Acceleration of Tropical Cyclones As a Proxy For Extratropical Interactions: Synoptic-Scale Patterns and Long-Term Trends

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.

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.

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 (≈ 0.5%) in the IBTrACs is designated as NR or MX. This fraction is higher in other basins (e.g., ≈ 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 20-50 o N, wherein tropical cyclones are more likely to interact with extratropical baroclinic waves.

Tangential and curvature acceleration
The acceleration of a hypothetical fluid element moving with the center of a tropical cyclone can be written as: where V is the forward speed and R is the radius of curvature of the track at a given location. Here,ŝ andn 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: 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, δt = 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: where R is the radius of curvature, R e is the radius of the Earth, and the d terms are expressed as follows: 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: Where T and N are the latitude and longitude, respectively of the circle's center, and α and β are obtained using: 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).

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 • -wide latitude bins and all instances classified as non-tropical were excluded.

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.
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 ≥ a τ , where τ 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 ≤ a τ . We tried a variety of thresholds for τ (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. Lagcomposites 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 τ = 0.9 for rapid acceleration and τ = 0.1 for rapid deceleration. For reference, within 30-40 o N latitude range, τ = 0.9 corresponds to a = 32 km/hr day −1 and the τ = 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 (≈ 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.
5.1 Tangential Acceleration 5.1.1 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 30-40 o N 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.
The ensemble average for rapid tangential deceleration cases (right column of Fig. 3) shows an entirely different synopticscale 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.

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. 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 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 ≈ 7 ms −1 . The tropical cyclone speed, averaged over the same 4-day period, is ≈ 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 ≈ 3 ms −1 while the tropical cyclone speed is ≈ 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. 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.

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 re-curving 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  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 ≈ 38%. These estimates are lower than the fraction of 44% during 1979-2017 in Bieli et al. (2019), and 46% during 1950in 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 35 o N-45 o N.  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.

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.

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 20-40 o N band.   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. 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: Where, µ{Y |X} is the conditional mean of Y given a variable X, and β o and β 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): where Y (τ |X) denotes the conditional estimate of Y at the quantile τ for a given X. By definition, 0 < τ < 1. In our case,  (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.
systems. The corresponding numerical values are shown in Table 3. Recall from Table 1 that the median value (τ = .5) of tangential acceleration is a small positive number. As such, τ < 0.5 is indicative of deceleration, while τ ≥ 0.5 is indicative of acceleration.
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 20-50 o N 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 τ ≤ 0.15 and negative slope for τ ≥ 0.85 (Table 3 and left columns of Fig. 13 ). It also appears that the trends for τ < 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 < τ < 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.
The QR results for curvature acceleration (Fig. 14 and Table 4) show statistically significant, weak positive trends for 0 < τ < 0.5. However, the trends switch to increasingly negative values above the median. As in the case of tangential acceleration, Figure 14. As in Fig. 13, but for curvature acceleration.
the decelerating trends in the upper quantiles of the distribution (τ ≥ 0.8) are statistically significant and outside the 95% confidence bounds of the OLS estimate of the trend in the mean.
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 <0.01 -0.14, -0.03 Figure 15. As in Fig. 13, but for translation speed.
consider the entire Atlantic, estimated trends from QR are nearly the same as the OLS trend with the exception of τ = 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.

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 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 ≈ 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 ≈ 50% for extratropical transition over the entire basin and storm lifetime. On the other hand, only ≈ 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 cycloneextratropical 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 (20-50 o N) 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.

Conclusions
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 (20-50 o N), 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.

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.

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.

Competing interests
The authors declare that they have no conflict of interest.

Financial Support
This work was supported by NSF through award #1433763