Anthropogenic effects on tropical cyclones near Western Europe

Abstract

There is less consensus on whether human activities have significantly altered tropical cyclone (TC) statistics, given the relatively short duration of reliable observed records. Understanding and projecting TC frequency change is more challenging in certain coastal regions with lower TC activity yet high exposure, such as Western Europe. Here, we show, with large-ensemble simulations, that the observed increase in TC frequency near Western Europe from 1966 to 2020 is likely linked to the anthropogenic aerosol effect. Under a future scenario featuring regionally controlled aerosol emissions and substantially increased greenhouse gas concentrations (Shared Socioeconomic Pathway 5-85), our simulations show a potential decrease in TC frequency near Western Europe by the end of the 21st century. These contrasting trends in historical and future TC frequencies are primarily due to the rise for 1966–2020 and potentially subsequent fall for 2030–2100 in TC genesis frequency in the North Atlantic. The response of large-scale environmental conditions to anthropogenic forcing is found to be crucial in explaining the historical and future changes in TC frequency near Western Europe.

Introduction

While tropical cyclones (TCs) and Western Europe may seem unrelated, historical encounters have been documented^1,2,3. When such encounters do occur, they may have a high impact. This is attributed not only to the damaging wind, heavy precipitation, high storm surge and rapid population and economic growth in coastal regions, but also to the relatively limited experience in preparedness and public awareness in Western Europe regarding these extremely destructive weather systems with tropical origin. For example, Hurricane Debbie (1961) struck Ireland as one of the most severe storms to affect the region, resulting in 18 fatalities and widespread damage⁴.

Counterintuitively, climatological analysis suggests that TCs hitting Western Europe are not as rare as one might think. Approximately 10% of Atlantic TCs have made landfall in Europe in the past four decades⁵, i.e., about one European landfall per year. More than half of the storms reaching Europe from the Atlantic tropics retain a warm cyclone core, bringing extreme winds at landfall⁶. However, TCs entering the midlatitudes sometimes lose their warm-core structure via extratropical transition upon reaching Western Europe^7,8,9,10,11. Strictly speaking, these transitioned storms are no longer considered tropical systems. Nevertheless, to distinguish them from extratropical cyclones generated in the midlatitudes, this study still refers to a storm as a “tropical cyclone” when it originates in the tropical Atlantic, even after undergoing extratropical transition. Regardless the TC stage when reaching Europe, the consequence of a TC landfall in Western Europe could be more catastrophic than those caused by mid-latitude cyclones, as the former are, on average, significantly more intense when they make landfall in Europe¹².

TC impacts are primarily associated with their hazards, such as strong winds, precipitation, and storm surge. Recent TC studies provide relatively high confidence that TC peak winds, precipitation and storm-surge-related flooding may increase with global warming^13,14,15,16. However, TC frequency (TCF), the number of TC occurrence over a given period and region, is one of the important TC metrics relevant to the overall hazard and risk. Despite its importance, TCF is arguably the least understood component under climate change, both globally and within individual ocean basins¹⁷. There are multiple reasons for this lack of understanding. First, it is extremely challenging to capture a comprehensive long-term trend in TCF using paleoclimate archive proxies¹⁸. Second, historical simulations with current-generation climate models do not always accurately represent the observed TCF¹⁹. Third, model simulations sometimes show inconsistent projections for TCF under global warming²⁰. More importantly, an accepted theory that can explain the global mean TCF and its temporal variations is still lacking¹⁷.

With the rapid development of high-performance computing, it is now possible to employ general circulation models with a relatively fine grid spacing to understand past and project potential future changes in TCF^21,22. In this study, we utilize a recently developed next-generation global modeling system known as Seamless System for Prediction and EArth System Research (SPEAR)²³. The SPEAR simulation suite can be considered as a unique global modeling system because it possesses the capability for TC simulations while conducting numerical experiments to distinguish the effects of anthropogenic aerosols and greenhouse gases (GHGs) on weather extremes simultaneously. This work is a follow-up investigation of a recent study that focused on the changes in TCF within the tropics²⁴. Here we extend the previous analysis to examine the impact of TC activity at mid-latitudes. In this study, we employ this modeling system, together with TC best-track observations, to investigate the following question:

How has TCF changed and will it change near Western Europe, and why?

Results

The TC frequency, TCF, is calculated as the frequency of TC appearances in 5°$\times$5° grid boxes based on 6-h records. A tropical cyclonic system is referred to as a “TC” here as long as it reaches a peak wind speed above gale-force (34 knots), regardless of the stage of TC’s lifecycle. The analysis period was confined from 1966 – 2020, i.e., the current geostationary satellite era in the North Atlantic²⁵.

Observations

Our analysis begins with the examination of TCF using the TC best track data. Figure 1a shows an increase in mean TCF from the period of 1966–1993 to 1993–2020. Two clusters with statistical significance can be visually identified, one over the tropical Atlantic Ocean and the other near Western Europe (magenta box in Fig. 1a which will be identified specifically with further analysis later). Compared to that in the tropics, the TCF increase is relatively weaker near Western Europe. However, this increase can be as high as 200% relative to the climatological annual mean TCF there (Fig. 1b).

Fig. 1: Analysis of observed TCF variations for 1966–2020.

a Shifts in TCF before and after 1993, with black “$\times$“ marks indicating significant changes at a 90% confidence level, determined by a two-sided bootstrap test (see Methods). b Epochal TCF difference as shown in (a) divided by the annual mean TCF in each grid. c–h Analysis of regional SVD based on SST and TCF data. c A synthesis of the SVD mode that reflects the mean global SST change. d Similar to (c), but for the SVD mode related to the internal climate variability featured by the IPO pattern. e The expansion coefficient (EC) for the global mean SST mode, overlayed with the global mean SST. f As in (e), but for the natural variability mode, overlayed with an inversed IPO index. g Squared covariance fraction (SCF) for the global mean SST mode (with SCF ≥ 50% marked by black dots). h As in (g), but for the natural variability mode. The magenta box in (a, b, g) highlights the region near Western Europe where the TCF increase is statistically significant in (a) and the global mean SST increase may dominate such TCF changes as shown in (g).

It is possible that these trends could be associated with the artificial changes in analysis technique and protocols to extract TCs in observations, specifically for the mid-latitude TCs for which they undergo extratropical transition. Supplementary Figure 1 shows that there is no discernible trend in the relative frequency of extratropical transition in the best track data, nor any notable tendency in the northmost latitude where TCs have been recorded. This suggests that the observed increase in TCF near Western Europe may be associated with changes in the climate system itself, rather than being related to artificial changes in TC recording.

The singular value decomposition (SVD, see Methods) analysis was then employed to decompose the possible relationships between the change in TCF in the North Atlantic and the variations of the climate system through the global sea surface temperatures (SSTs)^21,24. The leading mode of the global SVD analysis effectively captures the scenarios of basin-wide TCF increase and global warming (Supplementary Fig. 2a–c), with the Expansion Coefficient (EC) showing the highest correlation with the global mean sea surface temperature (SST) increase (Supplementary Table 1). The second SVD mode closely resemble the Interdecadal Pacific Oscillation^26,27 (IPO) setup (Supplementary Fig. 2d–f and Supplementary Table 1).

A regional SVD analysis²⁴ (see Methods) was performed to further target the TCF change near Western Europe. Different from a global SVD, a regional SVD utilizes the TCF information of each grid box and the global SST field (see Methods). The regional SVD analysis shows a consistent decomposition similar to that of the global SVD analysis, with the leading mode reflecting the mean increase in global SST and the second mode resembling the IPO configuration (Fig. 1c-f).

An advantage of regional SVD is that it allows us to identify if TCF changes for each grid box are highly correlated with global warming mode or IPO mode by comparing the squared covariance fraction (SCF) of the two modes. Figure 1g, h highlight the dominant role of the mean SST increase on the TCF increase in the deep Atlantic tropics, near the US east coast, and near Western Europe.

Based on this observational analysis, we can now identify an area near Western Europe (the magenta box in Fig. 1a and g), where we observe both a significant increase in TCF for 1966–2020 and the predominant influence of global mean sea surface warming (i.e., anthropogenic forcing) on the TCF change there. We do not directly analyze the number of landfalling TCs in Western Europe due to an insufficient sample size for statistical testing. However, this limitation can be addressed by analyzing the TCs within the magenta box in Fig. 1a. This box is small enough to assume that the wind field may intersect land boundaries in Western Europe, yet large enough to include enough TC samples for statistical testing.

One should note that this SVD analysis is purely statistical and may not perfectly separate the effects of anthropogenic climate change from natural variability from a physical perspective, particularly considering that the two factors—i.e., anthropogenic change and internal climate variability—might interact with each other. Nevertheless, this SVD analysis provides a convenient way to identify the region where anthropogenic change may significantly alter the TCF. The TCF change in the magenta box, as shown in Fig. 1 near Western Europe, is the focus of the following analysis.

Simulations

The extensive SPEAR simulations conducted under different climate forcings offer valuable opportunities to explore the reasons behind the historical increase in TCF near Western Europe and to understand the potential future changes. Here our focus is on the individual impacts of two anthropogenic forcings—specifically aerosols versus greenhouse gases (GHGs)—on the changes in TCF near Western Europe during two distinct periods: historically, from 1966–2020; and in the future, from 2030–2100. We employed three sets of large-ensemble simulations: (1) those including anthropogenic aerosol and GHG forcing covering 1966–2100 (referred to as AllForc), (2) those with only anthropogenic GHG forcing covering 1966–2020 (AllForc_NoAE), and (3) those with natural forcing only covering 1921–2100 (NatForc). Two Shared Socioeconomic Pathways (SSPs) are considered in future scenario simulations: SSP2-45 and SSP5-85. Next, we investigate the TCF trend difference within multiple pairs of simulation suites to isolate the impacts of individual external forcings on TCF changes (see Methods for details).

We find an increase in TCF for 1966–2020 in simulations under the anthropogenic aerosol effect (Fig. 2a), but not with GHG or natural forcing for the same period (Fig. 2b, c). Combining the anthropogenic aerosol and GHG effects, an increase in TCF near Western Europe persists for 1966–2020 (Fig. 2d). The simulated TCF trend near Western Europe has comparable magnitudes as found in observations (Fig. 1). These results indicate that the increases in TCF are primarily owing to the anthropogenic aerosol changes with slight offset by GHG.

Fig. 2: Ensemble mean TCF Trends under anthropogenic forcing.

The trends are derived from ensemble mean annual TCF, forced by (a) anthropogenic aerosol effect (AllForc minus AllForc_NoAE), (b) anthropogenic greenhouse gases (AllForc_NoAE minus NatForc), (c) natural forcing (NatForc minus CNTL) and (d) the combined effects of anthropogenic aerosols and greenhouse gases (AllForc minus NatForc), for the period 1966–2020. e As in (b), but for the period 2030–2100 under SSP2-45. f As in (b), but for the period 2030–2100 under SSP5-85. Black dots indicate locations where the average TCF trends between two sets of experiments show statistical differences at a 90% confidence level, as determined by a two-sided t-test. The magenta boxes correspond to that in Fig. 1, highlighting the region near Western Europe.

A previous study²² revealed that the TCF in North Atlantic may be mainly influenced by the aerosol emission in Europe and the US, rather than emissions from other regions worldwide. Some SSPs assume a future scenario characterized by well-controlled aerosol emissions in Europe and the US, but a substantially increased greenhouse gas concentration globally (Supplementary Fig. 3). When we employ such a scenario as external forcing in our simulations and compare to the results under natural forcing (i.e., AllForc minus NatForc), we project a reduction in the TCF near Western Europe for 2030–2100 under SSP2-45, mainly due to the anthropogenic GHG effect (Fig. 2e). This reduction becomes statistically significant in the future following SSP5-85 near Western Europe, again, primarily due to the anthropogenic GHG effect (Fig. 2f).

Next, we apply a Total Analysis to decompose the TCF change into contributions from TC genesis, TC track, and the nonlinear combination of the two (see Methods and Supplementary Fig. 4). The changes in genesis contribute considerably to both the increase in TCF near Western Europe under anthropogenic aerosol effect for 1966–2020, and the decrease under the GHG effect for the period 2030–2100 (Table 1). The track contribution is also an important factor for the TCF increase with aerosol forcing, but not under the GHG effect.

Table 1 The contribution of genesis, track, and the nonlinear combination of the two to the simulated total TCF change near Western Europe

We then utilize the Origin Analysis (see Methods) to identify the key genesis areas where TCs originate and subsequently affect the TCF near Western Europe through direct genesis change and/or track change as they move toward Western Europe. Supplementary Figure 5a suggests that the TC genesis increase in the main development region (MDR; 10°-20°N, 60°-15°W) primarily contributes to the TCF increase near Western Europe for 1966–2020 under the aerosol effect, and conversely, the TC genesis reduction there contributes to the TCF reduction for 2030–2100 with GHG forcing (Supplementary Fig. 5d). Track change for TCs originating close to Africa also appears to play a secondly role in the TCF increase near Western Europe for the period 1966–2020 under the aerosol effect. With the strong control of genesis under both aerosol and GHG effects during the two periods, we next only focus on the genesis change.

TC genesis is largely controlled by the large-scale environmental conditions, and the Genesis Potential Index (GPI) serves as a useful proxy to understand this environmental control. A popular choice of GPI was proposed by Emanuel and Nolan²⁸ (hereafter the ENGPI), and a new GPI was also developed recently based on environmental dynamical factors²⁹ (hereafter DGPI). Comparing to the simulated tropical cyclone genesis frequency (TGF, Fig. 3a and d), DGPI can well reproduce the increase in genesis for the period 1966–2020 under the aerosol effect, and the subsequent decrease for 2030–2100 with GHG forcing. However, ENGPI fails to indicate the simulated TGF reduction in the future (Fig. 3f). Consequently, we exclusively utilize DGPI for the following analysis.

Fig. 3: Tropical cyclone genesis (TGF) frequency trend.

Trends of ensemble mean TGF in simulations under (a) anthropogenic aerosol effect (1966–2020) and (d) GHG effect (2030–2100), respectively, in a unit of genesis count per year. Trends of ensemble mean (b, e) DGPI and (c, f) ENGPI under (b, c) anthropogenic aerosol effect (1966–2020) and (e, f) GHG effect (2030–2100), respectively. White dots indicate locations where the trend is statistically significant at 90% confidence intensity based on a two-sided t-test. Within the magenta box near Western Europe, the red font “TCF” and “$\Uparrow$” in (a–c) highlight the simulated increase in TCF under the aerosol effect for the period 1966–2020, as shown in Fig. 2a. Similarly, the blue font “TCF” and “$\Downarrow$” in (d–f) indicate the reduction in TCF as shown in Fig. 2f under the GHG effect for 2030–2100.

By breaking down the DGPI contributions from its four factors, it becomes evident that the reduction in vertical wind shear is the dominant factor contributing to the increase in TGF over the MDR for period 1966–2020 under the aerosol effect (Table 2 and Supplementary Fig. 6a–e). With the vertical wind shear further decomposed, the change in zonal shear is mainly responsible for the overall shear reduction (Supplementary Fig. 7b). This is mainly attributed to a weakening of subtropical jet over the MDR at 200 hPa (Supplementary Fig. 7d). It has been argued^{22,24,30,31,32} that the potential jet weakening in the past a few decades may be linked to a stronger mid-latitude low-tropospheric warming (Supplementary Fig. 8). This, in turn, perturbs and weakens the climatological subtropical jet through thermal wind adjustment.

Table 2 Decomposition of DGPI trend

For the period 2030–2100 with GHG forcing, the weakening of ascending motion over the MDR emerges as a leading factor (Table 1, Supplementary Fig. 6f–j) contributing to the negative trend of DGPI. Further analysis reveals that the MDR region may experience a weaker SST increase under the GHG effect for 2030–2100, surrounded by much warmer SSTs in the mid-latitude North Atlantic, South Atlantic, and eastern equatorial Pacific (Supplementary Fig. 9a). Such an SST pattern creates a relatively “dry” region over the MDR with reduced convection (Supplementary Fig. 9b), resulting in a weakening of ascending motion there (Supplementary Fig. 9c).

TC hazard

The change in TCF is an essential factor influencing TC-related risk changes in coastal regions. However, to assess this, changes in other TC characteristics must also be considered. Under the combined effects of aerosols and GHGs, there is an initial increase (1966–2020) and then a subsequent decrease (2030–2100) in TCF near Western Europe in our simulations (Fig. 4a). However, there are no clear trends in TC intensity near Western Europe in observations or model simulations for both present-day and future (Fig. 4b). If the Accumulated Cyclone Energy (ACE, Bell et al., 2000), a measure combining TCF and TC intensity, is chosen to indicating the potential change in TC hazard, the associated risk near Western Europe have been increasing since 1966 and could drop in the future, primarily due to the changes in TCF in that region.

Fig. 4: Observed and simulated TC changes in the past and projection into future.

a Annual TCF near western Europe. The thin line shows the TCF change in HURDAT, taken as observation, for 1966–2020. The thick lines shown model ensemble mean change for 1966–2020 in AllForc and 2030-2100 under SSP5-85, respectively. The shading shows the range of all ensembles. b As in (a), but for the annual mean maximum wind speed (knots) for the TCs near Western Europe (within the magenta box in Fig. 1a) based on the 6-h records. c As in (b), but for the annual mean accumulated cyclone energy (ACE, 10⁴ knots2) for the TCs near Western Europe. If an ensemble trend shows statistically significant change at 5% level, a fitted thick black line is added for the period, as shown in (a) and (c).

Discussion

Two kinds of temperature changes may be associated with the historical and future changes in TCF near Western Europe. First, for the increase in TCF for the period 1966–2020, it is the mid-latitude atmospheric warming that weakens the subtropical jet over the MDR region through thermal wind adjustment, subsequently reducing vertical wind shear. This, in turn, favors TC genesis in the deep tropical Atlantic. Therefore, the reduction of aerosol emissions in Europe and the US in the past few decades may be the reason for the recent increase in TCF near Western Europe.

Second, concerning the decrease in TCF near Western Europe for period 2030–2100, the Atlantic MDR region exhibits a relatively weaker SST increase compared to the surrounding maritime regions under the GHG forcing, along with a substantially flattened aerosol emission curve in the western world. These factors lead to reduced convection and ascending motion over the MDR, subsequently suppressing TC genesis that in turn leads to a reduction in TCF near Western Europe.

In terms of TC hazard changes, the ACE near Western Europe may have increased for the period 1966–2020 but is expected to decrease for 2030-2100. This change in risk is primarily driven by the change in TCF since the mean TC intensity does not show any significant trend in simulations for both past and future. One should note that the TC precipitation-related hazard, which also changes under anthropogenic climate change, is not considered here. For example, a prior study³³ indicated that even with a potential decrease in the number of TCs making landfall over the eastern U.S. in the future, the intensity of TC extreme precipitation could be expected to rise, leading to an increase in TC hazard potential.

If we assume that the TCF near Western Europe tends to follow the mean change in the basin, most climate models projects a decrease in TCF in North Atlantic into the future¹⁶, which aligns with our simulations. However, there is still no consensus on the changes in TCF near Western Europe. Previous studies with prescribed SST distributions under global warming have suggested the possibility of increased TCF near European Atlantic coast^34,35. Here we found an opposite change, but with a fully coupled GCM, larger ensemble members, and an extended and continuous simulation period from past to the end of 21st century.

We also showed that the future ACE near Western Europe may decrease, dominated by the reduction in TCF in that region, with no significant change in TC intensity. It might be surprising to observe a lack of TC intensity change near Western Europe, especially given the relatively high confidence in the increasing fraction of major TCs relative to total TCs globally in the future^16,36. However, major TCs often reach their peak intensity in the warm tropics, which is far from Western Europe that we are focusing on in this study. The environmental changes at mid-latitudes may further complicate the understanding of general tropical cyclone intensity changes, which are established based on a tropical environment. In addition, the North Atlantic is a basin where we have very low confidence in the poleward migration of TCF compared to, for example, the western North Pacific^16,37,38,39. Therefore, a reduction in TC-related hazards in Western Europe may be plausible in the future under global warming.

Methods

Data

The TC best track

The TC best track data used in this study was based on the HURDAT best track data⁴⁰ as observational records. Our analysis started in 1966, which is considered the starting year of the geostationary satellite era for North Atlantic hurricane observation. We retained only the best track records from the equator to 60°N. For each TC, we included data from the first time it reached tropical-storm strength (34 kt) to the last instance it maintained this strength, regardless of its status during the lifecycle, whether it remained a tropical cyclone or underwent an extratropical transition. The TC frequency, TCF, is calculated as the frequency of TC appearances in 5°$\times$5° grid boxes based on 6-h records. The same data selection criteria and pre-processing were applied to the modeled best track data.

Environmental conditions

We utilized the monthly sea surface temperature (SST) records with 1 deg latitude/longitude grid spacing from the Hadley Centre Sea Ice and Sea Surface Temperature data set⁴¹ known as HadISST. The HadISST data goes back to 1870 but we only used the records for 1966–2020 in this study. For the mean atmospheric conditions, the ERA5 monthly reanalysis data from the European Centre for Medium-Range Weather Forecasts were employed⁴². Based on the seasonality of TCs in the whole North Atlantic basin and near Western Europe (Supplementary Fig. 10), we focused on the environmental conditions during August to October.

Climate indices

The ENSO time series were represented by the oceanic Niño index (ONI). The interdecadal pacific oscillation (IPO) index was estimated as the second principal component of the empirical orthogonal function analysis after standardization for the 13 year filtered global SST²⁷. The Atlantic Multidecadal Oscillation (AMO) was computed as the area weighted average of SST over the North Atlantic with detrending⁴³. The Atlantic Meridional Mode (AMM), describing the meridional variability in the tropical Atlantic Ocean, was calculated based on SST and 10-m wind field^44,45,46.

Large-ensemble simulations

We used the SPEAR global modeling system²³. The version employed here consists of a 50 km-resolution mesh for the atmosphere and land components, and a 1 degree ( ~ 100 km) resolution for the sea-ice and ocean components with refinement to 1/3 degree near the Equator^47,48,49. The SPEAR model can simulate the broad-scale distribution of global TCs^21,23, but with a limited ability to resolve major TCs. A previously developed TC tracking algorithm⁵⁰ was modified and utilized for TC identification and tracking in the modeling world every 6 h, consistent with the observed best tracks. The TC identification procedure requires a maximum wind speed of 16.5 m s^-1 or higher and a well-established warm core defined based on the 300-500-hPa temperature field. The tracking algorithm requires a minimum duration of 36 h. However, the warm-core criterion is not required anymore once a TC is identified and tracked. This means that losing the warm core due to extratropical transition does not terminate a TC lifecycle in the simulated best track, consistent with the observed best track. In this way, the SPEAR model can effectively reproduce the seasonality of TC frequency compared to the observation, both in terms of the global mean value and the TC count near Western Europe (Supplementary Fig. 10).

The initial-condition large-ensemble experiments were conducted with SPEAR. We performed three large-ensemble simulations (AllForc, AllForc_NoAE and NatForc), which are introduced as follows.

AllForc

There are 30 ensemble members in this suite. The simulation period extends from 1966–2014 with historical external forcing, and from 2015–2100 following the Shared Socioeconomic Pathways (SSP2-45 and SSP5-85, respectively). This suite utilized prescribed external forcing including anthropogenic effect (such as greenhouse gases, anthropogenic aerosols, and ozone) and natural forcing (such as volcanic eruptions, dust, and solar constant change). The natural aerosols—e.g., the African dust having a large impact on North Atlantic TC climatology⁵¹—were carefully handled following other previously developed models^48,49.

AllForc_NoAE

Like AllForc, but with fixed anthropogenic aerosol forcing, such as sulfates, organic carbon and black carbon, set at the level as in year 1921. There are 12 ensemble members covering 1966–2020. It was shown previously²⁴ that 12 members can effectively remove the climate internal variability by taking the ensemble mean.

NatForc

Like AllForc, but with fixed anthropogenic forcing at the level of 1921. There are 30 ensemble members covering 1966–2100.

We attempted to decompose the impacts of anthropogenic forcing on TCF into anthropogenic GHG forcing and anthropogenic aerosol forcing as follows:

• Anthropogenic aerosol forcing (1966–2020): the ensemble-mean TCF trend difference between experiments AllForc minus AllForc_NoAE.

• Anthropogenic GHG forcing (1966–2020): the ensemble-mean TCF trend difference between experiments AllForc_NoAE minus NatForc.

• Anthropogenic GHG forcing (2030-2100): the ensemble-mean TCF trend difference between experiments AllForc minus NatForc. It has been recently reported that the TCF over North Atlantic has been mainly influenced by the aerosol emission in the US and Europe, which may be substantially flattened out after 2030 owing to pollution control measures over Europe (Supplementary Fig. 3 using sulfate aerosol as an example). This suggests that the difference of simulated TCF trends between AllForc and NatForc for 2030-2100 should be mainly due to the anthropogenic GHG forcing.

SVD analysis

The singular value decomposition (SVD) was used here to explore the synchronized temporal and spatial relationship between observed SST and TCF matrixes. For each SVD mode, a pair of expansion coefficient (EC) time series were generated for SST and TCF. To show the fraction of co-variability between the SST and TCF patterns in each mode, a squared covariance fraction (SFC) was calculated in a unit of percentage.

Following a recent study²⁴, global and regional SVD approaches were employed. Both approaches utilize the global SST field as one input. For the other input matrix, the global SVD utilizes basin-wide TCF, whereas the TCF information on one and its eight neighboring grids are used for one regional SVD practice. The regional SVD is repeated until all the grids in the North Atlantic basin is covered. In our analysis, most of regional SVD result in two leading modes corresponding to global warming and IPO based on the SFC ranking.

The global SVD was employed in Supplementary Fig. 2, with the regional SVD in Fig. 1. The SST and TCF fields were weighted by the cosine of latitude before performing the matrix analysis.

Decomposition of TCF trends

We utilized two previously developed empirical methods⁵² to break down the TCF trends into genesis and/or track contributions.

The first empirical approach is the Total Analysis. The results of the Total Analysis are shown in Table 1 and Supplementary Fig. 4.

The TCF in an individual grid $A$ can be written as

$$\bar{f}={\iint }_{\!C}\bar{g}\times \bar{t}d{A}_{o}$$

(1)

where $\bar{f}=f\left(A\right)$ is the TCF in an individual grid $A$, $g=g\left({A}_{o}\right)$ is the frequency of TC genesis in a remote grid cell ${A}_{o}$, $t=t(A,{A}_{o})$ is the probability that a TC is generated in the grid ${A}_{o}$ and then propagated to grid $A$ (i.e., track effect), and $C$ is the region over which the integration is calculated. The overbars represent the climatological means.

Now we decompose $f$ in 1 year with the climatological mean $\left(\bar{f}\right)$ and the anomaly $\left({f}^{{\prime} }\right)$ in this year, i.e., $f=\bar{f}+{f}^{{\prime} }$, and Eq. (1) can be then rewritten as

$$\bar{{\rm{f}}}+{{\rm{f}}}^{{\prime} }={\iint }_{\!{\rm{C}}}\left(\bar{{\rm{g}}}+{{\rm{g}}}^{{\prime} }\right)\times \left(\bar{{\rm{t}}}+{{\rm{t}}}^{{\prime} }\right){\rm{d}}{{\rm{A}}}_{{\rm{o}}}$$

(2)

where $\bar{g}$ and $\bar{t}$ are the climatological means and ${g}^{{\prime} }$ and ${t}^{{\prime} }$ are the anomalies in that year. Substituting Eq. (1) in Eq. (2) yields

$${{\rm{f}}}^{{\prime} }={\iint }_{\!{\rm{C}}}{{\rm{g}}}^{{\prime} }\times \bar{{\rm{t}}}{\rm{d}}{{\rm{A}}}_{{\rm{o}}}+{\iint }_{\!{\rm{C}}}\bar{g}\times {t}^{{\prime} }d{A}_{o}+{\iint }_{\!{\rm{C}}}{{\rm{g}}}^{{\prime} }\times {{\rm{t}}}^{{\prime} }{\rm{d}}{{\rm{A}}}_{{\rm{o}}}$$

(3)

The map of TCF trend, denoted as $\frac{\partial }{\partial t}\left(\bar{f}+{f}^{{\prime} }\right)=\frac{\partial }{\partial t}{f}^{{\prime} }$, can be then decomposed with Eq. (3) as

$$\frac{\partial }{\partial {\rm{t}}}{{\rm{f}}}^{{\prime} }=\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}{{\rm{g}}}^{{\prime} }\times \bar{{\rm{t}}}{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}\bar{g}\times {t}^{{\prime} }d{A}_{o}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}{{\rm{g}}}^{{\prime} }\times {{\rm{t}}}^{{\prime} }{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right).$$

(4)

Next we apply Eq. (4) to experiment 1, a reference experiment, which can be written as

$$\frac{\partial }{\partial {\rm{t}}}{{\rm{f}}}_{1}^{{\prime} }=\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}{{\rm{g}}}_{1}^{{\prime} }\times \bar{{{\rm{t}}}_{1}}{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}\bar{{g}_{1}}\times {t}_{1}^{{\prime} }d{A}_{o}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}{{\rm{g}}}_{1}^{{\prime} }\times {{\rm{t}}}_{1}^{{\prime} }\,{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right).$$

(5)

We may also apply Eq. (4) to experiment 2, a sensitivity experiment, which can be written as

$$\begin{array}{l}\frac{\partial }{\partial {\rm{t}}}{{\rm{f}}}_{2}^{{\prime} }=\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}{{\rm{g}}}_{2}^{{\prime} }\times \left(\bar{{{\rm{t}}}_{1}}+\overline{\Delta {\rm{t}}}\right)\,{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{\!{\rm{C}}}\left(\bar{{{\rm{g}}}_{1}}+\overline{\Delta {\rm{g}}}\right)\times {{\rm{t}}}_{2}^{{\prime} }\,{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)\\\qquad\quad+\,\frac{\partial }{\partial {\rm{t}}}\left({\iint_{{\rm{C}}}}{{\rm{g}}}_{2}^{{\prime} }\times {{\rm{t}}}_{2}^{{\prime} }\,{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right),\end{array}$$

(6)

where $\overline{\Delta t}=\bar{{t}_{2}}-\bar{{t}_{1}}$ and $\overline{\Delta g}=\bar{{g}_{2}}-\bar{{g}_{1}}$, which represent the difference of climatological mean of track probability and genesis frequency, respectively, in experiment 2 relative to experiment 1.

By taking the difference of Eqs. (6) and (5) we have

$$\begin{array}{l}\underbrace{\frac{\partial }{\partial {\rm{t}}}{{\rm{f}}}_{2}^{{\prime} }-\frac{\partial }{\partial {\rm{t}}}{{\rm{f}}}_{1}^{{\prime} }}_{\text{df}}=\underbrace{\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{{\rm{g}}}_{2}^{{\prime} }\times {\overline{{{\rm{t}}}_{1}}}{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)-\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{{\rm{g}}}_{1}^{{\prime} }\times {\overline{{{\rm{t}}}_{1}}}{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)}_{\text{dg}}\\+\,\underbrace{\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{\overline{{g}_{1}}}\times {t}_{2}^{{\prime} }d{A}_{o}\right)-\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{\overline{{g}_{1}}}\times {t}_{1}^{{\prime} }d{A}_{o}\right)}_{\text{dt}}\\+\,\underbrace{\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{{\rm{g}}}_{2}^{{\prime} }\times {{\rm{t}}}_{2}^{{\prime} }{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)-\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{{\rm{g}}}_{1}^{{\prime} }\times {{\rm{t}}}_{1}^{{\prime} }{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{{\rm{g}}}_{2}^{{\prime} }\times {\overline{\Delta {\rm{t}}}}\,{\rm{d}}{{\rm{A}}}_{{\rm{o}}}\right)+\frac{\partial }{\partial {\rm{t}}}\left({\iint }_{{\rm{C}}}{\overline{\Delta g}}\times {t}_{2}^{{\prime} }d{A}_{o}\right)}_{\text{dn}}{,}\end{array}$$

(7)

where ${df}$ shows the TCF trend difference between experiments 2 and 1, and ${dg}$, ${dt}$ and ${dn}$ represent changes due to genesis effect, track effect, and nonlinear combination of the two.

The second empirical approach is the Origin Analysis. The result of the Origin Analysis is shown in Supplementary Fig. 5.

The Origin Analysis for TCF trend has been recently derived and employed in another study²⁴. Here we only briefly introduce this method, which can be conveniently written as

$$d{f}_{B,{A}_{o}}=d{g}_{B,{A}_{o}}+d{t}_{B,{A}_{o}}+d{n}_{B,{A}_{o}}$$

(8)

where $d{f}_{B,{A}_{o}}$ shows the total genesis and track effects of a remote genesis grid ${A}_{o}$ on the TCF trend difference between the two experiments in the region of $B$ (referring to the magenta box near Western Europe in Fig. 1a in this study). The three terms on the r.h.s., $d{f}_{B,{A}_{o}}$, $d{g}_{B,{A}_{o}}$ and $d{n}_{B,{A}_{o}}$, show the breakdown effects of genesis, track, and nonlinear combination of the two, respectively, from a remote genesis grid ${A}_{o}$ on the mean TCF change in the region of $B$.

The total analysis reveals the contribution of each of the three factors—genesis effect, track effect, and their nonlinear combination as shown in Eq. (7)—to the change in TCF across the entire domain. However, the total analysis cannot pinpoint the specific locations where these changes significantly impact local TCF. Conversely, the origin analysis, described in Eq. (8), identifies the specific locations contributing to the projected change in TCF near Western Europe.

Genesis Potential Index (GPI)

Two kinds of GPI were utilized in this study: the ENGPI²⁸ and DGPI⁵³. The DGPI is composed with dynamical environmental factors, which can be written as

$${DGPI}=\underbrace{{\left(2.0+0.1\times {V}_{s}\right)}^{-1.7}}_{V-{SHEAR}}\,\underbrace{{\left(5.5-\frac{d{u}_{500}}{{dy}}\times {10}^{5}\right)}^{2.3}}_{M-{SHEAR}}\,\underbrace{{\left(5.0-20\times {\omega }_{500}\right)}^{3.4}}_{{OMEGA}}\,\underbrace{{\left(5.5+\left|{\zeta }_{a850}\times {10}^{5}\right|\right)}^{2.4}}_{{VORT}}{e}^{-11.8}-1.0$$

(9)

where ${V}_{s}$ is the vertical wind shear magnitude (m s^-1) between 200 and 850 hPa, ${u}_{500}$ is the zonal wind (m s^-1) at 500 hPa, $\left(-\frac{d{u}_{500}}{{dy}}\right)$ denotes the meridional shear vorticity (s^-1) at 500 hPa, ${\omega }_{500}$ is the vertical velocity in a pressure coordinate (Pa s^-1), ${\zeta }_{a850}$ is the absolute vorticity (s^-1) at 850 hPa, and $e$ is the natural base. The calculated DGPI value was fixed to zero between 5^oN-5^oS or where the relative SST (i.e., local SST minus tropical mean SST) becomes negative^29,53.

We took the logarithm of Eq. (9) to estimate the relative contribution of each term to the change of DPGI, which can be written as

$$\begin{array}{l}log ({DGPI}+1)=log (V-{SHEAR})+log (M-{SHEAR})\\\qquad\qquad\qquad\qquad+\,log ({OMEGA})+log ({VORT})-11.8\end{array}$$

(10)

The linear trend of each in Eq. (10) was compared to obtain the relative contribution of individual environmental factors to the total DPGI trend, as given in Table 2.

The ENGPI is defined as²⁸

$${ENGPI}={\left|{10}^{5}{\zeta }_{a850}\right|}^{\frac{3}{2}}{\left(\frac{{RH}}{50}\right)}^{3}{\left(\frac{{V}_{{pot}}}{70}\right)}^{3}{\left(1+0.1{V}_{s}\right)}^{-2}$$

(11)

where ${V}_{{pot}}$ is the maximum potential intensity (m s^-1) defined by the local thermodynamic profile⁵⁴, and RH denotes the relative humidity (%) at 600 hPa.

Statistical significance test

We assessed the statistical significance between two linear trends using a t-test. For the epochal TCF change (e.g., in Fig. 1a), a bootstrap method was applied. We resampled the two tested populations in pairs 10,000 times, calculated the mean difference for each pair, and generated a new distribution with 10,000 samples. From this distribution, we derived the 90% confidence intervals.