A Characterisation of Alpine Mesocyclone Occurrence

This work presents a characterization of mesocyclone occurrence and frequency in the Alpine region, as observed from the Swiss operational radar network. Five years of radar data are processed with a thunderstorm detection and tracking algorithm and subsequently with a new mesocyclone detection algorithm. A quality assessment of the radar domain provides additional information on the reliability of the tracking algorithms throughout the domain. The resulting data set provides the first insight into the spatio-temporal distribution of mesocyclones in the Swiss domain, with a more detailed focus on the 5 influence of synoptic weather, diurnal cycle and terrain. Both on the northern and southern side of the Alps mesocyclonic signatures in thunderstorms occur regularly. The regions with highest occurrence are predominantly the Southern Prealps and to a lesser degree the Northern Prealps. The parallels to hail research over the same region are discussed.

eastern Germany in June 2018, highlighting the importance of the large-scale flow on widespread severe weather outbreaks including supercells. With the potential of severe convection rising not only globally (Diffenbaugh et al., 2013), but also in central Europe Mohr and Kunz, 2013;Púcik et al., 2017), we have a large incentive to better understand and characterize mesocyclones in the Swiss domain.
provide topographical context for our analyses and investigate the first-order influences of terrain. To characterize the meteorological and topographical environment of convection, we use a synoptic type weather classification and a digital elevation model. The so-called Gross Wetter Types (GWT) weather classification provides 8 different weather types over Switzerland that are based on the synoptic flow at 500 hPa geopotential height (Weusthoff, 2011). The classes directly correspond to the eight cardinal flow directions.

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The operational radar network of Switzerland, Rad4Alp, consists in 5 polarimetric C-band radars (see Fig. 1), as described in Germann et al. (2016) and MeteoSwiss (2018a). They are situated throughout the country at altitudes from 900 m ASL to 3000 m ASL and provide a good coverage of both the plains, as well as the Alpine region. The data is processed at a resolution of 500 m x 1°. With the observation range extending up to 246 km, the coverage extends far beyond the country boundaries and allows the observation of convective evolution that is approaching Switzerland. Each radar performs 20 elevation scans 105 between -0.5°and 40°every 5 minutes. The high temporal resolution facilitates observing convective life cycles, particularly in complex environments such as the Alpine terrain. The large range of elevation scans provides a dense vertical layering of observations, allowing an as close to the surface as possible measurement of precipitation over complex terrain and extending up to high altitudes to cover the vertical extent of convection.
We use the 2-D Cartesian maximum reflectivity product, as well as the 3-D dealiased Doppler velocity in polar coordinates. 110 Due to relatively low Nyquist velocities in the raw Doppler velocity and complex airflow situations in thunderstorms, the aliased Doppler velocity poses a challenging de-aliasing problem. Therefore, we initialize the Region-based Recursive Doppler Dealiasing (R2D2) algorithm (Feldmann et al., 2020) with a radial wind estimate from COSMO-1 analysis data (Consortium for Small Scale Modelling, 2018) to remove all velocity aliases. During this 5-year period, all 5 radars provide homogeneous data coverage with the same, synchronised scan strategy and COSMO-1 data is available. Prior to 2016 the two high altitude 115 radars were not yet installed and COSMO was operated at a 2 km spatial resolution.

Methods
To reliably detect mesocyclones in an Alpine context, we combine a 2-D thunderstorm detection and tracking algorithm with a 3-D mesocyclone detection algorithm. The mesocyclone detection activates within the identified thunderstorms.

Thunderstorm Detection And Tracking (T-DaTing) 120
The thunderstorm detection is based on a dynamic threshold algorithm, which works very similarly to MeteoSwiss's operational Thunderstorm Radar Tracking (TRT) algorithm (Hering et al., 2004). Cells are identified based on thresholds in the Cartesian maximum reflectivity field. Adjoining cells' boundaries are identified by using a watershed algorithm. From one timestep to the next, the motion of the cells is estimated by the pySTEPS optical flow (Pulkkinen et al., 2019) approach. Newly identified cells in the next time step with a large spatial overlap to previously advected cells are then matched. A more detailed description 125 of the T-DaTing algorithm can be found in Appendix A. Key differences between TRT and T-DaTing are a fixed minimal detection threshold in T-DaTing, as opposed to the dynamic minimum threshold in TRT and the cell advection with optical flow in T-DaTing versus extrapolating previous motion in TRT.

Mesocyclone Detection
Within the contours of the identified thunderstorms cells, the mesocyclone detection algorithm becomes active. This algorithm 130 is modelled after the existing approaches of Stumpf et al. (1998) and Hengstebeck et al. (2018), but tailored to the specific requirements of the Swiss radar network. Identifying mesocyclonic rotation in radar data relies on estimating vertical rotation (around a vertical axis) from Doppler velocity data (Stumpf et al., 1998). As Doppler velocity only measures the radial component of the full velocity vector, it denotes the incoming or outgoing velocity of particles with respect to the radar. The azimuthal derivative is an approximation of vertical rotation (Miller et al., 2013) and corresponds to roughly half of the vertical 135 vorticity component (see Sect. B, Eq. B2). Areas of consistently high positive or negative azimuthal derivative indicate rotation phenomena. As there is no clear preference in rotation direction in Switzerland (Houze et al., 1993), we retain detections for both directions. At each radar elevation we employ object detection techniques to identify these areas and compute additional rotational metrics such as rotational velocity and vorticity per object (see Sect. B, Eqs. B2 and B1). All identified objects that meet the detection criteria are grouped within each cell and evaluated for vertical and temporal continuity (Hengstebeck et al.,140 2018). The definition of a mesocyclone applied here requires a minimum vorticity of 10 −2 s −1 (Hengstebeck et al., 2018), a minimum rotational velocity of 10 m s −1 (Stumpf et al., 1998) and a signature depth of 3000 m (Stumpf et al., 1998). All of these criteria linearly decrease towards far ranges to compensate for decreasing spatial resolution (Stumpf et al., 1998), allowing for detections at more than 100 km distance from the radar and compensating for the decreasing spatial resolution.
Signatures must persist over at least three detections, each at maximum two time steps apart. A detailed description of the 145 algorithm is provided in Appendix B.

Data Quality Assessment
Considering the complexity of radar observations in mountainous terrain, this section introduces a method of estimating observational uncertainties within a radar network. We combine different aspects of the radar network to obtain a qualitative index 150 that represents the relative quality of observations at a given location.
The considered properties are theoretical visibility, minimum and maximum altitude of measurements, spatial resolution and numerical noise stemming from data quantization. These metrics are assessed for each radar and merged onto a Cartesian grid, where the highest quality metric is retained. The metrics are then rescaled between 0 (lowest quality) and 1 (highest quality) and combined into a general quality index. A detailed description of the computation of the quality index is in Appendix C.

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This results in a spatial map of the quality index of the radar network. It is a qualitative index and only represents a relative comparison of detection probability, not a quantitative measure of correcting for detection gaps.
While the components contributing to the quality index are based on the full radar network and represent impacts to all radar products, no all observed meteorological phenomena are impacted equally by the limitations. The selection here is tailored to convective phenomena that can reach very high altitudes and require a high spatial resolution. Other combinations of these 160 components lead to differing results, however the overall spatial pattern of the quality index is robust and representative of radar product quality in general.  in the background, we can see the clear influence orography has on the quality index. This is primarily a consequence of radar beam blockage, which decreases visibility, particularly at low levels. Two noticeable artefacts are a dip in quality to the Northeast of La Dôle and a similar gap in observations to the West of Lema radar. These artifacts stem from constructions in the vicinity of the radars blocking the visibility. The obstruction of Lema is more recent and does not affect the entire analysis period. The decrease in quality in the main Alpine ridge is caused by beam blockage of terrain.

Mesocyclone Characterization
As an introduction to mesocyclonic rotation in an Alpine context, we first show an example case from the Southern Prealps that are very prone to thunder-and hailstorms (Nisi et al., 2018;Schemm et al., 2016). Figure 2 shows the radar reflectivity, Doppler velocity and vertically integrated liquid (VIL) measured from Monte Lema radar (marked with A in Fig. 1) at 17:30 UTC on August 20th, 2019. In the reflectivity data we can clearly see the location of the convective cell at 10-15 km range 175 and 90-150°azimuth with values exceeding 45 dBZ, indicating strong convection. The shape of the area of high reflectivity shows the typical hook-echo, which suggests the presence of prominent rotation (Markowski, 2002;Kumjian and Ryzhkov, 2008). The storm here is observed at an altitude of approximately 2500 m ASL. In the Doppler velocity data, we can see the opposition of inbound (red, following the Swiss convention of depicting Doppler velocity) and outbound (blue) velocities close to the hook, here presenting anticyclonic rotation (indicated with arrows), confirming the presence of a mesocyclone. While 180 these signatures are quite clear, the rotational velocity is not particularly high in comparison to supercells in other regions (e.g. in the Great Plains, USA), here averaging around 12 m s −1 . We can also see that VIL is elevated in the area of highest reflectivity, but not extremely high. This indicates significant precipitation, but not necessarily hail. The proximity to the radar may lead to an underestimation of VIL, as the upper part of the storm is above the highest radar beam. To represent the spatial heterogeneity in Switzerland, two additional case studies from the high Alpine region (marked B in Fig. 1) and the Rhine  From here we will inspect the overall distribution and occurrence of mesocyclonic rotation over the Swiss domain during the 5 analyzed years and compare this to the general occurrence of thunderstorms and the quality of the radar network. Table   1 gives an overview of the annual average convective activity. Switzerland, with generally higher temperatures and frequently high relative humidity MeteoSwiss, 2018b).
These conditions are more conducive to convective initiation and development. Topography can induce convection through valley wind systems (Linder et al., 1999;Rampanelli et al., 2004;Nisi et al., 2016). Particularly in the afternoon hours, upslope winds cause convergence over ridges and can provide the initial lift needed to overcome convective inhibition. We can also see that the frequency of thunderstorm detections is higher in the vicinity of the radars. If we compare the spatial distribution 205 of thunderstorms to the relative quality map of the Swiss domain, we can clearly see that more thunderstorms are detected in locations where the quality index is high. While we do not establish a quantitative relationship, a lower quality index increases the probability of underestimating thunderstorm occurrence. Nonetheless, the dominant spatial trends of convective preference in the Prealps are meteorologically consistent with orographic convection and can be confirmed with lightning climatologies (Enno et al., 2020;MeteoSwiss, 2016). The clearest deviation from meteorological expectations can be seen to the Northeast 210 and Southwest of the Jura. Beam blockage significantly lowers the capability of La Dôle radar to accurately observe convective events in these areas. While we may underestimate thunderstorm occurence in the inner Alpine regions, where the quality index is lower, the reduced convective activity here is confirmed by independent lightning climatologies (Enno et al., 2020;MeteoSwiss, 2016). Moreover, the spatial patterns do not significantly change in the vicinity of the Alpine radars Plaine Morte and Weissfluh, where the quality index is higher.

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Shifting our focus to the annual average spatial distribution of thunderstorm tracks that contain a mesocyclone in Fig. 3  that hail is a known severe weather consequence of mesocyclones, this overlap reinforces the robustness of the obtained spatial distribution. We can see a lesser dependence of detections on the quality index. This may be due to the fact, that mesocyclones generally have a large vertical extent and can be detected in multiple consecutive elevation scans, thus being less dependent on accurate measurements in single elevation scans. Range-dependent rotation thresholds compensate for decreasing measurement resolution with range and allow mesocyclones to be detected even beyond a range of 100 km per radar. The most issues 225 can still be noted over the Jura, where the beam blockage of La Dôle radar impacts the first 10 elevation scans. The beam blockage in this area is severe enough, that confirmed cases of mesocyclones are missed in this region. This is illustrated by the case study of a tornado near Neuchatel in Grazioli et al. (2019), in which the data from both a mobile, X-band radar that was tracking this storm cell, and the operational C-band data, are analyzed. The rotation is clearly visible in the X-band data, however from La Dôle radar the rotation is undetectable and the location is at a far range from Albis radar.  to 12 · 10 −2 s −1 , with a mean of 2 · 10 −2 s −1 . The typical mesocyclone definition (Stumpf et al., 1998) requires a vorticity of 10 −2 s −1 , showing that the average event is twice as strong and the extremes exceed this value by an order of magnitude.
The lower minimum value stems from the use of range-dependent thresholds, where we lower the vorticity requirement with 235 increasing distance to the radars to compensate for decreasing spatial resolution (see Appendix B).
The largest cluster of high vorticity values is located around the Ticino hot spot. But also the Napf area and Zurich Oberland show consistently elevated values of vorticity. This is not the case for the Bernese Alps, where the vorticity values are on the low end of the spectrum and close to the detection threshold. The topography is significantly more complex here, which may impact a storms capability to maintain strong rotation.

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The spatial overlap of the strongest rotation concurring with the largest size hail in the Napf region and Southern Ticino established in longer-term hail climatologies (NCCS, 2021) indicates that stronger rotation usually favours larger hail (Allen, 2018;Blair et al., 2017;Witt et al., 2018). However the differences in the Bernese Alps, where we have large hail, but low rotation velocities and Zurich Oberland, where we have high rotation velocities, but smaller hail show that there may also be other factors at play and warrants further investigation. The Bernese Alps have a reduced quality index, due to beam blockage to 245 the Northeast of Plaine Morte radar. This may interfere with the ability to reliably detect and estimate the intensity of vortices.
Discrepancies may also be owed to the relatively short duration of the 5 year analysis.

Dependency on Synoptic Weather Situation
The synoptic weather classification Gross Wetter Types (GWT) provides insight in which synoptical flow situations mesocyclones are likely to occur. Roughly 10 % of days with Westerly flow produce at least one mesocyclone. Southerly flow is more prevalent to the South of the Alps, but already leads to much less mesocyclone cases. To the North, there are only few cases that are displaced further North, as descending air crossing the Alps does not provide favorable conditions. Other flow directions play a very small role and are only responsible for very few cases (<5 %).

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As the track lines in Fig. 5 a)  While Southwesterly flow also plays an important role in hailstorms, it is not the dominant weather class (Nisi et al., 2018).

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Hailstorms predominantly form in Westerly flow, which is also the most frequent weather class. With hail also occurring much more frequently Nisi et al., 2018), it appears that Westerly flow yields conditions that are sufficient for hail production, but not as frequently for mesocyclone formation. Westerly flow also leads to a hail hotspot in the Northern Jura, where the quality of Doppler velocity data is limited and we potentially miss mesocyclones.

Diurnal Cycle
The occurrence of mesocyclones shows a pronounced diurnal cycle that mirrors the cycle of convection in general (see Fig. 6 a)). The majority of storms occur in the afternoon and first half of the night, with the peak of formation at 15 UTC. Mesocyclones, however, show a local, smaller peak, during the second half of the night as well (0-4 UTC) and then a minimum in the early morning at 4 UTC. Thunderstorms in general drop to a lower occurrence from 0-10 UTC, but can initiate at all hours of 290 the day. The base frequency at unfavourable hours in the late night and early morning is almost constant. In comparison to this frequency distribution, there is also a diurnal cycle reflected in cumulated storm area and track length, as shown in Fig. 6 b). The storm area refers to the cumulative area over the entire storm track, whereas the track length refers to the overall distance along the path of the storm track. The behaviour of the track duration mirrors the track length (not shown 295 here). In contrast to the occurrence histogram, the global peak of both variables is at 12 UTC, before the peak mesocyclone occurrence time in the day. A local peak is additionally found at 4 UTC during the minimum of mesocyclone occurrence. Even though the sample size is very small (<10), this shows parallels to research conducted on hailstorms, where the longest and largest storms also occur outside hours of the convective peak (Nisi et al., 2018). Due to the significant drop in convective activity at this time of day, this indicates a significant overlap between mesocyclones identified here and hailstorms analyzed 300 in Nisi et al. (2018). In spite of the small sample present, this agreement with severe hailstorm behaviour also reinforces the notion found in Nisi et al. (2018) that convective storms that initiate during unfavourable hours of the day are more likely to be severe, whereas the most active hours of the day contain a larger fraction of less intense storms. As this hypothesis based on the small sample in the mesocyclone data set is rather speculative, it should be revisited, once longer homogeneous data series are available.

Terrain
Utilizing the data from the digital elevation model, we can see that the majority of rotating storms move uphill during their lifetime. With the majority of storms occurring in Ticino (∼ 60 % of mesocyclones are detected from Lema radar) and a Southwesterly flow direction dominating here, many storms follow a Northeasterly path towards the main Alpine ridge (see Fig. 5), 310 thus moving uphill. As Fig. 7 a) shows, in the South of the Alps, up to an altitude of approximately 1500 m, the storms do not show intensity correlation to the altitude. Beyond that, higher altitude negatively impacts the upper potential of intensity metrics such as rotational velocity and vorticity, here shown by the decreasing trend in the 95th percentile. The same effect can be seen to the North of the Alps, however at a lower altitude. With the storm tracks being more parallel to the Alps (see Fig. 5), less storms move uphill and encounter higher altitudes. In both cases the lowering in intensity is mirrored by a lowering in case 315 numbers with altitude. Similar trends can be observed for vertical extent and maximum reflectivity (not shown). Storms with weak rotation occur throughout the entire domain and dominate the intensity distribution, however with increasing altitude the upper percentiles decrease, indicating a limit to the potential rotational intensity a storm can achieve in this environment. As the number distribution with altitude shows, the majority of storms are detected in lower altitude regions. This concentration in relatively flat areas within the Prealpine region, such as the larger valleys and lakes, is also shown in Fig. 3. At high altitudes 320 beyond 1500 m ASL the terrain becomes increasingly complex with steep slopes and rapid altitude changes. We hypothesize that this could impact the low-level dynamics of a supercell, disturbing the generation of vorticity at the outflow boundary and its advection back into the storm in the inflow. As the quality index also decreases over the main Alpine ridge, the probability of underestimating mesocyclone occurrence 325 here also rises. However, as shown in Enno et al. (2020) and MeteoSwiss (2016), the overall thunderstorm frequency, derived from radar-independent lightning data, also decreases significantly here, indicating that we are observing a true trend and not a limitation of the radar network.
With the majority of storms located in the Prealpine regions, orographic triggers for convective initiation play an important role in Switzerland Linder et al., 1999). The main Alpine ridge poses a strong separation for thunderstorms. With 330 the thunderstorm frequency dropping substantially over the inner Alpine regions in Fig. 3 a), we can see that thunderstorm tracks generally do not persist crossing the Alpine ridge. In Fig. 3 b) we can see the inner Alpine regions devoid of rotation detections. Additionally, Fig. 5 a) shows only one mesocyclone track crossing the Alps, while all other tracks heading towards the main Alpine ridge decay prior. This supports the hypothesis that high altitude mountainous terrain has an inhibiting impact on the rotation dynamics of a thunderstorm. This tendency can also be observed in hailstorms (Nisi et al., 2018), indicating a probable overlap between the two storm 355 populations. The importance of Southwesterly flow to convection in central and Western Europe is also shown in (Wapler and James, 2014) and (Mohr et al., 2020), which highlights the significance of synoptic flow for large regions.
With mesocyclones being rather rare events, longer timelines are necessary to establish robust assessments of interannual variability and seasonal trends. The spatial distribution can also be evaluated more robustly with a longer analysis period, as low-activity regions are currently dominated by the characteristics of single events. Data prior to 2016 was not used in this 360 study, as major changes in the radar network took place at that time.
The spatial distribution of both thunderstorms and mesocyclones shows that terrain has a clear influence on the initiation of convection. Similarly, the inner Alpine regions are devoid of mesocyclones, indicating that steep, high altitude environments have a negative influence on rotational dynamics. Rotational metrics show a negative correlation with increasingly high altitudes as well.

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After establishing this first time assessment of mesocyclones in Switzerland, future work is required to clarify the severe weather consequences of mesocyclones in Switzerland and further investigate the interactions with the complex terrain.
Code and data availability. The T-DaTing algorithm is available in the pySTEPS package (PySteps developers, 2021). The data set of mesocyclones has been published in Feldmann et al. (2021). The Thunderstorm Detection and Tracking (T-DaTing) algorithm utilizes image processing, computer vision and optical flow techniques to identify thunderstorms and track them in time. The 2-D Cartesian maximum reflectivity field of the Swiss operational radar network is used as input. Its spatial resolution is 1 x 1 km 2 and it is generated every 5 minutes. All thresholds are tuned to this input data (Hering et al., 2004), but are adaptable to other data sets. This algorithm has been published as a part of the pySTEPS package (PySteps developers, 2021).

A1 Thunderstorm Detection
The detection of thunderstorms follows a dynamic, multi-threshold approach. The procedure is modelled after MeteoSwiss's operationally running TRT algorithm (Hering et al., 2004). All thresholds are listed in Table A1 and stem from Hering et al. (2004).
Utilizing the 2-D maximum reflectivity composite from all five radars, in a first step, all areas below the minimum reflectivity 380 Z min are discarded. All remaining areas need to have a peak reflectivity value exceeding Z p and be larger than the area A min .
We chose a relatively large size limit here, as we are interested in supercellular convection, which generally takes place on larger spatial scales. The next step uses local maxima within the area boundaries to determine whether these should be further split into separate convective cells. To excessive splitting in areas of very high reflectivity values, where there are many extreme local maxima, the data is saturated at the maximum reflectivity Z max . Within these areas exceeding Z min , a local maximum This produces the labelled areas for the identified thunderstorm cells. The detection part of the algorithm can be performed on any length of data and does not require temporal continuity. It yields results very similar to Hering et al. (2004), the main deviations are a larger minimum size and the introduction of the minimum distance between maxima. Additionally contours are slightly larger, as they always extent to the boundary of Z min .

A2 Thunderstorm Tracking
After detecting the thunderstorm cells, the tracking part of the algorithm estimates the future path of each cell, propagates it and matches it to the detected cells in the next time step.
The movement of the cells is estimated from three consecutive frames of the 2-D input data. The Lucas Kanade optical flow algorithm (Lucas and Takeo, 1981) applied to the current and previous two time steps of the maximum reflectivity field yields 400 the projected movement for the next time step (Pulkkinen et al., 2019). Each cell of the previous time step is propagated according to the results from the optical flow. This is then compared to the identified cells of the current time step. If the overlap between two cells is more than 50 %, they are considered as the same cell and assigned the same ID as before. If there is no overlap to a new cell, the cell track ends and this ID is no longer used. If there is no previous cell matching a new cell, a new ID is generated and thus a new track initiated. If a cell splits, the smaller fraction is considered a new cell and obtains 405 a new ID. In case of merging, the smaller (area) cell is considered decayed, where the track of the larger one continues in the merged cell.
For each step, the x and y coordinates, maximum reflectivity, centroids, area and distance from last detection are recorded.
In a final step the detections from each time step are resorted into the tracks assigned to their IDs. Tracks shorter than three detections are rejected.

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The tracking procedure follows the same steps as Hering et al. (2004). However where previously the cell motion from one detection to the next was estimated by the past track of the cell, we extrapolate the motion from one detection to the next T-DaTing provides the constraints for the mesocyclone detection algorithm. The detected thunderstorm areas are used as a mask to filter out data unrelated to convection. Additionally, all rotation detected within a cell is assigned to this cell.

B1 Data Preparation
To filter the relevant data, the detected thunderstorm areas are dilated with a 5 x 5 km 2 kernel. Since mesocyclones can be located outside of the area of largest reflectivity (Kumjian and Ryzhkov, 2008), we consider areas slightly larger than each 420 detected cell. One by one, the algorithm then iterates through the detected cells.
To compute rotation, the dealiased velocity data from all 5 radars and 20 elevations is used. The dealiasing procedure is performed with the novel algorithm R2D2 and COSMO-1 analysis data is used as a first guess. As the velocity data is in polar coordinates, the filter obtained from the Cartesian reflectivity filter is regridded to the polar grid of each radar. Additionally the first 5 km in range from each radar are excluded from processing, due to excessive noise in the data.

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For each elevation the azimuthal velocity shear is computed using a centered-difference method. In case of residual velocity folds or dealiasing errors, a quality check is in place. If an area of more than three adjacent pixels exceeds the Nyquist velocity (Fabry, 2015) of the corresponding elevation, the Nyquist interval is added or subtracted to reduce the absolute value of the shear in this area. With Nyquist velocities being quite low (Feldmann et al., 2020), particularly in the lower elevations, the azimuthal shear can physically exceed the Nyquist interval. However, usually this will occur in isolated high-shear gates and 430 not in larger areas. Velocity folds and dealiasing errors however produce contiguous lines of erroneous azimuthal shear and can thus be corrected for in this method. The mesocyclone detection presented here is thus less sensitive to dealiasing errors, as long as the edges of folds can be distinguished from physical shear and the estimation of rotational velocity does not cross a velocity alias.

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Within each elevation, the convective cells are evaluated iteratively. From the azimuthal shear dv dΘ , first pattern vectors are constructed. Consecutive areas of shear exceeding a threshold dv dΘ are conserved, if they exceed 1 km in length and contain at least three gates. All other data is discarded. These pattern vectors are merged over the ranges using 8-bit connectivity. If pattern vectors neighbor each other over a corner, or directly, they are considered one area. These resulting areas are then further evaluated. They each need to exceed a minimum rotational velocity and vorticity threshold ∆v (Eq. B1) and ζ (Eq. B2, 440 see Table B1). Additionally, their aspect ratio needs to be less than 1:3, approximating circular objects: where ∆x is the Cartesian distance between the velocity maxima.
All rotation areas identified in this way are collected. For each area the location of the centroids, size, rotational metrics, elevation and thunderstorm ID are recorded. Within one cell, more than one detection is possible per elevation, as rotational signatures can be fragmented. Positive and negative azimuthal shear are evaluated separately, to differentiate cyclonic and anticyclonic rotation signatures.

B3 Vertical Continuity
After processing all elevations of one radar, the detected rotation objects are merged. All objects of one thunderstorm ID are considered to belong together and are stacked vertically, as the storm structure can be slanted and detections can be discontinuous due to residual aliasing in the velocity data. Additionally, the vertical depth of the lowest and highest detection must exceed a certain depth h.
455 Figure B1 shows a schematic overview of the detection process until this point. Figure B1 a) shows the process within a radar elevation. First the data is filtered with the contours identified in T-DaTing, here approximated with the dark grey cloud (1.).
Then the velocity data (2.) is evaluated. Here green denotes outbound velocity from the radar and red inbound. From the velocity, the azimuthal derivative is derived (3.), which results in anomalies in the derivative around the velocity couplet. Cyclonic anomalies are shown in light red here and anticyclonic anomalies in light green. Within these anomalies the rotational velocity 460 and vorticity are computed and measured against thresholds, here resulting in one final rotation object shown in blue (4.).
In Fig. B1 b) the aggregation of rotation objects within a thunderstorm contour is shown. Detections (blue ovals) from each elevation (dashed slices) within the contour contribute to the overall vertical structure. To these identified objects the vertical continuity constraints on h are applied. After exceeding all criteria, the objects are summarized as one rotation column (light blue column) for the corresponding convective cell. Also here, anticyclonic and cyclonic signatures are considered separately 465 and must each fulfill all criteria to be recorded and are stored as separate columns.

B4 Range Dependent Thresholds
All detection criteria are range dependent thresholds T (Stumpf et al., 1998). The thresholds are most strict at a range of 20 km at T m and decrease outwards until 100 km to T o , from where they remain stationary. Within 20 km they decrease towards the 470 radar to T i . The decrease of the thresholds with range compensates for the reduction in resolution in the data. Within 20 km, the decreased thresholds aim to allow for detections in the noisy shear data at small azimuthal distances. The following table depicts the values chosen in the algorithm here. Table B1. Mesocyclone detection thresholds following Stumpf et al. (1998) and Hengstebeck et al. (2018).
variable unit inner threshold ( Ti) maximum threshold ( Tm) outer threshold ( To) azimuthal shear ( dv dΘ ) s −1 1 · 10 −3 3 · 10 −3 1 · 10 −3 rotational velocity (∆v) m s −1 6 10 6 vorticity (ζ) s −1 6 · 10 −3 10 −2 6 · 10 −3 vertical depth (h) m 0 3000 1000 The range dependent thresholds help detecting significant rotation in complex observation situations. Due to the complex 475 nature of the Swiss terrain, there is often no visibility of the lower portion of a storm. Additionally, the environmental conditions allowing for supercellular convection in Switzerland generally show a lower vertical shear than e.g. in the US plains. We tuned the thresholds by investigating visually confirmed cases of supercellular convection and range dependent thresholds that relax at very close and far ranges. While this may detect more storms as supercells, that were merely exhibiting significant rotation but otherwise lack the typical storm structure, we avoid missing detections due to observational issues.

B5 Temporal Continuity
Within a valid thunderstorm track, rotation of the same sign must have been detected at least 3 times within 10 minutes of each other. Additionally the rotation track must leave the range of 20 km around a radar. In strong linear wind situations, the geometric nature of the radial velocity produces artificial rotation signatures at opposing sides of the radar that remain stationary. These can produce false detections, but are easily removable considering that thunderstorms generally propagate. The theoretical visibility corresponds to the unblocked fraction of a radar beam at each location. It is derived combining the effective earth radius model (AMS Glossary of Meteorology, 2012) with a refractive index of 5/4 and a digital elevation model to estimate beam blockage. The vertical sum over all 20 elevations is computed on a 2-D polar grid for each radar. In a similar fashion, the minimum and maximum altitudes of measurements are obtained from the altitude of the lowest and highest radar beam with 100 % visibility, yielding each a 2-D polar grid per radar. The resolution corresponds to the distance of each radar 495 bin to its azimuthal neighbours. As we here work with the azimuthal derivative of Doppler velocity, we additionally introduce the quantization noise. The numeric resolution at which the Doppler velocity is stored introduces a small level of noise. The azimuthal derivative is strongly range-dependent, as it utilizes the azimuthal resolution. In the vicinity of the radars this noise reaches high levels and thus impacts the data quality. We here compute the noise level by dividing the numerical resolution by the azimuthal resolution.

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After obtaining the radar-based grids for each variable, these are regridded to a 1 km resolution Cartesian grid, where the highest-quality index at each location of overlap is retained. The contribution of each variable is shown in Fig. C1.
To constrain the fields to values that correspond to strong quality degradations, some fields are saturated at threshold values.
The minimum altitude field's upper bound is is saturated at 5 km ASL, corresponding to an inability to observe the lower 505 atmosphere. The maximum altitude field's lower bound is saturated at 11 km, indicating a lack of convective top observations.
The noise field's upper bound is saturated at 3 · 10 −3 s −1 , which is a critical threshold for rotation detection.
Each Cartesian field of a characteristic is then rescaled between 0 and 1, utilizing the highest and lowest values present in the domain, so that 0 represents the lowest quality value and 1 the highest quality value. The normalization for the positively (Eq. C1), as well as negatively (Eq. C2) correlating variables is given in the following: index = V p_norm · (h min,p_norm + h max,n_norm + ϵ n_norm + ∆Θ 2 n_norm ) 4 As visibility can degrade the quality to zero in absolute terms, it is used as a multiplicative factor. The other variables do not 520 directly influence each other and are thus averaged at equal weights. To account for both horizontal and vertical azimuthal resolution, it is squared.

Appendix D: Case studies
Case B, as indicated in the map of Fig. 2, is located in the Valais Alps and was observed from Plaine Morte radar. It shows a case in complex, high-altitude terrain, observed at ∼ 4800 m ASL. Figure D1 shows the supercell at 10-30 km range and 525 200-240°azimuth, in the Doppler velocity panel the location and direction of rotation is indicated with arrows. The hook shape in the reflectivity is less evident here compared to the event presented in Fig.2  During the evolution of the storm, the reflectivity data also shows significant attenuation behind the storm core. Probability of hail is also estimated to be close to 100 % throughout large parts of the track, however no hail was reported on the ground, Foresti, L., Sideris, I. V., Panziera, L., Nerini, D., and Germann, U.: A 10-year radar-based analysis of orographic precipitation growth and decay patterns over the Swiss Alpine region, Quarterly Journal of the Royal Meteorological Society, 144, 2277-2301, https://doi.org/10.1002/qj.3364, 2018.