Fig. 13 and Table 3, we note that the OLS estimate of the trend is weakly
positive when data from all months over the entire Atlantic are considered.
However, the OLS estimate is not statistically significant for the 20–50oN
region. As expected, the regression quantiles show a fuller picture. The
slopes of the individual quantiles provide an estimate of the trends of the
specific portions of the probability distribution. The key finding here is
that the magnitudes of both rapid deceleration and rapid acceleration show a
statistically-significant reducing trend. This is reflected in the positive
slope for $\tau\leq 0.15$ and negative slope for $\tau\geq 0.85$ (Table 3 and
left columns of Fig. 13 ). It also appears that the trends for $\tau<0.5$ are
generally positive, implying a reduction in the magnitude of tangential
deceleration at all quantile thresholds. On the other hand, the positive
slopes seen for $0.5<\tau<0.8$ suggest that there is an increasing trend in
the values of tangential acceleration that are closer to the median. This
shift towards less-extreme acceleration is noted in all three regional
categories, albeit with varying degree of statistical significance. The trends
in these quantiles are, however, weaker compared with those of the tails. From
the right column of Fig. 13, it is clear that the trends of the tails of the
distribution are significant and fall outside the 95% confidence bounds of the
OLS estimate of the trend.

Figure 14: As in Fig. 13, but for curvature acceleration. Table 4: Quantile trends of curvature acceleration over 1966-2019 (km hr-1 day-1 year-1 ) for months and regions labeled below. Trends of magnitude below $0.01$ are not reported. | Entire Atlantic | 20–50oN | 20–50oN
---|---|---|---
| All Months | Jul-Oct | Aug-Sep
$\tau$ | Trend | Change | p | 95% Conf | Trend | Change | p | 95% conf. | Trend | Change | p | 95% conf.
OLS | -0.02 | -5 | <0.01 | [-0.03, -0.01] | -0.04 | -11 | <0.01 | [-0.06, -0.02] | -0.06 | -15 | <0.01 | [-0.08, -0.04]
0.05 | 0.01 | 42 | <0.01 | 0.01, 0.01 | 0.01 | 40 | <0.01 | 0.00, 0.01 | 0.01 | 27 | 0.04 | 0.00, 0.01
0.10 | 0.01 | 32 | <0.01 | 0.01, 0.02 | 0.01 | 25 | <0.01 | 0.00, 0.02 | 0.01 | 16 | 0.05 | 0.00, 0.01
0.15 | 0.01 | 23 | <0.01 | 0.01, 0.02 | 0.01 | 14 | 0.01 | 0.00, 0.01 | <0.01 | 7 | 0.25 | -0.00, 0.01
0.20 | 0.01 | 17 | <0.01 | 0.01, 0.02 | 0.01 | 13 | <0.01 | 0.00, 0.02 | 0.01 | 7 | 0.22 | -0.00, 0.01
0.30 | 0.02 | 15 | <0.01 | 0.01, 0.02 | 0.01 | 10 | 0.01 | 0.00, 0.02 | 0.01 | 7 | 0.11 | -0.00, 0.02
0.50 | 0.02 | 8 | <0.01 | 0.01, 0.03 | <0.01 | 1 | 0.55 | -0.01, 0.02 | -0.01 | -4 | 0.37 | -0.02, 0.01
0.70 | – | 0 | 0.72 | -0.01, 0.02 | -0.03 | -7 | 0.01 | -0.05, -0.01 | -0.04 | -11 | <0.01 | -0.06, -0.02
0.80 | -0.03 | -7 | <0.01 | -0.05, -0.01 | -0.06 | -11 | <0.01 | -0.08, -0.03 | -0.08 | -15 | <0.01 | -0.11, -0.05
0.85 | -0.06 | -11 | <0.01 | -0.08, -0.03 | -0.09 | -14 | <0.01 | -0.13, -0.05 | -0.12 | -20 | <0.01 | -0.16, -0.08
0.90 | -0.09 | -13 | <0.01 | -0.12, -0.06 | -0.12 | -15 | <0.01 | -0.16, -0.07 | -0.18 | -22 | <0.01 | -0.23, -0.12
0.95 | -0.15 | -15 | <0.01 | -0.20, -0.09 | -0.22 | -20 | <0.01 | -0.31, -0.13 | -0.33 | -29 | <0.01 | -0.43, -0.22

The QR results for curvature acceleration (Fig. 14 and Table 4) show
statistically significant, weak positive trends for $0<\tau<0.5$. However, the
trends switch to increasingly negative values above the median. As in the case
of tangential acceleration, the decelerating trends in the upper quantiles of
the distribution ($\tau\geq 0.8)$ are statistically significant and outside
the 95% confidence bounds of the OLS estimate of the trend in the mean.

Figure 15: As in Fig. 13, but for translation speed. Table 5: Quantile trends of translation speed over 1966-2019 (km hr-1 year-1 ) for months and regions labeled below. Trends of magnitude below $0.01$ are not reported. | Entire Atlantic | 20–50oN | 20–50oN
---|---|---|---
| All Months | Jul-Oct | Aug-Sep
$\tau$ | Trend | Change | p | 95% Conf | Trend | Change | p | 95% conf. | Trend | Change | p | 95% conf.
OLS | -0.01 | -2 | 0.05 | -0.01, 0.0 | -0.01 | -3 | 0.04 | -0.02, -0.0 | -0.04 | -9 | <0.01 | -0.05, -0.02
0.05 | – | -13 | <0.01 | -0.02, -0.01 | -0.02 | -17 | <0.01 | -0.03, -0.01 | -0.02 | -17 | <0.01 | -0.03, -0.01
0.10 | – | -6 | 0.02 | -0.01, -0.00 | -0.01 | -8 | 0.02 | -0.02, -0.00 | -0.01 | -9 | 0.04 | -0.02, -0.00
0.15 | – | -2 | 0.46 | -0.01, 0.00 | – | -1 | 0.98 | -0.01, 0.01 | – | -1 | 0.93 | -0.01, 0.01
0.20 | – | -2 | 0.52 | -0.01, 0.01 | – | -2 | 0.66 | -0.01, 0.01 | – | -2 | 0.73 | -0.01, 0.01
0.30 | – | -1 | 0.61 | -0.01, 0.01 | -0.01 | -3 | 0.25 | -0.02, 0.00 | – | -7 | 0.01 | -0.03, -0.00
0.50 | – | -1 | 0.99 | -0.01, 0.01 | -0.01 | -5 | 0.01 | -0.02, -0.00 | -0.04 | -12 | <0.01 | -0.05, -0.03
0.70 | – | -2 | 0.34 | -0.01, 0.01 | -0.01 | -3 | 0.18 | -0.02, 0.00 | -0.04 | -10 | <0.01 | -0.06, -0.03
0.80 | -0.01 | -2 | 0.32 | -0.02, 0.01 | -0.02 | -5 | 0.02 | -0.04, -0.00 | -0.07 | -13 | <0.01 | -0.09, -0.05
0.85 | -0.03 | -5 | <0.01 | -0.04, -0.01 | -0.03 | -5 | 0.01 | -0.05, -0.01 | -0.09 | -15 | <0.01 | -0.12, -0.07
0.90 | -0.03 | -4 | <0.01 | -0.04, -0.01 | – | – | 0.96 | -0.03, 0.03 | -0.09 | -14 | <0.01 | -0.13, -0.06
0.95 | 0.02 | 2 | 0.20 | -0.01, 0.05 | -0.01 | -2 | 0.70 | -0.07, 0.04 | -0.08 | -10 | <0.01 | -0.14, -0.03

For completeness, we also show the corresponding QR results for translation
speed (Fig. 15 and Table 5). The OLS estimate of the trend is nearly the same
value as it was for the annual-mean speeds. However, it is now statistically
significant. The change in the p-value reflects the fact that the sample size
is much higher since the data is not averaged annually. When we consider the
entire Atlantic, estimated trends from QR are nearly the same as the OLS trend
with the exception of $\tau=0.95$. However, when we consider the subsets of
the data for 20–50${}^{o}N$, there are some notable differences. In
particular, for August-September, the trends in the fastest translation speeds
are even more negative.

Tables 3, 4 and 5 also include the percent changes defined using the first and
last value in the linear fit over the period 1966–2019. If we subjectively
assume that a statistically significant change of magnitude at least 10% over
the past 54 years can be deemed _robust_ , then the key outcome of the QR is
the following: The trends in the tails of the distribution of the
accelerations and speeds are most robust for the August-September months. For
the extratropical region (20–50${}^{o}N$), both rapid tangential acceleration
and deceleration show robust reductions. This indicates a general narrowing of
the tangential acceleration distribution over time. The curvature acceleration
shows an increase for the lower quantiles and reduction for the upper. This
suggests a shift in the curvature acceleration towards smaller values,
consistent with the results for tangential acceleration. Forward speed shows
mostly reducing trends for both upper and lower tails, indicating that
extremes in speeds are reducing over time.

##  8 Discussion

Ensemble-average composites of atmospheric fields show distinct synoptic-scale
patterns when they are categorized on the basis of the acceleration of
tropical cyclones. The composites for rapid tangential acceleration outside
the deep tropics depict a synoptic-scale pattern that is consistent with the
extratropical transition of tropical cyclones. This is unsurprising since it
is generally known that tropical storms speed up during extratropical
transition. The novel aspect here is that we have recovered the signal of
extratropical transition from the perspective of acceleration. The composites
show a poleward moving tropical cyclone that is straddled by an upstream
trough and a downstream ridge. Subsequently, the tropical cyclone merges with
the extratropical wavepacket ahead of the trough in an arrangement that is
conducive for further baroclinic development. Features commonly associated
with extratropical transition such as the downstream ridge-building,
amplification of the upper-level jet streak and downstream development can be
clearly seen in the composite maps (Fig. 3 and Fig. 4a-e). The composites for
rapid curvature acceleration also show the impact of the phasing of the
tropical cyclone and the extratropical wavepacket. For this category, we
recover a synoptic-scale pattern that is similar to the one obtained in
composites based on the recurvature of tropical cyclones (Aiyyer, 2015).

In contrast, the composite fields for rapid tangential and curvature
deceleration show a tropical cyclone that approaches an extratropical ridge.
The upstream trough remains at a distance and the tropical cyclone does not
merge with the extratropical wavepacket, but instead remains equatorward of it
over the following few days. The tropical cyclone and the extratropical ridge
– at least locally – can be viewed as a vortex dipole. The combined system
remains relatively stationary compared to the progressive pattern for rapid
acceleration. This arrangement qualitatively resembles a dipole block — an
important mode of persistent anomalies in the atmosphere (e.g., McWilliams,
1980; Pelly and Hoskins, 2003). The canonical dipole block is depicted as a
vortex pair comprised of a warm anticyclone and a low-latitude cut-off cyclone
(e.g., Haines and Marshall, 1987; McTaggart-Cowan et al., 2006). The dynamics
of blocked flows are rich and the subject of a variety of theories that are
far from settled (e.g. Woollings and Barriopedro, 2018). In the present case,
the slowly propagating cyclone-anticyclone pair is likely an outcome of a
fortuitous phasing of the tropical cyclone and the extratropical ridge.

Our study takes a complementary view of the extratropical interaction
described in Riboldi et al. (2019). In particular, we note the close
correspondence between their composite sea-level pressure and potential
vorticity composites (their Fig. 10) for decelerating troughs and our
geopotential composites for rapidly decelerating tropical cyclones (right
columns of Fig. 3 and Fig. 6). The vortex dipole can be seen in all three
figures. Riboldi et al. (2019) conditioned their composites on the basis of
the acceleration of the upstream trough interacting with recurving typhoons in
the western North Pacific. We recover the same pattern when we condition the
composites based on rapidly decelerating tropical cyclones in the North
Atlantic.

The interaction between the tropical cyclone and the extratropical wavepacket
that leads to the deceleration of the entire system can be viewed from a PV
perspective. As noted by Riboldi et al. (2019), both adiabatic and diabatic
pathways are active in this interaction. In the former, the induced flow from
the cyclonic vortex (tropical cyclone) will be westward within the poleward
anticyclonic vortex (ridge). The induced flow from the ridge will also be
westward at the location of the tropical cyclone. The combined effect will be
a mutual westward advection, and thus reduced eastward motion in the earth-
relative frame. The latter, diabatic pathway relies on the amplification of
the ridge through the action of precipitating convection in the vicinity of
the tropical cyclone. The negative vertical gradient of diabatic heating in
upper levels of the tropical cyclone implies that its anticyclonic outflow is
a source of low PV air (e.g., Wu and Emanuel, 1993). The advection of this low
PV air by the irrotational component of the outflow and its role in ridge-
building has been extensively documented (e.g., Atallah et al., 2007; Riemer
et al., 2008; Grams et al., 2013; Archambault et al., 2015). Riboldi et al.
(2019) also showed that the ridge is more amplified for rapidly decelerating
troughs as compared to accelerating troughs. They implicated stronger latent
heating and irrotational outflow for this difference. Our composites also show
a stronger ridge for rapid tropical cyclone deceleration as compared to rapid
acceleration. This can be noted by comparing the left and right columns of
Figs. 4 and 7. The amplification of the ridge also results in the slow-down of
the upstream trough, and as shown by Riboldi et al. (2019) yields frequent
downstream atmospheric blocking events.

The tracks of TC in the vicinity of extratropical wavetrains and subtropical
ridges are sensitive to the existence of bifurcation points (e.g., Grams et
al., 2013; Riemer and Jones, 2014), and small shifts in positions can yield
different outcomes for motion and extratropical transition. Bifurcation points
also exist in the case of tropical-cyclone cut-off low interactions (Pantillon
et al., 2016). Our acceleration-based composites have further highlighted the
impact of the phasing of the tropical cyclone and the extratropical wavepacket
in mediating the interactions between them.

While there is some storm-to-storm variability, in an average sense the
tangential acceleration peaks 18 hours prior to completion of extratropical
transition. Interestingly, the forward speed peaks around the time of
completion of extratropical transition. Curvature acceleration increases
rapidly prior to extratropical transition and remains nearly steady after this
time. Composite time series also show that the curvature acceleration peaks at
track recurvature while the forward speed is nearly at its minimum. The
tangential acceleration shows a sharp, steady increase around recurvature.
This is consistent with the observations that extratropical transition is
typically completed within 2-4 days of recurvature. A related relevant
question is the following: Is rapid tangential acceleration a sign of imminent
extratropical transition? We found that $\approx 65\%$ of the storms that
comprised the composites for rapid acceleration (Left column: Fig. 3)
completed the transition within 3 days of the reference time (day 0). This is
substantially higher than the climatological fraction of $\approx 50\%$ for
extratropical transition over the entire basin and storm lifetime. On the
other hand, only $\approx 39\%$ of the storms that comprised the composites
for rapid deceleration (Right column: Fig. 3) completed the transition within
a similar time range. This fraction is substantially lower than the
climatological fraction. It is, however, consistent with the observation made
earlier that the synoptic-scale pattern for rapid deceleration promotes
recurvature rather than extratropical transition. Furthermore, not all
recurving storms become extratropical (Evans et al., 2017).

The composites show that rapid acceleration and deceleration can be viewed as
a proxy for distinct types of tropical cyclone-extratropical interactions. It
is of interest, therefore, to ascertain whether any trends in tropical cyclone
accelerations can be found in the track data. For this, we use quantile
regression to examine the linear trends over the entire distribution. The
tails of acceleration and translation speed show statistically significant
trends. The trends for the extratropical regions of the Atlantic (20–50oN) are
most robust for August-September. Both rapid tangential acceleration and
deceleration have reduced over the past five decades. The trends for curvature
acceleration show increases for the lower quantiles and decreases for the
upper quantiles. The forward speed, particularly values above the median, also
shows robust decreases for the August-September months. This supports the
general conclusion of Kossin (2018) that tropical cyclones have slowed down in
the past few decades.

We have not explored the physical basis for the trends discussed above. We,
however, speculate that they are indicative of systematic changes in the
interaction between tropical cyclones and extratropical waves. It is, however,
unclear from our preliminary examination whether the trends reflect changes in
the frequency or some measure of the _strength_ of the interactions. We also
recognize that the notion of strength of interaction needs a firm and
objective definition. Nevertheless, there are some recent findings related to
the atmospheric general circulation that may be relevant to this point. First,
there is growing evidence for a poleward shift in the stormtrack of
extratropical baroclinic eddies. As noted by Tamarin and Kaspi (2017) and
references therein, this shift has been found in both reanalysis data and
climate model simulations. Separately, Coumou et al. (2015) found a robust
decrease of the zonal wind and the amplitude of synoptic-scale Rossby waves in
the ERA-interim reanalysis over the Northern hemisphere during the months
June-August. We hypothesize that the poleward shift of the extratropical waves
and their weakening could potentially account for the acceleration trends
reported here. This, however, needs to be examined further if any robust
conclusion regarding attribution to climate change is to be made.

When we separate tropical cyclones on the basis of their acceleration and
consider ensemble average composites of atmospheric fields (e.g.,
geopotential), we get two broad sets of synoptic-scale patterns. The composite
for rapid tangential acceleration shows a poleward moving tropical cyclone
straddled by an upstream trough and a downstream ridge. The subsequent merger
of the tropical cyclone and the developing extratropical wavepacket is
consistent with the process of extratropical transition. The composite for
rapid curvature acceleration shows a prominent downstream ridge that promotes
recurvature. On the other hand, the synoptic-scale pattern for rapid
tangential as well as curvature deceleration takes the form of a cyclone-
anticyclone dipole with a ridge directly poleward of the tropical cyclone. We
note the qualitative resemblance of this arrangement with the canonical dipole
block. Some of our findings from the perspective of tropical cyclone
acceleration closely match those of Riboldi et al. (2019), who conditioned
their diagnostics on the basis of the acceleration of the upstream trough and
recurving western north Pacific typhoons.

Accelerations and speed show robust trends in the tails of their distribution.
For the extratropical region of the Atlantic (20–50oN), and particularly for
the months August-September, peak acceleration/deceleration, as well as speeds
of tropical cyclones, have reduced over the past 5 decades. The reduction in
the tails of the speed distribution provide complementary evidence for a
general slowing trend of tropical cyclones reported by Kossin (2018). We also
suggest that the robust reduction in the tails of the acceleration
distribution is indicative of a systematic change in the interaction of
tropical cyclones with extratropical baroclinic waves. We have not, however,
examined the underlying processes. We speculate that poleward shift and
decreasing amplitude of extratropical Rossby waves found in other studies may
account for the acceleration trends. Detailed modeling and observational
studies are needed to better understand the source of these trends.

##  9 Data and code availability

The reanalysis data used here can be obtained from the European Center for
Medium-Range Weather Forecasts archived at
https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim/.
The tracks of Atlantic tropical cyclones were obtained from the IBTrACS
database available from https://www.ncdc.noaa.gov/ibtracs/. Authors will
provide computer code developed for this paper to anyone who is interested.

##  10 Author contributions

AA wrote the computer code for all analysis and visualization, and wrote the
text of the paper. TW derived the expression for the radius of curvature, and
assisted with editing the text and interpretation of the results.

##  11 Competing interests

The authors declare that they have no conflict of interest.

##  12 Financial Support

This work was supported by NSF through award #1433763

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