For the development and demonstration of the SyNC composites, the North Atlantic TC season 2005 was simulated using the non-hydrostatic numerical weather prediction and climate model ICON (, ICON partnership (DWD; MPI-M; DKRZ; KIT; C2SM) (2024). ICON release 2024.10. World Data Center for Climate (WDCC) at DKRZ) in limited area mode. The model domain spans the North Atlantic ocean (5 to 45° N, 105 to 18° W) using a triangular grid with 5 km (grid R2B9) horizontal grid length, 80 vertical levels up to 23 km and a time step of 25 s. Initial and six-hourly boundary conditions were taken from ECMWF IFS HRES analysis product. Sea surface temperature was prescribed using daily fields online-interpolated from monthly mean input, itself derived from the ECMWF 6-hourly IFS HRES analysis for 2005. Simulations ran from 1 July to 1 December 2005, including a two week spin-up. The selected months were chosen to capture the climatological peak of hurricane activity while balancing computational cost. The model physics is represented by a set of parametrisations: the prognostic turbulent kinetic energy (TKE) scheme for turbulences , the ecRad scheme for radiation , the TERRA scheme for land surface processes and the two-moment scheme of for clouds, predicting mass and number concentrations of cloud droplets, ice crystals, rain, snow, graupel and hail. Cloud droplets' growth is implemented by saturation adjustment, whereby updraft-induced water vapor supersaturation is reduced to 100 % by condensation on cloud droplets. Cloud droplets are formed by the cloud condensation nuclei (CCN) activation scheme of . The CCN concentration is prescribed to 500 cm-3 representing average conditions over the North Atlantic . Deep and shallow convection parametrisations are switched off to align our setup with convection-permitting ICON studies from , and . showed, that ICON is able to sufficiently capture the water and energy budgets, the cloud distribution in the tropics and the location of the InterTropical Convergence Zone (ITCZ) and hence is able to reproduce key features of the climate system without convection parametrisations at 5 km. Additionally, demonstrated that both simulated TC numbers and Accumulated Cyclone Energy (ACE) in ICON are much closer to observational values when the deep convection parametrization is switched off.

An ensemble of eight members was computed to increase the TC group size and assess the internal variability in the simulations. Ensemble members were created according to the method described by by perturbing the initial specific moisture field. Random perturbations on the order of a rounding error (±10-13 kgkg-1) were added to the initial moisture field. The initially small perturbations grew as the simulations proceeded. Since the model is only constrained by the 2005 large-scale environment at the lateral domain boundaries, each member has some degree of freedom to evolve into its own internal state within the domain. Consequently, the simulations represent eight plausible realizations of the 2005 season rather than its exact reproduction. The simulated TC tracks therefore diverge from observed tracks (Fig.  in Appendix A).

TCs were identified using the multi-parameter TC tracking algorithm of . The algorithm employs three typical TC characteristics: a surface pressure depression, a cyclonic wind field and a warm core located in the upper troposphere. These characteristics are detected by the algorithm at each time step using four parameters, each evaluated across multiple threshold values (shown in parentheses): 1.

A local sea level pressure minimum within a given distance (pmin,dist [50, 100, 150] in km).

After cyclone detection, simulated TCs were filtered to exclude weak and short-lived systems based on the following criteria: minimum lifetime of 48 h and reaching a minimum central pressure (pmin) of 990 hPa or lower. We employed the pressure based intensity scale by , which covers pressure categories (cat_pres) from 1–5 starting at a pressure of ≤ 990 hPa being cat_pres of 1. The pressure based intensity scale has multiple benefits: pressure measurements are more accurate than wind measurements, pmin is a strong indicator of potential damage and the climatological spread in pressure distribution is better captured by numerical models than for maximum winds . The wind-pressure relationship of TCs is poorly represented in numerical models often revealing too weak winds for a given central pressure with increasing error towards intense TCs . In climate models with horizontal grid lengths of ≈ 20–200 km, the simulated wind-pressure relationship improves with increasing resolution by better resolving the vortex leading to a more realistic representation of its structure and the development of intense tropical cyclones (Cat 3–5; ). Storm-resolving models operating at approximately ≈ 2–10 km horizontal grid length further improve simulated storm structure and intensity compared to coarser-resolution models, although model-dependent biases remain . Possible sources of this model dependence include the choice of dynamical core and the model's physics parametrization, which determine the surface drag in the boundary layer and diabatic heating through cloud processes and by that influence the simulated TC intensities and structures . Accordingly, pressure-based metrics are more robust and well-suited for analyzing TC activity in numerical models, as demonstrated in the study by .

To enable meaningful comparisons between TCs with different lifetimes, the evolution of each storm is normalized, inspired by the method of . The time axis is rescaled to an interval of [0, 1], where tnorm = 0 corresponds to genesis, tnorm = 0.5 to the time of minimum central pressure (i.e., maximum intensity), and tnorm = 1 to storm lysis. Between these three fix points, the normalized time axis is linearly interpolated to the tracking time steps. Accordingly, the intensification phase spans from tnorm ∈ [0, 0.5] and the decay phase from tnorm ∈ [0.5, 1]. TC genesis and lysis are defined by the start and end points of the detected TC tracks.

The goal of the SYmmetrized-Normalized cyclone (SyNC) composite approach is to reduce composite blurring from misaligned vortex structures. Each TC is transformed to an axisymmetric vortex and spatially normalized based on the eyewall radius and the storm size. That way, eyewalls and storm borders are aligned when compositing the symmetrized-normalized TCs. In this section, all processing steps of SyNC are described in detail. There are four main steps to obtain SyNC composites (see Table ): 1.

Cyclone-centered projection of the TC from a sphere to a plane.

First, each TC is projected from the Earth's sphere to a plane using a cyclone-centered Lambert azimuthal equal-area projection. This creates a Cartesian grid (x, y, z) with the grid origin located at the cyclone center addressing the irregular spacing of the grid due to the curvature of the Earth. Therefore, the projected grid preserves the true size of a cyclone and enables the comparison of cyclones across different latitudes. The projected horizontal grid length is set to match the model grid length (Δx=5 km) to avoid data extrapolation or interpolation, thereby minimizing data modification in this initial step. Additionally, the model output is reduced to a 1000 km × 1000 km square around the TC center to speed up the post-processing. This defines the extent of the data and determines Rmax⁡.

Second, the eyewall and the storm's size are detected based on the tangential wind field (see Fig. a). The location of the eyewall is approximated by RMW . The horizontal extent of the TC is defined as the radius where the wind speed reaches 17 ms-1 (, R17, from now referred to as Rout). RMW is identified for each vertical level, what allows to further estimate the eyewall tilt. When the tangential wind becomes anticyclonic at upper-levels, RMW is taken from the last level below, where winds are still cyclonic. Rout is detected from the tangential wind mean between the surface and 2 km. This ensures better representation of the storm size compared to detecting Rout only at a single vertical level. The 2 km level was selected, since it leads to the largest TC extents and with that conservatively keeps most of the vortex data in the analysis (find more details and a sensitivity experiment in Appendix ). Rout is maintained for all height levels. Otherwise, the anticyclonic outflow would unrealistically narrow the vortex size at upper-levels. Note that the cyclone center is defined as the location of the sea level pressure minimum and is assumed not to vary with height. This assumption can introduce errors in radial and tangential wind components in the presence of vortex tilt, particularly at upper levels. However, errors mainly affect radial winds, while tangential winds are only weakly impacted . Therefore, the wind radii detection are not expected to be strongly affected by this simplification. To make the wind radii detection robust, some additional rules are implemented: RMW is forced to a minimum/maximum of 15 km/400 km and Rout is capped at a maximum of 700 km. In case of a narrow Rout-RMW ring, Rout is increased until a minimum distance of 30 km between RMW and Rout is fulfilled to avoid extensive extrapolation of data points in case of a narrow Rout-RMW ring. Additionally, to exclude detected extreme radii, detected RMW and Rout are excluded when exceeding 300 % or 600 % of the median of this level, respectively, and replaced with a rolling average of radii in their neighboring sectors. These thresholds were selected based on statistics of observed wind radii and Rout-RMW distances. During testing of the algorithm, the thresholds were rounded and adjusted to the simulated TC structure in such a way that the thresholds were only applied when physical radius detection would not have been possible without them. The thresholds are especially necessary for obtaining feasible radii in the early stage of a TC, where the vortex structure is less pronounced and above 15 km, where the vortex ends or the anticyclonic outflow complicates the radii detection. For more details about threshold selection and when they are applied see Sect. . The RMW and Rout detection is done for 10 circle sectors (i.e., 36° sectors) individually around the cyclone center to account for vortex asymmetry (Fig. a). The detection resolution of 36° was chosen such that each sector contains at least one grid cell within the detection minimum of RMW (illustrated in Fig. b in Appendix B), which is a necessary condition to detect RMW for each sector. Hence, the maximum number of detection sectors is dependent on the data resolution, whereof for higher resolution, also a higher number of detection sectors can be employed. A high number of detection sectors can improve the detection of vortex asymmetries, as shown by a sensitivity experiment of AI to the number of detection sectors (Sect. ). These findings suggest that the highest feasible number of detection sectors should be selected. The 10 detected Rout values are smoothed by a rolling mean over 3 data points to avoid spikes in the TC size. After this, the resolution of detected RMW and Rout is increased by linearly interpolating the detected radii from 36° sectors to 1° sectors (Fig. b). This allows for a more continuous vortex normalization in the next step.

The spatial normalization is conducted such that the TC center is located at the grid origin, while the storm's eyewall/edge are forced to a normalized radius of 1/8, respectively (Fig. b). The normalized radii of 1 and 8 are chosen to approximately preserve the ratio between the RMW and Rout of the simulated TCs, thereby minimizing data loss and extrapolation during storm normalization. The initial sensitivity analysis (Sect. ) revealed that both RMW and Rout vary substantially within the simulated TCs. Near maximum intensity, simulated RMW values are approximately ≈ 30–50 km, while Rout is about ≈ 350 km, yielding RMW / Rout ratios between 6 and 11. To account for this structural variability while maintaining a representative normalization, an intermediate ratio of 1/8 was selected. Observed North Atlantic TCs exhibit a smaller RMW / Rout ratio of ≈ 1 : 5 (see observed radii in Fig.  in Appendix B), indicating that the choice of ratio is dataset-dependent and may require adjustment when applied to other TC datasets.

The radial normalization of the cyclone is employed in cylindrical coordinates (x, y, z → rtrue, φtrue, z). Based on the eyewall and border distance to the origin (rtrue), a one dimensional linear interpolation function is defined, that transforms the real radius to the unit-less normalized radius (rnorm) by assigning RMW a value of 1, Rout a value of 8 and Rmax⁡ a value of 20 (rtrue → rnorm). Hence, each grid cell of the projected grid obtains a new normalized radius while preserving the angles (rtrue, φtrue, z → rnorm, φtrue, z). The normalization is done for each of the 1° sectors individually, which forces any TC to be an approximately axisymmetric vortex. After the radius transformation, any data field (ϕ) can be interpolated from the transformed grid to a normalized grid by applying 2D cubic interpolation (ϕ (rnorm, φtrue, z) → ϕ* (rnorm, φnorm, z), Fig. c). Note that the radius transformation and data interpolation are conducted for each height level, hence the full three dimensional fields of the TCs are symmetrized and normalized. This also straightens the eyewall, which is necessary to consistently align the eyewall and its associated cloud structures throughout the vortex. Such alignment can be beneficial for investigating processes within the eyewall, such as cloud microphysics and the associated latent heating (further discussed in Sect.  and ). Last, the normalized grid is converted from cylindrical to Cartesian coordinates, from which SyNC composites are calculated.

The asymmetry index (AI) is calculated to assess the vortex shapes of the different cyclone groups and to estimate the relevance of the vortex symmetrization. The AI is defined as the ratio of the maximum radius to the effective radius of four quadrants . Here, we calculate AI for the overall storm using Rout and for the eyewall using RMW. Instead of estimating asymmetry based on four quadrants, all detection sectors (s1,s2,…,sn) are used, such that AI is defined as the following: 1Rmax⁡=max⁡(Rs1,Rs2,…Rsn)2Reff=∑i=1nRsi2n3AI=Rmax⁡Reff-1 where R is the detected Rout or RMW in the tangential wind field for each vertical model level, i the sector index and n the total number of detection sectors. Hence, AI of 0 indicates a perfectly symmetric structure.

To assess the significance of differences between cyclone groups, we employ independent two-sided permutation tests. The test statistic is the group mean, with the null hypothesis stating that the means of the cyclone groups are equal. By randomly drawing cyclone fields from the two groups, synthetic cyclone groups are generated. This process is repeated 10 000 times. The distribution of the synthetic group means is then used to estimate the confidence interval for the null hypothesis . The null hypothesis is rejected at a significance level of 0.05.

The permutation tests are conducted for each grid cell in the azimuthally averaged composites. To correct for multiple testing along the radius- and height-axis, and the associated risk of falsely rejecting the null hypothesis , we tighten the statistics by controlling the false discovery rate (FDR) at a level of 0.05, applying the method of .

The simulated TCs are validated by comparing their characteristics with observed cyclones from the HURDAT2 best track dataset . HURDAT2 is a post-storm data reanalysis of satellite, aircraft and weather station measurements and provides best estimates of North Atlantic TC tracks, central pressure and peak winds. To be consistent, observed TCs were filtered with the same criteria as the simulated TCs regarding their lifetime and minimum pressure. In addition, only storms that developed between 15 July and 1 December were considered, consistent with the chosen simulation period.

To evaluate the ICON-simulated TCs, the relationship between simulated wind and central pressure is compared to observations in Fig. . The simulated wind-pressure relationship displays a bias near the model surface (Fig. a–b), where most simulated 10 m winds are weaker than observed winds for a given central pressure. This suggests a model bias that may be related to the surface drag parameterization. As discussed in Sect. , such behavior is commonly found in numerical models across a range of horizontal resolutions . To minimize the influence of surface parameterization, a model level is identified where the wind-pressure relationship aligns well with observations for two reasons: First, it provides a wind-based intensity estimate for simulated TCs that is consistent with simulated pressure-based estimates (see Sect. ), exploiting the higher confidence in the simulated central pressure. Second, it enables a comparison of wind magnitudes and wind field structures between model and observations (see Sect. ) while accepting and excluding model biases near the surface. Indeed, the fit improves at higher altitudes until 0.13 km (Fig. c), where the best fits is located with a MSE of only 9 m2s-2. Above 0.13 km, TC winds appear too strong for a given central pressure. Therefore, the 0.13 km level is selected for further comparisons between observed and simulated wind fields in following sections, as it offers the best alignment with observations while also being rather close to the surface. Notably, the model reproduces intense stages of TCs accurately, covering the observed range of high winds and low pressures, although it slightly under-represents weaker stages (i.e., high central pressures). The TC tracker likely struggles to detect the weak and very early stages of TCs, when the storm's central pressure is close to the ambient pressure . As a result, these stages are missed in our analysis.

In order to place the simulated TC life cycles, frequencies and intensities into context, key TC characteristics of the simulated TCs (Fig. , blue) are compared to characteristics of the North Atlantic climatology (HURDAT2, 1980–2024, black) and the observed 2005 hurricane season (red). As discussed in Sect. , the simulated dataset represents plausible realizations of the highly active 2005 hurricane season. Consequently, the simulated activity is not expected to exactly reproduce the observed 2005 season nor to correspond to the climatological mean. Nevertheless, the simulated lifetime and month of genesis (Fig. d and h) show good agreement with the observed 2005 season and climatology. Simulated TCs predominantly form between August and October, aligning with the observed peak TC activity (Fig. h). However, the model fails to generate TCs during the late months of the North Atlantic TC season (November). On average, simulated TCs last approximately eight days (Fig. d), consistent with observed behavior. A comparison of storm tracks and additional intensification metrics can be found in Sect. .

Regarding storm intensity, the model shows a tendency to produce more intense TCs, as indicated by the significantly lower median central pressure of 938 hPa compared to the climatological median of 967 hPa (Fig. e) and a notably higher median maximum winds of 67 ms-1 compared to the observed 46 ms-1 (Fig. f). Simulated TC also intensify more rapidly than observed climatology (Fig. g). This tendency towards more intense and rapidly intensifying storms may originate from the model's initiation and forcing using the extremely active TC season 2005. The hypothesis is supported by the central pressure and pressure decrease distributions of the observed season 2005, which do not show significant differences from the model. However, with a median of only 4 simulated TCs season⁻¹ (Fig. a), the model clearly underestimates TC frequency compared to the observed 13 storms in 2005 and the climatological median of 6 TCs season⁻¹ within July to December. Since the number of major hurricanes (cat_pres 3–5) is close to observed ones (Fig. b) and the distribution of TC categories is skewed towards higher categories (Fig. c), this suggests that the model generates a too high fraction of major TCs. The weaker storms (cat_pres 1–2) exist in the model but their frequency is underestimated compared to the climatology and the 2005 season. This imbalance between weak and intense storm frequency and the overall low number of simulated TCs could partially stem from the model setup, as coupled ocean-atmosphere ICON simulations run globally at a convection-permitting resolution with a horizontal grid length of 5 km reproduce the observed annual TC counts more accurately . Nevertheless, having various storm intensities ranging from cat_pres 1 to cat_pres 5 storms, the simulated TC group is suitable for testing and demonstrating the SyNC framework.

To validate the vortex structure of the simulated TCs, azimuthally averaged wind profiles at maximum intensity are compared between simulated and observed TCs (Fig. ). The median values of wind radii R33 (radius where wind reaches 33 ms-1 ≃ 64 knots), R25 (25 ms-1 ≃ 50 knots), and R17 (17.5 ms-1 ≃ 34 knots) for the simulated TCs are close to those observed. While the spread of R33 and R25 radii also aligns with observations, the spreads of simulated R17 and RMW are slightly lower in the model. Additionally, the median simulated RMW is smaller than observed values. This suggest that the TC eyes are narrower and the vortex structures in the model tend to be slightly more uniform than those observed. Despite small discrepancies, there is overall good agreement between modeled and observed vortex structures and storm sizes, indicating that ICON realistically captures vortex structures.

This section evaluates the ability of SyNC to preserve mesoscale features in composites. Data fields are identified, which do or do not benefit from SyNC, thereby clarifying its relevance for different research applications. A comparison of the two composite methods of the intense group composed at their lifetime maximum intensity can be found in Figs.  and (and additional data fields in Fig.  in Appendix D). Overall, the SyNC composite fields often reveal more pronounced extreme values in the vertical cross sections (positive and negative) compared to the centered-only composites, as illustrated by the probability distribution functions (PDFs) of respective fields (Fig. c, f, i and l). The enhanced extremes are attributed to improved alignment of vortex structures and associated storm features, which helps preserve these characteristics more effectively in the group average. Most fields show substantial improvement due to the SyNC method's alignment of the eyewall: Vertical winds indicate stronger eyewall updrafts and stronger downdrafts within the eye (Fig. b). Temperature tendencies of the cloud microphysical scheme reveal approximately 10 Kh-1 higher latent heating within the eyewall (Fig. e). Additionally, stronger cooling (evaporative cooling of rain and ice melting), is more distinctly positioned on the inner and outer flanks of the eyewall updraft. Cloud water and precipitation (Fig. e and h) also show extended maxima within the eyewall. Surface precipitation rates (Fig. ) are also better preserved by SyNC indicating maximum rates 10 mmh-1 higher than in the centered-only approach. This highlights the improved representation of microphysical signals and precipitation achieved by vertically aligning the eyewalls throughout the depth of the TCs, with implications for physical understanding and TC risk assessments. The super-gradient outflow above the boundary layer (Fig. h) is sharpened in the SyNC composite. Tangential winds not only show a larger peak near the eyewall in the lower atmosphere (Fig. k), but also indicate stronger winds throughout the vortex due to a better alignment of the vortex borders. The border alignment avoids overlaying environmental and storm regions, which also benefits the equivalent potential temperature field (Fig. k). The SyNC composite maintains a higher θe especially in the storm's outer region. However, due to the relatively uniform radial nature of the θe field, it gains the least from the SyNC compositing. A similar behavior is found for water vapor and longwave radiative cooling, both of which are also radially uniform (Fig. n and q).

Similar results are found for the weak storms (Figs. , and ), which are structurally more variable than the intense one. It is worth mentioning that due to the large variability of eyewall radii in the weak group, secondary peaks in updraft (Fig. a) or latent heating (Fig. a) may be misinterpreted as features of outer rainbands. However, the SyNC composite clarifies that these are indeed eyewall features.

To statistically quantify the impact of the SyNC compositing method, the Kolmogorov-Smirnov (KS) test statistic is calculated for each variable, measuring the distance between the PDFs of the centered-only and SyNC composite fields. Overall, KS statistics of the weak group (Figs. c, f, i and l, and c) are comparable to or higher than those of the intense group (Figs. c, f, i and l, and c), suggesting that the weak group benefits slightly more from the SyNC approach. Accordingly, the benefit of preserving mesoscale features by SyNC depends on the degree of structural variability within the TC group, with the benefit likely emerging even for a relatively small TC group size. Nevertheless, with overall KS statistics of around 0.1 and larger extreme values, the SyNC method successfully sharpens the composite fields of both, weak (i.e., structurally varying) and intense (i.e., structurally more uniform) cyclone groups.

In addition to preserving mesoscale features, SyNC is found to enhance the sensitivity of statistical tests between cyclone groups as demonstated in this section. Figures  and display the radial wind and temperature tendencies due to saturation adjustment (parametrized cloud droplet growth) for both the weak and intense TC group, along with their differences. Statistically significant differences between the two groups are determined via a false-discovery rate corrected permutation test at a 0.05 significance level and are indicated by the hatched areas (Figs. i, j and i, j). Interestingly, the regions of significant change differ between the two compositing methods, although the underlying cyclone groups are identical. While the centered-only composite shows the most prominent differences in radial winds, it misses several mesoscale features that are detected by the SyNC composite (Fig. j): Significantly stronger super-gradient outflow above the boundary layer, significantly stronger inflow throughout the vortex and significantly stronger mid-level outflow, potentially induced by rainbands, for intense TCs. There are two main reasons for these differences in detected significance. First, the SyNC composite better aligns the vortex and their mesoscale features, which can amplify the observed differences between the two groups, as shown in Figs. j and j. Second, the eyewall alignment can reduce the data spread within a TC group, thereby improving the statistical power of the statistical test . The within-group spread of radial wind is illustrated by the IQR cross sections of each TC group per composite method in Fig. c, d, g, h and k. Radial wind IQRs of weak TCs are relatively similar between the composite methods. On the contrary, the intense TCs exhibit a large IQR in the centered-only composite around the eyewall, which is nearly twice that of the intense SyNC composite. To illustrate the impact of the large IQR on the power of the statistical test, box plots (Fig. k) show the radial wind distributions of all TCs at a selected grid cell (black star) for both composite methods. For the radial wind, the selected grid cell is located at low levels at the inner side of the eyewall, where super-gradient outflow is forming. First, the box plot medians of two cyclone groups are slightly more apart in the SyNC composite than in the centered-only composite. Second, the IQR of the centered-only intense TCs is larger than for the SyNC composite, spreading from negative (inward) to positive (outward) radial winds. This large IQR likely is a result of the their distinct though slightly displaced eyewalls: At the selected grid cell, inflow is observed for TCs with more narrow eyewalls, while for others already super gradient wind is formed at this distance. The resulting large within-group spread in the data causes the storm group distributions to overlap much more for the centered-only composite than for the SyNC composite, which increases the p-value of statistical testing for the centered-only composite. The eyewall alignment of the SyNC composite results in only outward radial winds at selected grid cells narrowing the within-group spread and reducing the p-value allowing for the detection of a significant difference between the TC groups with the SyNC approach. In the temperature tendency due to saturation adjustment (Fig. ), the centered-only composite method even fails to detect any significant changes (Fig. i), whereas the SyNC method reveals significantly enhanced latent heating in the intense storms (Fig. j), as expected. Controversy, the median differences between the weak and intense TCs is slightly larger for the centered-only approach (Fig. i, k) than for SyNC. In the SyNC approach, especially the weak group benefits from the eyewall alignment resulting in the amplification of the heating signal (Fig. b) there producing smaller median differences between the weak and intense TC groups (Fig. k). However, the within-group variance reduction of the intense TCs by the SyNC composite (Fig. h, k) increases the sensitivity of the statistical testing, outweighing the smaller median differences, and hence detecting a significant difference between the two groups (Fig. j). Thus, by mitigating small eyewall displacements and reducing within-group variance, the SyNC composite proves valuable even for relatively well-organized, more homogeneously structured TC groups, increasing the accuracy of statistical analyses.