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Concurrent Changes to Hadley Circulation and the Meridional Distribution of Tropical Cyclones

Poleward trends in seasonal-mean latitudes of tropical cyclones (TCs) have been identified in direct observations from 1980 to present. Paleoclimate reconstructions also indicate poleward-equatorward migrations over centennial to millennial timescales. Hadley circulation (HC) is often both implicitly and explicitly invoked to provide dynamical linkages to these shifts, although no direct analysis of concurrent changes in the recent period has been presented. Here the observational TC record (1981-2016) and the ERA-Interim, JRA55 and MERRA2 reanalyses are studied to examine potential relationships between the two. A zonally-asymmetric HC is defined by employing Helmholtz theory for vector decomposition and this permits the derivation of novel HC diagnostics local to TC basins. Coherent variations in both long-term linear trends and detrended interannual variability are found. TC genesis and lifetime maximum intensity latitudes share trend sign and magnitude with shifts in local HC extent, with rates being ~0.25 plus/minus 0.1 degrees latitude decade-1. Both these lifecycle stages in hemispheric means and all Pacific TC basins, as well as poleward-extreme North Atlantic lysis latitudes, shared ~35% of their interannual variability with HC extent. Local HC intensity is linked only to eastern North Pacific TC latitudes, where strong local overturning corresponds to equatorward TC shifts. Examination of potential dynamical linkages implicates La Ni\~na-like sea surface temperature gradients to poleward HC termini. This corresponds to increased tropical and reduced subtropical vertical wind shear everywhere except in the North Atlantic and western North Pacific, where the opposite is true. These results quantify a long-hypothesized link between TCs and the large-scale oceanic-atmospheric state.


Introduction
Tropical cyclones (TCs) play an important role in the climate system and are useful indicators of climate variability. Since there are strong regional signals of ongoing climate variability in both the Atlantic and Indo-Pacific Oceans (e.g. Rhein et al. 2013;Li et al. 2015), the responses of TCs to these signals are of great interest.
TCs are also hypothesized to play an active role in influencing climate at both the local and global scales (e.g. Emanuel 2008; Manucharyan et al. 2011;Fedorov et al. 2010Fedorov et al. , 2013Huang et al. 2017). TCs represent important extreme climate events and impact financial markets, especially the insurance and reinsurance industries (Pielke 2007;Reed et al. 2015). In this respect, TC tracks are of great physical and societal relevance.
Numerous approaches have been used to quantify TC tracks and their variability in climate records and numerical simulations. A binary classification of 'straight-moving' (typically zonal propagation) versus 'recurving' (moving poleward after genesis and curving back upon themselves) is very widely employed.
Other metrics include point and track densities (e.g., Elsner et al. 2012), trajectory mass moments (e.g., Nakamura et al. 2009), and probabilistic clustering (e.g., Gaffney et al. 2007;Kossin et al. 2010). A description of TCs using zonal and meridional averages along the lifecycle has been employed in a number of recent analyses (e.g., Kossin et al 2014Kossin et al , 2016Wu et al. 2015;Wang et al. 2016). This approach has particular merit when relating TC activity to hemispheric climate modulations.
Considerable intraseasonal and interannual variability as well as long-term trend in TC tracks is well documented, although substantial issues remain for analysis.
Difficulty persists since available timeseries are short and changes in operational centers and practices occur throughout the available record (e.g., Sandgathe 1987;Chia and Ropelewski 2002;Landsea 2015;Klotzbach and Landsea 2015;Landsea et al 2010). A poleward migration in the seasonal-mean latitude of TC lifetimemaximum intensity (LMI) in both hemispheres has been identified with rates of 0.48 and 0.56 latitude decade -1 between 1982 and 2012, in the Northern and Southern Hemisphere (NH, SH) respectively ). Daloz and Camargo (2017) found LMI migration corresponds to poleward migration of Pacific TC genesis.
Changes in TC latitudes, linked to recurvature, have also been identified regionally in both the western North Pacific and North Atlantic (Wu and Wang 2004;Kossin et al. 2010;Ha et al. 2014;Daloz et al. 2015;Mei and Xie 2016;Hart et al. 2016;Kossin et al. 2016). Over centennial and millennial timescales, TC latitudes have been shown to migrate poleward and equatorward at various times in numerous paleoclimatic reconstructions (e.g. Baldini et al. 2016;Hengstum et al. 2016).
Coincident with these poleward migrations in seasonal-mean TC latitudes, there has been an expansion of the dominant feature of the large-scale tropical atmospheric flow, the Hadley Circulation (HC, e.g. Lucas et al. 2014). Reported magnitudes for the migration of the HC poleward extent are approximately 0.5 to 0.81 latitude decade -1 (e.g. Hu and Fu 2007;Stachnick and Schumacher 2011;Davis and Rosenlof 2012;Allen et al. 2012;Nguyen et al. 2013; Davis and Birner 2013). There is thus some amount of consistency between the reported poleward trends in TC latitudes and HC extent.
Since TC tracks are influenced by their environmental large-scale winds and SST, links to large-scale structure of the tropical circulation are of great interest (Latif et al. 2006;Kossin et al. 2010;Vecchi et al. 2013a).
The HC is often implicitly and explicitly invoked to provide a mechanistic interpretation of the poleward-equatorward migration of seasonal-mean TC latitudes. Kossin et al. (2014Kossin et al. ( , 2016 relate the recent poleward migration of TCs to increases in seasonal-mean VWS in the tropics and decreases in the subtropics by subtracting composites of an early and late period, thus implicitly invoking HC as it is known to have migrated poleward over the period. This pattern corresponds to an increase in TC potential intensity (connected to tropical SSTs and ocean-atmosphere thermal disequilibria). They went on to indeed hypothesize that these changes are directly linked to the well-documented expansion of the HC (e.g. Fu et al. 2006;Lucas et al. 2014).
Furthermore, Baldini et al. (2016) Zhang and Wang 2013;Schwendike et al. 2014;Schwendike et al. 2015;Zhang and Wang 2015;Nguyen et al. 2017). This method is particularly appropriate for studying TCs in relation to the HC as HC is notably zonally asymmetric. Wang (2013, 2015) used this diagnostic to examine how the Atlantic and eastern North Pacific local HC effects TC frequency and intensity.
Here we present a novel analysis of TC-HC concurrencies using the 35-year observational TC record and three reanalysis products to address the hypothesized connection directly. Specifically, the analysis has the following aims: 1. Identify poleward-equatorward migrations in seasonal-mean TC latitudes along the cyclone lifecycle (genesis, LMI and lysis).
2. Diagnose the local HC, and compute and discuss the magnitudes of longterm linear trends in these diagnostics directly in relation to concurrent trends in seasonal-mean TC latitudes.
3. Directly relate interannual HC modulations to TC latitudes irrespective of any long-term linear trends in either.
As far as the authors are aware, this is the first attempt to make such an explicit covariance analysis between TC and local HC. The structure of this paper is as follows: in section 2 the data and methodology are detailed. Section 3 describes changes in TC meridional distribution over recent decades. Sections 4 and 5 analyze the HC meridional extent and intensity and their relationship to TC latitudes respectively. A brief exploration of potential dynamical linkages is provided in section 6 before a summary in section 7.

Data and Methodology
a. Observational TC data TC track data is taken from the International Best Track Archive for Climate Stewardship (IBTrACS) v03r10 (Knapp et al. 2010). This archive is maintained by the United States' National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center and is considered the most complete set of global historical TC data (e.g., Kossin et al. 2014;Walsh et al. 2016;Kossin 2017).
Uncertainties in TC observational records have a strong impact on analysis reliability (e.g. Landsea et al. 2010;Landsea 2015;Klotzbach and Landsea 2015;Daloz et al. 2015). Data have improved since 1980 with global satellite coverage but even post-satellite records contain significant uncertainties (Ren et al. 2011;Barcikowska et al. 2012;Torn and Snyder 2012;Landsea and Franklin 2013). The length of reliable records is important for trend detection since natural variability at decadal and longer scales is high (Sobel et al. 2016).
Inhomogeneities also hamper analyses, and there is particular observational bias towards times and locations when TCs are within a forecaster's 'realm of interest' (i.e. the system is intense and there is landfall risk). This bias chiefly affects records of genesis and lysis as this is when cyclones are typically weak and far from landfall . To maximize robustness and analyze sensitivity, where possible it is optimal to use more than one dataset (Camargo and Sobel 2010;Schreck et al. 2014).
We use IBrACS-WMO (the archive's own homogenization product) and another aggregation combining National Hurricane Center data (aka. RSMC Miami, aka. HURDAT2), which covers the Atlantic and eastern North and Central Pacific, and the JTWC, which covers all other basins (together referred to as NHC-JTWC). We employ both IBTrACS-WMO and NHC-JTWC, in all basins except the North Atlantic and eastern North Pacific (where the NHC is the WMO observational agency). We only show analysis using the IBTrACS-WMO data for the North Atlantic and eastern North Pacific. We note that using two datasets does not NH and SH means are constructed from both IBTrACS-WMO and NHC-JTWC. We deem this a valid approach in the NH since the majority of TCs there occur in the western North Pacific where two independent records exist. Regional boundaries used in this study (defined following WMO guidelines) and all TCs (by key lifecycle point) are shown in figure 1a.
For consistency and reproducibility, we examine periods when tracks are considered either 'tropical' or 'subtropical' as indicated by archive flags, a categorization that is standardized by IBTrACS. We also use only the 'main' (archive's terminology) time series of all TCs as denoted by archive flags. The inclusion of wind speed data is variable across ocean basins and time. Again for consistency, we define genesis with a constant wind speed threshold. Some tracks in the archive do not include any wind speed data and are thus excluded from the analysis.
We consider three specific stages covering the TC lifecycle: 'genesis', 'lifetime maximum intensity' (LMI), and 'lysis' (figure 1b,c). Here, the genesis location is defined as the location of the TC center when it first reaches tropical storm intensity (defined as maximum sustained wind speed ≥ 18 m/s, 33 kts). If a TC's first recorded wind speed is above this threshold, this first point is taken as genesis. Such tracks are <1% of the archive and their inclusion/exclusion does not affect the conclusions reached. LMI is the time at which the highest magnitude maximum sustained wind speed over the entire lifecycle is recorded. LMI can be viewed as the most robust measure as this depends solely on the maximum intensity which will occur well into the lifecycle whereas genesis and lysis will be more sensitive to operational changes and forecaster subjectivity. Lysis location is the position of the track when its 'nature' (archive's terminology) is last recorded as tropical. In practice, TCs at this point in their lifecycle may indeed experience actual lysis, i.e. a disintegration of the defining coherent warm core, or may undergo extratropical transition (ET). Determining ET in observational data is non-trivial (e.g., Studholme et al. 2015); thus, aggregating actual warm core disintegration and ET into the category of 'lysis' in this analysis is considered to be a reasonable and meaningful approximation.

b. Hadley circulation extent and intensity diagnostics
Estimates for HC extent and intensity are derived from three reanalyzes: ERA-Interim (Dee et al. 2011), JRA55 (Kobayashi et al. 2015 and MERRA2 (Gelaro et al. 2017) using three-dimensional monthly means of daily means on their native grids (3/4 x 3/4 for ERA-Interim, 1/2 x 1/2 for JRA55, 1/2 x 2/3 degrees for MERRA2) at all available pressure levels. It is important to use multiple reanalyzes as considerable variation in HC has been shown to exist between them (e.g. Nyugen et al. 2013). These data are then linearly interpolated onto 1/4 horizontal resolution and 10 hPa vertical resolution in pressure coordinates to aid comparison.
To diagnose the local HC, we employ the Helmholtz decomposition following Schwendike et al. (2014). This takes advantage of the fact that a vector field in R 3 may be unambiguously partitioned into two contributions: (i) a divergent (aka. irrotational) component where ∇ × ≡ 0 and (ii) a non-divergent component where ∇ . ≡ 0 (e.g. Bourne and Kendall 1992). This is necessary for defining the zonally asymmetric HC since the commonly-used Stokes streamfunction computed using hemispheric zonal-mean meridional velocities, [ ] 0 2 , depends upon the assumption of nondivergence, i.e. / + / = 0 (using standard geophysical notation; e.g. Oort and Rasmusson 1970;Oort and Yienger 1996). It therefore requires there to be no zonal component to the net mass flux. In a zonalmean of the atmospheric wind field over an entire hemisphere this condition is trivially satisfied. However, between any two arbitrary zonal bands 1 and 2 , where 2 − 1 < 2 , this ceases to be true. Over such regional domains, the net zonal mass flux is non-negligible and the streamfunction may not be computed from .
Using the divergent component of the Helmholtz-decomposed winds ensures that this condition is satisfied. In the interest of brevity, we direct the reader to Schwendike et al. (2014) for a full derivation of this approach. Summarizing, vertical motion can thus be written as: where is vertical motion in pressure coordinates and subscripts and denote the vertical velocity in the meridional and zonal planes respectively. The component can be viewed as the meridional overturning circulation (i.e. Hadley circulation) and the component as zonal overturning, (Walker circulation). In this analysis, we are only interested in which satisfies: where is the divergent component of the meridional velocity. Although this method assures and are two unique orthogonal circulations, it does not imply independence between the zonal and meridional components of the flow, and such a coupling has been implicated in interbasin associations (e.g. Chiang et al. 2000;Chiang et al. 2002). The meridional streamfunction in spherical coordinates for the local HC can thus be derived as (Zhang and Wang 2013;Nyugen et al. 2017): where a is the mean radius of the planet and g is gravitational acceleration.
The integration is taken from the top of the atmosphere which yields positive (negative) values for annual-mean in the NH (SH) tropics. This corresponds to a clockwise (counter-clockwise) circulation when viewed from the East. We compute between zonal bands corresponding to different TC basins: North Atlantic (20W-70W), eastern North Pacific (105W-150W), western North Pacific and South Pacific (130E-180E), and South Indian (50E-110E). We verified all results against reasonable perturbations (i.e. ±10) around these boundaries and they had no meaningful effect on results.
The HC is characterized with two diagnostics derived from : HC extent and intensity. Traditionally HC extent has been defined as the =0 isoline (e.g. Oort and Yienger 1996). However, in the zonally asymmetric HC this line is not necessarily crossed (figure 2). Nguyen et al. (2017) first encountered this issue when looking at regional HC in the SH. They devised a new definition of the edge of the local HC, defining it as where the overturning weakens to a specified threshold percentage of the maximum overturning within the tropical cell. The edge of the HC is therefore taken as the average position of the weakened-peak-value between 700-400 hPa. We use 800-400 hPa as we found that shallow cells, particularly in the

Figures 1 b and c show climatological distributions of all TC lifecycle points in
the WMO and NHC-JTWC datasets respectively. TC genesis is generally confined between the Equator and ±20N and is more tightly bound in the SH. This is possibly due to differences in operational procedures (e.g. Hodges et al. 2017 it would stand to reason that while the SH trend has continued on, the NH LMI poleward migration has halted in the most recent period. This is confirmed by inspection of timeseries (see figure 8). There is also a notable agreement between datasets in the hemispheric mean trend estimates for poleward migration of LMI in both hemispheres (shown as red horizontal lines in figure 3).
Both datasets also reveal a robust poleward migration of the most equatorward (below the 50 th percentile) NH LMI locations (significant at the 95% level in the WMO). By contrast, there are considerable uncertainties concerning migration at the most poleward (above the 50 th percentile) TC LMI latitudes in the NH. In SH LMI, there is no robustness in trends below the 40 th percentile (most equatorward LMI locations), but both datasets at the 95% confidence level show that the 60% most poleward LMI latitudes are migrating further southward. Again, this phenomenon occurs at a rate of 0.4latitude decade -1 .
NH TC genesis is migrating poleward at a faster rate than the LMI, with a rate of 0.4latitude decade -1 . This is confirmed by the two datasets and is robust at the 95% significance level. This trend is dominated by the poleward migration of the most equatorward (below the 50 th percentile) half of genesis latitudes, while the trend for the poleward half is not statistically robust. In the SH, while the NHC-JTWC dataset shows a robust trend in the mean genesis latitude of a poleward migration at 0.43latitude decade -1 , this trend is not identified in the WMO data.
Quantile regressions for NH ocean basins (Figure 4)  In the South Pacific, we find a statistically robust mean LMI poleward migration in both datasets of 0.42latitude decade -1 (figure 5a). We also find a poleward migration in mean genesis latitudes in NHC-JTWC of 0.58 latitude decade -1 but it is not significant in the WMO data. These trends are matched in the South Indian (figure 5d, e, f). We find statistically significant trends in seasonal mean LMI in both datasets with differing magnitude: WMO has 0.5 latitude decade -1 and NHC-JTWC 0.45latitude decade -1 .
Taken in aggregate, these trends can be summarized by four major points: • A poleward migration of seasonal-mean TC LMI occurs in both the NH (0.1latitude decade -1 ) and SH (0.45latitude decade -1 ) in unweighted hemispheric averages.
• Notable uncertainties remain despite efforts for dataset homogenization and ever-lengthening time series.

Results: Hadley circulation extent and comparison to TC latitudes
The climatological divergent winds and meridional overturning in the ERA-Interim reanalysis (figure 2) shows that HC extent varies notably from basin to basin.
It is particularly more poleward in western Pacific. Three main centers of action are clear: over the African continent, the Indo-Pacific region and the Americas. The Intertropical Convergence Zone (ITCZ) is clearly seen with values of ̅ at 500 hPa approaching zero and convergence in the near-surface wind vectors.

a. Long-term Trends
Persistent poleward shifts over the second half of the last century in HC extent are well documented and observable in a number of diagnostics, with the strongest trends identified in the 1980s and 1990s (see review by Lucas et al. 2014). Figure 6 shows the annual and TC-seasonal mean timeseries derived for this analysis Comparing HC and TC poleward trends reveals reasonable overall coherence within a shared relatively tight range of estimated magnitudes.
Summarising, in all but a few cases (in particular in the Northern Pacific), HC and TCs have tended poleward together with rates ~0.25 ±0.1latitude decade -1 (table 2, figures 3,4,5). TCs in the SH exhibit the strongest poleward migration of 0.45latitude decade -1 at LMI while over the same period SH HC has shifted poleward at a mean rate of 0.3latitude decade -1 . In the NH, while the HC has also shifted poleward at 0.3latitude decade -1 (albeit less conclusive and with much higher interannual variability), TC LMI has shifted at a mean rate of approximately 0.1latitude decade -1 .

b. Shared Interannual Variability
When we directly regress detrended seasonal-mean TC latitudes onto seasonalmean local HC extent, we find robust statistical covariance across the TC lifecycle occurring irrespective of long-term shifts (Figure 7). In general, we find Pacific and North Atlantic TC genesis shares variability with HC extent (r=0.6, figure 7a). The covariance strength is lower for LMI (r=0.5, figure 7b) and negligible for lysis (r < 0.4, figure 7c). Different reanalysis products generally produce similar results, but there are some differences between the two TC observational records.
In particular, the covariance between genesis and LMI latitudes and HC extent appears to be predominantly a Pacific phenomenon. At genesis, although notable covariance is found with North Atlantic TC latitudes, R 2 values are half that of the NH Pacific basins (figure 7a). In the South Indian, there is no notable relationship whatsoever.
Two hemispheric-mean timeseries demonstrate the covariance strength itself has This set of regressions is repeated for the equatorward and poleward parts of the seasonal TC latitudes but are not produced here since they are more or less consistent with the means. The exception is that the most poleward quartile [ P(75) ] of North Atlantic lysis latitudes are found to significantly covary with local HC extent (r=0.62). As in the hemispheric case, we see that the observed covariance is time dependent (figure 9). In particular, it is very weak in the 1990s but strong in the 1980s and 2000s.
In aggregate, these results indicate that TC genesis and LMI latitudes share longterm trend sign and magnitude with concurrent shifts in local HC extent with rates around ~0.25 latitude decade -1 . Seasonal-mean TC genesis and LMI mean latitudes in both hemispheres and in all Pacific basins, as well as poleward-extreme North Atlantic lysis latitudes, share ~35% share of their interannual variability with HC extent.

a. Long-term Trends
HC intensity has been subject to notable debate in the recent past.
Thermodynamic scaling arguments predict a weakening of convective mass flux in the tropics resulting from changes in atmospheric humidity (Held and Soden 2006). intensity ranging from -0.5 to 12.7 x 10 9 kg s -1 decade -1 . In the SH, trends ranged from -3.2 to 9.0 x10 9 kg s -1 decade -1 . Between 1981 and 2009, annual-means trends for the present analysis ( figure 10a, b) in the NH range from -0.1 to 6.8 x10 9 kg s -1 decade -1 and in the SH from 0.4 to 5.3 x10 9 kg s -1 decade -1 . Thus, our estimates largely agree with Nguyen et al. (2013) despite different HC algorithms and reanalysis products.
All HC intensity timeseries exhibit very considerable interannual variability.
Annual-mean NH HC shows persistent intensification (

b. Shared Interannual Variability
Regressions between detrended seasonal-mean HC intensity and seasonal-mean TC latitudes (figure 11) do not indicate any robust covariance across hemispheric means in all but one ocean basin. We find a robust link between seasonal-mean eastern North Pacific HC intensity and seasonal-mean latitudes of TC genesis and LMI in all reanalysis products. The same conclusions also hold for the most equatorward and poleward edges of genesis and LMI latitudes.
Corresponding time series of TC genesis equatorward extreme latitudes ( Figure   12) shows strong, time-invariant negative covariance (r= -0.75). A more intense eastern North Pacific HC is associated with equatorward shifts in TC genesis and LMI there. The flow in this basin is strongly influenced by the Walker circulation, orthogonal to the HC, which makes it unlike other basins. This zonal influence might perhaps be related to this anomalous negative covariance. Note also that over this period there is no trend consistent across reanalysis products for an intensification or weakening of the local overturning circulation ( kg s -1 decade -1 ) that concluding any coherent relationship is somewhat dubious.
Results indicate there is no common interannual variability between seasonal-mean TC latitudes and HC intensity, except in the eastern North Pacific.

Potential dynamical linkages
Significant uncertainties remain in fundamental understanding of both TCs' relationship to large-scale climate dynamics, and the HC despite it being the oldest known large-scale atmospheric circulation, (e.g. Gastineau et al. 2011;Levine and Schneider 2011;Holton et al. 2013;Gleixner et al. 2013;Zhan et al. 2017;Yan et al. 2017). It is well understood that TCs are strongly sensitive to both SSTs and VWS (e.g. Murakami et al. 2011;Kossin et al. 2014;Kossin et al. 2016;Yan et al. 2017). Regressing the hemispheric-mean HC extent diagnostic against seasonal means of these quantities from ERA-Interim reveals strongly coherent spatial patterns implicated in potential underlying dynamical linkages ( figure 13).
We see a more poleward HC is linked to reduced meridional SST gradients in all ocean basins and warm SST anomalies at TC latitudes in the North Atlantic, western North Pacific and South Pacific. There are even slight warm anomalies in the eastern North Pacific and South Indian SSTs around TC locations despite generally being cooler in these basins on the whole (figure 13a). This pattern is remarkably reminiscent of a strong La Niña event (e.g. Lim et al. 2016) and links between an expanded HC and La Niña have been noted before (e.g. Seager et al. 2005;Seager et al. 2010). In idealized numerical experiments, HC extent has been shown to have a complex relationship to absolute SSTs and meridional SST gradients (e.g. Walker and Schneider 2006;Levine and Schneider 2011;Gastineau et al. 2011;Seo et al. 2014).
Tropical VWS generally increases and subtropical VWS generally decreases with a more poleward HC (figure 13b). Kossin et al. (2014) arrived at the same result by subtracting zonally averaged composites over 1980-1994 and 1995-2010, implicitly linking TC poleward migrations to HC. Here, we arrive at the same general conclusion but additionally reveal strong zonal asymmetries. In particular we see tropical (subtropical) VWS reduction (increase) in the North Atlantic and western North Pacific, i.e. the inverse of the zonally integrated pattern.
In the eastern North Pacific, we find more intense local HC strongly reduces equatorward VWS (figure 14b) and is linked to basin-wide warmer SST ( figure 14a).
This environmental change is linked to an equatorward shift in seasonal-mean TC latitudes. With this method, we are able to identify basin specific heterogeneity which may explain the differences we observe in trends and covariance. These linkages beg further analysis.
In recent decades, SSTs have been trending towards a 'La Niña-like' anomaly pattern similar to the one identified in figure 13a (e.g. Lim et al. 2016).

Summary and discussion
We present an analysis comparing seasonal-mean poleward-equatorward migrations Over the same period, both hemispheres' mean HC extent has shifted poleward at an approximate rate of 0.3latitude decade -1 . There are no robust poleward shifts in local HC extent that occur in all reanalyses. However, reanalysis products generally agree on the sign and magnitude of trends. Detecting local trends is challenging in part due to very high interannual variability. Over the entire period, HC intensity averaged over TC seasons has no consistent trend. Reanalyzes agree that hemispheric mean HC overturning has strengthened, although at the resolution of individual TC basins this is not evident. These findings are broadly in a greement with other works (e.g. Hu and Fu 2007;Johanson and Fu 2009;Stachnik and Schumacher 2011;Allen et al. 2012;David and Rosenlof 2012;Nguyen et al. 2013; David and Birner 2013).
After removing long-term trends, we find that latitudes of seasonal-mean TC genesis and LMI in the hemispheric mean and in the Pacific basins have approximately 35% of their interannual variability in common with HC extent. We also find that the poleward extremes in North Atlantic TC lysis latitudes and local HC extent share 40% of their detrended interannual variability. HC intensity has little-to-no relation to TC latitudes everywhere except in the eastern North Pacific where there is a strong negative covariance. As far as we are aware, this is the first attempt to derive statistics of this type. Thus, we find quantitative evidence for concurrent TC and HC meridional shifts at both interannual and long-term timescales. Notable issues remain with available data and uncertainty is considerable.
At the hemispheric scale, we find a more poleward HC is linked to reduced meridional SST gradients and warm SST anomalies at TC latitudes in such a way as to resemble a La Niña-like oceanic state. This corresponds to tropical (subtropical) VWS generally increasing (decreasing). Locally, the inverse is observed in the North Some scholars have concluded that contemporary models are capable of simulating TCs with acceptable veracity (e.g. Zhao and Held 2010;Murakami et al. 2013Murakami et al. , 2015Han et al. 2016). However, using modeling to study HC, ITCZ dynamics and TC tracks remains a difficult undertaking since characteristic spatial scales are orders of magnitude apart. In this respect, there is much work to be done to improve physical understanding and projections of future HC and TC track changes (e.g., Levine and Scheider 2015;Daloz et al. 2015).

Circulation
In a zonally-asymmetric HC, extent is notably harder to robustly identify than in the hemispheric zonal mean. In the latter, Hadley cell termini can be identified with the 500 ℎ = 0 isoline whereas in the former, this line is not necessarily crossed at all. To account for this, we implemented and built upon the approach of Nyugen et al. (2017). We detail this in the methods section. In implementing this algorithm, it became clear that a few notable 'edge cases' exist where unexpected results are produced. We document these here for two reasons. First, it is clear that the specifics of any diagnostic algorithm have a strong effect upon the resultant time series. Therefore, explicitly demonstrating how they work is important for clarity.
Second, we include this appendix to aid reproducibility.
The first case is when a second maximum in the overturning exists in the midlatitudes of the same sign as the tropical cell. The HC over the western Pacific warm pool region is a particular example of this (figure A.1a). This second higherlatitude maximum is often greater in magnitude than its tropical counterpart. The weakening threshold algorithm we implement here does a good job at identifying the terminus (blue vertical line at 28N) despite this second maximum and the fact that the zero isoline is never crossed. This situation seems to occur when the local HC is merged or dominated by monsoonal flow in the boreal summer.
The second case we highlight is shown in figure A.           Regressions between seasonal-mean HC extent and seasonal-mean TC meridional distribution at different lifecycle stages. All timeseries had their linear trends removed. Pink shadingshows regressions that exceed 95% confidence estimated using two-tailed p values from t-statistics. As there are no two independent observational records in the North Atlantic andeastern North Pacific, only the WMO data is shown for these basins.    Regressions between seasonal-mean HC intensity and seasonal-mean TC meridional distribution at different lifecycle stages. All timeseries had their linear trends removed. Pinkshading shows regressions that exceed 95% confidence estimated using two-tailed p valuesfrom t-statistics. As there are no two independent observational records in the North Atlanticand eastern North Pacific, only the WMO data is shown for these basins.          Regressions between seasonal-mean HC extent and seasonal-mean TC meridional distribution at different lifecycle stages. All timeseries had their linear trends removed. Pink shadingshows regressions that exceed 95% confidence estimated using two-tailed p values from t-statistics. As there are no two independent observational records in the North Atlantic andeastern North Pacific, only the WMO data is shown for these basins.    Regressions between seasonal-mean HC intensity and seasonal-mean TC meridional distribution at different lifecycle stages. All timeseries had their linear trends removed. Pinkshading shows regressions that exceed 95% confidence estimated using two-tailed p valuesfrom t-statistics. As there are no two independent observational records in the North Atlanticand eastern North Pacific, only the WMO data is shown for these basins.