## 2 Data and Methodology
### Methodology  
The Weather Research and Forecasting Model (WRF-ARW version 4.1.2 [43]) was used to perform the simulations. The domain had horizontal dimensions of 530 \(\times\) 530 grid points (Figure 1) and 60 hybrid sigma-pressure vertical levels, with a model top of 40 hPa. The time step was 15 s, and the horizontal resolution was 3 km. All simulations were initialized at 12:00 p.m. UTC 17 September 2020 and ended 12 h later at 12:00 a.m. UTC 18 September 2020, while the first 6 h were considered as spin-up and only the last 6 h were used as forecast. The boundary conditions were updated every 3 h.  
Four microphysics parameterizations of varying degrees of complexity were chosen to carry out the sensitivity study: the single-moment WSM6 [44], the double-moment  
Figure 1: WRF model domain employed in this study, consisting of 530 by 530 grid points with horizontal spacing of 3 km, along with the Medicare Ianos track calculated every 6 h from the ERA-5 reanalysis.  
warm rain only WDM6 [45], the double-moment rain and ice new Thompson [46], and the double-moment rain and ice/snow/graupel Morrison [47] schemes.  
The other physical parameterizations used were the Yonsei University scheme for the boundary layer [48], the revised MM5 Monin-Obukhov scheme for surface layer physics [49], the Noah land surface model [50] for surface processes, and the Dudhia [51] and RRTM [52] for short- and longwave radiation schemes, respectively. No cumulus parameterization was activated, and we assumed that convection was explicitly represented at 3 km horizontal resolution.  
With the aim of objectively measuring the tropical-like characteristics of the simulated cyclone, the Hart three-dimensional cyclone phase space [53] was calculated for each simulation. The phase space was represented by two diagrams: the first featured the lower level (900-600 hPa) thermal wind (\(-\mathrm{V_{T}}^{\mathrm{L}}\)) against the upper level (600-300 hPa) thermal wind (\(-\mathrm{V_{T}}^{\mathrm{U}}\)), highlighting the depth (shallow/deep) and the thermal anomaly (cold/warm) of the low pressure system's core; the second informed us about its thermal symmetry by showing the 900-600 hPa storm-relative thickness symmetry (B) against the lower level thermal wind, evidencing its symmetric/non-frontal or asymmetric/frontal structure. The thermal wind was calculated as the vertical derivative of the geopotential height perturbation (the difference between the maximum and minimum values) every 50 hPa within a radius of 200 km from the minimum mean sea-level pressure (MSLP) center. While [PERSON] [53] employed a radius of 500 km adequate for tropical cyclone dimensions, a radius of 200 km, in line with other authors [19; 26; 54], was used to account for the smaller TLC spatial scales (ranging from 50 to 200 km [55]). The symmetry parameter B was calculated as the difference between the mean 900-600 hPa layer thickness of the right and left semicircles with respect to the trajectory of the system. We performed the calculation every 10 degrees and picked the highest value of B to remove any chance of inaccuracy due to trajectory noise, similarly to [PERSON] et al. [28]. Hurricanes and medicanes are generally considered to have undergone tropical transition when they become thermally axisymmetric and have a deep warm core, which is objectively determined by simultaneously satisfying that the parameter B falls below 10 m and that both the lower- and the upper-level thermal winds are positive.