Radar Network–Based Detection of Mesocyclones at the German Weather Service

FEBRUARY 2018 H E N G S T EBECK ET AL. 299

THOMAS HENGSTEBECK,KATHRIN WAPLER, AND DIRK HEIZENREDER Deutscher Wetterdienst, Offenbach, Germany

PAUL JOE Environment and Climate Change Canada, Toronto, Ontario, Canada

(Manuscript received 29 November 2016, in ﬁnal form 23 October 2017)

ABSTRACT

The radar network of the German Weather Service [Deutscher Wetterdienst (DWD)] provides 3D Doppler data in high spatial and temporal resolution, supporting the identiﬁcation and tracking of dynamic small-scale weather phenomena. The software framework Polarimetric Radar Algorithms (POLARA) has been developed at DWD to better exploit the capabilities of the existing remote sensing data. The data processing and quality assurance implemented in POLARA include a dual-PRF dealiasing algorithm with error correction. Azimuthal shear information is derived and processed in the mesocyclone detection algorithm (MCD). Low- and midlevel azimuthal shear and track products are available as composite (multiradar) products. Azimuthal shear may be considered as a proxy for rotation. The MCD results and azimuthal shear products are part of the severe weather detection algorithms of DWD and are provided to the forecaster on the NinJo meteorological workstation system. The forecaster analyzes potentially severe cells by combining near-storm environment data with the MCD product as well as with the instantaneous azimuthal shear products (mid- and low level) and their tracks. These products and tracks are used to diagnose threat potential by means of azimuthal shear intensity and track longevity. Feedback from forecasters has shown the utility of the algorithms to analyze and diagnose severe convective cells in Germany and in adjacent Europe. In this paper, the abovementioned algorithms and products are presented in detail and case studies illustrating us- ability and performance are shown.

1. Introduction high spatial and temporal resolution so that small-scale dynamic severe weather phenomena, such as mesocy- Severe weather associated with convective storms clones, can be resolved. poses a serious threat to life and property. The presence In the context of radar meteorology, observations of of storm-scale rotation, or mesocyclones, increases the mesocyclonic signatures in the form of storm-scale Ran- risk of heavy rain, severe hail, strong wind gusts, and kine vortices have been analyzed (Donaldson 1970; tornadoes within these storms. Thus, the real-time de- Burgess 1976) and several mesocyclone detection algo- tection of mesocyclonic shear gives valuable additional rithms have been developed in recent decades (Zrnic´ information for the meteorological warning management et al. 1985; Stumpf et al. 1998; Joe et al. 2004). The op- of a national weather service. The radar network of the erational mesocyclone detection algorithm (MCD) at German Weather Service [Deutscher Wetterdienst DWD uses a pattern vector approach as described in (DWD)] offers scanning of the lower atmosphere with Zrnic´ et al. (1985) to identify the regions of high shear within the center of the mesocyclonic rotation. An important aspect of the DWD algorithm is the merging of Denotes content that is immediately available upon publica- 2D mesocyclone features from multiple network radars tion as open access. in overlapping regions to create a single 3D detection. A similar technique was demonstrated in the multiple-radar Corresponding author: Thomas Hengstebeck, thomas.hengstebeck@ severe storm analysis program for three neighboring dwd.de WSR-88D radar systems (Stumpf 2002).

DOI: 10.1175/JTECH-D-16-0230.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/06/21 01:06 PM UTC 300 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 35

The mesocyclone objects are ranked and assigned a severity index using mesocyclone object properties like shear and rotational velocity. This is provided to the forecaster, as guidance, through the NinJo meteorological workstation system (Koppert et al. 2004). Meteorol- ogists then judge the significance of the mesocyclone detections using this severity metric, applying persistency, consistency checks (track of mesocyclone detections), and forecaster judgment (additional occurrences of severe weather features like hook echoes, interpretation of near-storm environment data, and large-scale forcing analysis). Further guidance is given by the azimuthal shear and corresponding track products. In this paper the scan strategy and the data acquisition within DWD’s radar network are outlined in section 2. Doppler wind data quality assurance issues of great im- portance for downstream applications are discussed in section 3. The mesocyclone detection and the rotation compositing are introduced in sections 4 and 5,respectively, as network-based algorithms. The operational applicability of the MCD and the rotation products and the advantages of the network approach are demon- FIG. 1. Radar network of DWD. Seventeen C-band weather radar strated in section 6 using case studies. Comparative sta- systems cover Germany completely. There are 16 dual-polarimetric tistical analyses of the MCD (through comparison of the systems and one single-polarimetric radar in Emden (emd). Maxi- MCD with previous studies and through comparison of mum unambiguous range of the lowermost elevation in the volume scan, which corresponds to a range of 180 km (dashed lines). the MCD network and single-site modes) and studies showing correlations between the cell lifetime and the cell’s rotational characteristics are presented in section 7. demanding dual-PRF ratios or single PRFs are used, al- The main conclusions are summarized in section 8. ways keeping the maximum unambiguous velocity at 2 32 m s 1 (see Table 1). Strong quality control of the radial velocity data is 2. Data needed for the mesocyclone detection and azimuthal DWD operates a network of 17 weather radar systems shear algorithms. The first step in quality control is delivering 2D and 3D radar data in 5-min intervals achieved by means of a zero Doppler velocity filter to (Helmert et al. 2014;seeFig. 1). Sixteen radar sites are remove stationary clutter and a set of data quality equipped with dual-polarimetric systems. In Emden threshold filters, including clutter correction (CCOR) (northwestern Germany) a single-polarimetric radar sys- and signal quality index (SQI) (Seltmann 2000). It is tem is in operation. The volume scan is composed of 10 notable that each pulse volume is composed of uniform elevation scans with elevation angles ranging from 0.58 to PRF samples. The clutter filter process is not compli- 258. This scan is configured such that both an adequate cated by nonuniform samples, which is the case for the maximum unambiguous Doppler velocity interval and a staggered PRT technique (Torres et al. 2004). maximum unambiguous range are achieved (Seltmann The volume scan data from all DWD radar stations et al. 2013). To obtain sufficient overlap between the radar are gathered at the central office of DWD in real time sites located at a mean nearest-neighbor distance of ap- by means of an automated file distribution system (AFD; proximately 140 km, a maximum range of 180 km was Deutscher Wetterdienst 2016a) and are available for determined to be required for the six lowermost elevation downstream applications. To adequately exploit the possi- scans. This is realized by implementing a 4:3 dual-PRF bilities of the polarimetric data, a software framework dealiasing scheme (Dazhang et al. 1984)withaso-called called Polarimetric Radar Algorithms (POLARA) was extended maximum unambiguous velocity yNyq,e of developed (Rathmann and Mott 2012). POLARA contains 2 32 m s 1. Since true Doppler velocities do not typically various algorithms, such as quality control, hydrometeor 2 exceed 64 m s 1, extended aliasing effects will be at classification, and quantitative precipitation estimation. most a single fold. For the higher elevations, shorter As part of quality control, the correction of dual-PRF ranges are sufficient for scanning the troposphere and less dealiasing errors is performed to eliminate spurious

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TABLE 1. DWD volume scan.

Elevation(s) PRF(s) PRF ratio Max unambiguous range/velocity 2 0.58–5.58 in 18 steps 800 Hz: 600 Hz 4:3 180 km/32 m s 1 2 8.08 1200 Hz: 800 Hz 3:2 125 km/32 m s 1 2 12.08, 17.08,258 1200 Hz: 800 Hz 3:2 125 km/32 m s 1 (radar Emden) 2 2410 Hz — 60 km/32 m s 1 (other radars) velocity errors in high shear regions. This is an essential of a detection–correction filtering algorithm. Within the prerequisite for the mesocyclone detection and azimuthal POLARA quality assurance module (Werner 2014), a shear algorithms. The quality-controlled radar elevation scan Laplacian filter based on Joe and May (2003) is used. The data are henceforth called base data. These base data are Laplacian filter basically uses a k 3 k pixel window, with k stored at the central office of the DWD in a long-term archive being an odd integer, to detect and then to calculate a system (Deutscher Wetterdienst 2016b). The radar base data correction value ycorr for the window’s central pixel’s ra- and the derived products are visualized in the radar and dial velocity value yc. The correction uses the related Storm Cell Identification and Tracking (SCIT) layers (Joe maximum unambiguous velocity yNyq,c, which is either et al. 2005) of the NinJo workstation (Koppert et al. 2004). yNyq,1 or yNyq,2. It is performed by comparing a phase- averaged mean value ymean, calculated within the ex- 3. Quality assurance of Doppler wind data at DWD tended unambiguous velocity interval from the central y0 pixel’s neighbors, to all possible corrections corr(n)with In this section one of the most critical problems in the n being the integer fold number, quality assurance of Doppler wind data at DWD is y y0 (n) 5 y 6 2n y , n # Nyq,e. (2) addressed: the correction of dual-PRF dealiasing errors. corr c Nyq,c y The reader is referred to appendix A for details con- Nyq,c cerning the dual-PRF dealiasing technique, which is The value y0 (n), which differs least from y , is used assumed to be known. corr mean as the corrected value ycorr, which is therefore defined as The two velocities y1 and y2 of azimuthally adjacent range bins, which enter into the dual-PRF dealiasing, y 5 y0 5 y 6 y corr corr(nmin) c 2nmin Nyq,c, (3) should ideally be equal [see Eq. (A1)], that is, showing apart from possible aliasing no further deviations. where nmin is determined by minimizing jycorr(n) 2 ymeanj However, small discrepancies are tolerable and the dual- with respect to n. PRF dealiasing works correctly as long as the (dealiased) By using a phase-averaging procedure [see, e.g., section absolute gate-to-gate velocity difference Dy stays within 2.3.8 on periodic variables in Bishop (2006)], acting within the following limit (Joe and May 2003): the extended velocity interval, aliasing within this interval 2y y y y does not impose problems, as Nyq,e and Nyq,e are treated Dy ,Df Nyq,1 5Df Nyq,2, Df 5 jf 2 f j (1) as identical values (analogous to 2p and p denoting the f f 1 2 1 2 same actual phase angle). It should be noted that Eqs. (2) and (3) are like Eqs. (A3) and (A4), respectively, except that Here, f and f are the PRFs related to y and y , re- 1 2 1 2 n in Eq. (3) is determined more robustly. spectively; and y and y are the associated maxi- min Nyq,1 Nyq,2 The dual-PRF dealiasing error correction in POLARA mum unambiguous velocities. In case of the 800-/600-Hz 2 is performed in two stages, which are described as follows: scan mode, velocity differences up to 2.65 m s 1 will not cause dealiasing errors. However, this tolerance will be d In a first stage, a large window (11 3 11 pixels) Laplacian exceeded because of ubiquitous noise fluctuations. filter is applied to the data without correcting the data. Corresponding errors typically appear as randomly Range bins with erroneous velocities are identified and scattered erroneous pixels. Additionally, in regions of marked. An identification is claimed when a corrected high shear, such as in atmospheric vortices, the tolerance value different from the original value can be calculated is naturally exceeded and erroneous data appear in small according to Eqs. (2) and (3). pixel groups. It shall be noted that dual-PRF dealiasing d In a second stage, a small window (5 3 5 pixels) errors may occur, even if the data in the individual ad- Laplacian filter is applied to the data, and the data are jacent beams are not aliased (Joe and May 2003). The corrected. However, only those range bins not marked distribution of dual-PRF dealiasing errors is discrete, as in the first stage (i.e., presumably valid, error-free the errors are multiples of 2 yNyq,1 or 2 yNyq,2 (May 2001). pixels) are used as neighbors within the Laplacian The dual-PRF dealiasing errors are corrected by means filter’s averaging procedure.

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FIG. 2. Simulations showing the performance of the dual-PRF dealiasing error correction for the two dual-PRF settings as used for the volume scan (see Table 1). When not zoomed in, vortices are marked by red circles. Graphs show a cross section through the center of the simulated mesovortex at constant range before (red curve) and after correction (green curve). Applying the two-stage Laplacian ﬁlter and correction algorithm removes these outliers successfully without smoothing the mesovortex.

21 It shall be noted that the dual-PRF dealiasing and velocity yrot 5 8.5 m s was used. The large-diameter 21 subsequent error correction, even when working per- simulation is based on a vortex with yrot 5 15 m s .It fectly, provide velocity data that may show aliasing within can be seen that for distances below approximately the extended maximum unambiguous velocity interval. 100 km, the quality assurance works almost perfectly. At Figure 2 shows the performance of the dual-PRF deal- distances between 100 and 180 km (the maximum un- iasing error correction by means of simulation. A vortex ambiguous range), the number of pixels inside the vor- core situated at a distance of 62 km from the radar site tex core showing erroneous values increases. However, (red-encircled area) embedded in a uniform wind field this number remains below 28%. has been modeled. It is important that the erroneous data The dual-PRF dealiasing error correction shows the pixels are corrected but shear structures like Rankine- obvious restriction of having enough pixels with valid combined vortices are not eliminated. radial velocity values within the Laplacian filter window. Figure 3 shows observational radar data before and af- Especially for contiguous radar echo areas consisting of ter applying the dual-PRF dealiasing error correction. At only a few pixels, a correction is difficult. However, there the radar site Munich (MUC), a test scan setup with a have not yet been observed erroneous mesocyclone de- 250 m 3 18 resolution was used. The 4-times-higher range tections or significantly large artifacts in the azimuthal resolution together with the 800-/600-Hz dual-PRF setup shear products (see the following sections) as a result of causes a lower number of samples per pulse volume remaining dealiasing errors. This can probably be at- (implying a degradation of data quality) in comparison to tributed to the use of geometrical thresholds, which in- the current operational scan setup, thus resulting in a hibit such small areas from producing significant effects. ‘‘worst-case scenario.’’ It can be seen that a vortex (white- encircled area) is recovered in the quality-controlled data. 4. The mesocyclone detection algorithm of DWD Figure 4 shows the performance of the dual-PRF a. Outline of the algorithm dealiasing error correction for different positions of a small (4-km diameter) and a large (10-km diameter) The mesocyclone detection algorithm can be config- vortex with respect to the radar site. For the small- ured for both the detection of cyclonic and anticyclonic diameter simulation, an observed vortex with rotational rotation. In its current operational configuration, the

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FIG. 3. Observational data (PPI plot) (left) before and (right) after dual-PRF dealiasing error correction. A mesocyclonic signature can be seen within the encircled area. Insets show zoomed-in images of the vortices.

MCD performs a search only for cyclonic rotation 1) the detection of pattern vectors (1D), (positive azimuthal shear), which is the dominant mode 2) the grouping of pattern vectors to features (2D), and of mesocyclonic rotation on the earth’s Northern 3) the combination of features to mesocyclone objects (3D). Hemisphere. Mesoanticyclones are found less frequently, typically in conjunction with cyclonically ro- 1) THE DETECTION OF PATTERN VECTORS tating systems, such as in the case of bow echoes with After correcting the radial velocity data for spurious ve- ‘‘bookend’’ vortices and cyclone–anticyclone couplets, locities, the next step is the calculation of the azimuthal shear in the case of left movers with splitting storms and in the for each elevation scan, whereby the possibility of aliasing case of supercells with a cyclonically rotating updraft, (folding within the extended maximum unambiguous velocity where anticyclonic shear can be observed in the mid- interval) must be considered. First, we deﬁne level (Bluestein 2013). Dy 5 y 2 y The mesocyclone detection algorithm basically fol- corr,2 corr,1 (4) lows the pattern vector approach introduced by Zrnic´ Dy 5Dy 6 2y , (5) et al. (1985). There are three parts to the approach 6 Nyq,e

where ycorr,1 and ycorr,2 are the quality assured (corrected) radial velocity values from azimuthally adjacent

range bins. Let Dycorr be that gate-to-gate velocity difference, which shows the smallest absolute value, jDy j 5 jDyj jDy j corr min( , 6 ). (6)

This deﬁnes the corrected gate-to-gate velocity difference, and the corresponding shear value is obtained as

s 5Dycorr/b with b being the center-to-center distance between the two adjacent radial velocity bins. Insignificant shear values are treated as missing values; that is, they are ignored by the subsequent pattern vector search. The original velocity values of all FIG. 4. Percentage of erroneous pixels within the core region of pixels are kept in memory to allow for exact calculations a simulated vortex with small (4 km) and large diameter (10 km). later on (of, e.g., shear, specific angular momentum, Discontinuity in the large vortex simulation at a range of approximately 110 km is due to the number of pixels in the vortex core rotational velocity). Thepffiffiffi noise level is determined by the Dy 3 s ’ 21 region suddenly decreasing from 42 to 36 (pixelization effect) for error of corr being 2 2ms with the single- 2 ranges exceeding 110 km. pixel velocity error s ’ 1.5 m s 1, where s is estimated

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FIG. 5. Observed rotational signature at the radar site Dresden at 1400 UTC 24 May 2010 during the occurrence of a tornadic supercell. Region of the detected rotational feature (orange circle). (a) Quality-controlled radial velocity data. (b) Corresponding detected feature with its pattern vectors. After combining all features detected in this region, a mesocyclone with severity level 4 was found. from corrected observational radial velocity data by rotations (more related to the late, mature stage of performing a 3 3 3 Laplacian filter analysis and in- mesocyclone development) as well as high angular mo- vestigating the deviations of the central pixel’s value mentum and large-scale rotations (more related to the from its mean value. Thus, shear values with related early stage of mesocyclone development). Thresholds as 2 gate-to-gate shear , 2ms 1 can be regarded as in- low as approximately one-third of those given in Zrnic´ significant (further reasoning, discussed at the end of et al. (1985) have proven suitable for the radar network this subsubsection, leads to a weaker threshold used of DWD. It shall be noted that threshold adjusting for operationally). In cyclonic detection mode, negative pattern vectors is necessary so that environmental dif- shear is treated as noise, which reduces the influence of ferences in mesocyclones and warning criteria can be possible azimuthal shear artifacts (e.g., remaining clut- considered (Crozier et al. 1991, p. 494, last paragraph). ter contamination) in regions of positive cyclonic shear. Picking up noisy azimuthal shear during the pattern A pattern vector is a sequence of positive azimuthal vector search is suppressed by the selection criteria for shear at constant range. Figure 5 shows an example of an significant pattern vectors [Eqs. (7) and (8)]andbythe observed Doppler rotation signature (typical velocity conditions for clustering pattern vectors to features (and couplet) and the pattern vectors that are identified features to mesocyclone objects) as discussed in the sections within the area of rotation. The pattern vector search 4a(2) and 4a(3) below. Using simulations we determined a accepts interruptions of one range bin within a pattern threshold of significant gate-to-gate shear lower than that 2 vector to account for data dropouts (data values below introduced above (approximately 0.8 m s 1). the reflectivity or azimuthal shear noise thresholds, or For the specific angular momentum and azimuthal 5 n residual azimuthal shear caused by incorrect radial ve- shear of a pattern vector, one can find that lpv åi51li n 5 n locities). Each pattern vector is filtered with respect to and spv åi51si/n with n being the number of azimuthal Doppler (specific) angular momentum lpv and azimuthal shear pixels that make up the pattern vector. Thus, the shear spv (Zrnic´ et al. 1985) so that only shear regions azimuthal shear of a pattern vector is in fact the mean above the noise threshold are accepted for further azimuthal shear of the contributing pixels and the shear analysis. The following set of thresholds is used: threshold of Eq. (7) could already be applied to the single pixels. Experience has shown that pattern vectors 2 s . 1:5ms21 km 1 and l . 30 m s21 km (7) can possess an embedded higher shear sequence (with pv pv lower shear at the start and end points), likely since . : 21 21 . 21 spv 3 0ms km or lpv 100 m s km. (8) vortices observed in radar data are smoothed due to radar resolution effects (Wood and Brown 1997). As a In applying the latter set of thresholds (the OR condi- result the mean shear drops below the threshold of tion), the idea is to identify high shear and small-scale Eq. (7) and an actually significant pattern vector can be

Unauthenticated | Downloaded 10/06/21 01:06 PM UTC FEBRUARY 2018 H E N G S T EBECK ET AL. 305 lost. Applying the low shear threshold given in Eq. (7) to value, and D3 is a simple average [for more details single pixels of the azimuthal shear data (prior to the see Eqs. (A7)–(A9) in the appendix of Zrnic´ et al. pattern vector search) preselects higher shear and pre- (1985)]. However, only the pattern vectors with the vents such loss. largest specific angular momentum (typically found in the core region of the rotation) are chosen to enter 2) THE GROUPING OF PATTERN VECTORS TO into the symmetry calculations: in the case of a vortex FEATURES field, these pattern vectors will cover the core region, The mesocyclone detection proceeds by grouping the whereas in the case of a linear wind event, such as a pattern vectors to features. Ideally, a feature corre- gust front, the pattern vectors are scattered along the sponds to a complete rotation signature within an ele- gust front and will violate the symmetry conditions. vation scan and consists of several pattern vectors The reason for introducing this core region restric- adjacent in range. However, in reality, there is always tion is that one frequently observes a vortex dis- some noise present [missing data as a result of signal torted by a convergence zone caused by the thun- filters; corrupted data, such as remnants of clutter or derstorm inflow. The pattern vectors extend into the wireless local area network (WLAN) interference convergence region and, without the large momen- spokes not fully removed by the quality assurance], and tum restriction, would then violate the symmetry the pattern vectors may be noncontiguous. Thus, the condition so that a possibly strong rotation would following criteria are used to extract only meaningful remain undetected. See Fig. 5 for an example of a features and, at the same time, allow for imperfect feature detected during the occurrence of a tornadic data: supercell. d First, the number of detected pattern vectors must 3) COMBINING FEATURES INTO 3D exceed a certain threshold that depends on the range MESOCYCLONE OBJECTS resolution and the minimum assumed vortex spatial Finally, the 2D georeferenced features from all radars extent. In Zrnic´ et al. (1985), for elevation scan data in the network are combined into three-dimensional with a 150-m range resolution, a minimum of six pattern vertically aligned mesocyclone objects (see Fig. 6)by vectors is required for feature detection so that vortex means of a connected components labeling algorithm diameters . 1 km can principally be resolved. Since (see, e.g., Shapiro and Stockman 2001, section 3.4). at DWD the volume scan data have a 1-km range Vertical alignment (overlap) between two 2D features is resolution, a smaller number of three pattern vectors is given if the offset of the feature centers is less than the currently used (requesting just two adjacent pattern sum of the feature radii. In this way, tilted mesocyclones vectors is not enough for suppressing chance coinci- (physical and perhaps created as a result of the time dences caused by noise, especially when considering the offsets between the scans) are taken into account. Fea- comparably low shear and angular momentum thresh- tures of all elevations and of all radar sites are consid- olds necessary for detecting significant rotational signa- ered (network approach). These 3D objects are referred tures). The adjacency criterion allows for a separation of to as mesocyclone objects and are candidates for (de- one range bin between the pattern vectors associated tected) mesocyclones. Compare also to Stumpf (2002), with the same feature. in which a similar technique for the feature combination d Second, symmetry criteria must be passed: the spatial was demonstrated. extension of features should be roughly equal in azimuth and range direction. The symmetry criteria, b. Mesocyclone object properties based on Zrnic´ et al. (1985), are as follows: Properties of the 3D mesocyclone object, such as : # # : 0 4 D1/Dr 1 7, (9) maximum azimuthal shear, maximum rotational velocity, height of the lowest detected rotation signature or 0:4 # D /D # 1:7, (10) 2 r above ground, total depth of the rotational column and : # # . mean and maximum reflectivity, vertically integrated or 1 6 D3/Dr 4 (only for range 140 km). (11) liquid water (VIL), and VIL density, are calculated Here, Dr is the feature diameter in the radial direction (see Table 2). These properties (also referred to as at- (distance between the pattern vector closest to the tributes) can be categorized into geographical coordinate, radar and the pattern vector farthest from the radar). shape, Doppler velocity, and reflectivity attributes. For a

The terms D1, D2, and D3 are estimates for the feature more robust calculation of coordinates and reﬂectivity- diameter in the azimuthal direction: D1 is the momen- related quantities, an expanded circular area of twice tum weighted diameter, D2 is a root-mean-square the diameter of the rotation features (i.e., mesocyclone

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obtain a mesocyclone object with the best possible sampling. The estimation of the detected mesocyclone’s severity (see section 4c) is mainly based on ‘‘maximum properties’’ (maximum shear, maximum rotational velocity). This complies with the requirements of the warning service, where an overestimation is more ac- ceptable than an underestimation. Furthermore, range degradation effects typically lead to underestimated parameters of rotational strength (too low shear, too low rotational velocity), so the ‘‘maximum picking’’ naturally selects the parameter with the best resolution available. A further solution is to homogenize the feature’s parameters if possible. Concerning the azimuthal shear, this can be done by applying a range correction (Newman FIG. 6. Schematic showing the merging of different features et al. 2013). This correction is also relevant for the rota- (orange patches) to a single 3D mesocyclone object (blue tion composites as introduced in section 5 and is one of column). Radar elevation scans are depicted as cones (black the major steps to be addressed in a future development contours). In case of detections from multiple radar sites (overlapping scan regions), the georeferenced features are (see section 8). merged into the same mesocyclone object. c. The mesocyclone severity metric object region) is considered. This is done in order to take To reject rotational signatures that were not associated into account the fact that the mesocyclone location and with a thunderstorm, the thresholds given in Table 3 are spatial extent do not usually coincide with the parent applied to all mesocyclone objects. In particular, at least two cell’s position and extent (as delineated by reflectivity). features are needed for successful mesocyclone detection. Calculated within this expanded area using the elevation The severity of the mesocyclone is computed using the scan base data, the reflectivity-related attributes reflect severity ranking shown in Table 4, which is based on ge- the parent cell’s properties. The expansion proved use- ometry and the strength of rotation. Severity levels 1–5 ful also for the calculation of geographical mesocyclone imply mesocyclonic rotation with increasing strength and coordinates, giving more robust and stable mesocyclone confidence. According to the Bureau of Meteorology (2016), positions especially in the case of gaps in the radial velocity data. In appendix B a detailed overview of all calculated attributes is given. TABLE 2. List of properties of mesocyclone objects. See text for There are limitations to the accuracy of these attri- details. butes imposed by the geometry of the volume scan. Category Attribute Description and unit Because of the spherical grid geometry of the elevation 8 scans, a detected feature shows a range-dependent res- Coordinate clat Latitude ( ) of mesocylone center 8 olution in the directions of azimuth and elevation, the and shape clon Longitude ( ) of mesocyclone center h Mesocyclone top (km) range resolution being constantly 1 km. For a range lo- meso, top hmeso, base Mesocyclone base (km) cation at 60, 120, and 180 km, the horizontal resolutions hmeso Mesocyclone depth (km) are 1.05, 2.09, and 3.14 km, respectively. The related dmeso Mesocyclone diameter (km) vertical resolutions show the same values because the dmeso, equi Mesocyclone equivalent diameter (km) 8 23 21 radar main lobe has a symmetrical 1 width. The heights Doppler smax Max azimuthal shear (10 s ) 23 21 of the lowermost elevation scan at the given range lo- velocity smean Mean azimuthal shear (10 s ) lmax Max specific angular cations are 0.21, 0.85, and 1.90 km, respectively. This 2 momentum (103 m2 s 1) implies a degradation of the accuracy of geometrical lmean Mean specific angular 2 (diameter, height), reflectivity-based, and rotational at- momentum (103 m2 s 1) 21 tributes with increasing range. Furthermore, rotational yrot, max Max rotational velocity (m s ) signatures close to the ground may be below the low- Reflectivity Zmax Max reflectivity (dBZ) ermost elevation scan when situated at large distances Zmean Mean reflectivity (dBZ) 2 from the radar. VIL Cell-based VIL (kg m 2) hecho top 18-dBZ echo-top height (km) The network approach is able to partly compensate for 23 these degradations by merging all detected features to VILdensity VIL density (g cm )

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TABLE 3. Thresholds applied to all detected mesocyclone objects. Vertical averaging, according to Eqs. (12)–(14), is also performed so that deep rotation is emphasized in com- Mesocyclone attribute, unit, and threshold operation Threshold value parison to shallow rotation and noise. The algorithm works on a composite grid in polar-stereographic projection Z dBZ . 10 mean with 1100 3 1200 pixels of approximately 1 km 3 1km hecho top km . 2 23 VILdensity gcm . 1 resolution. A given grid cell of the composite is assigned , hmeso, base km 5 a sample containing (sj, zj, hj) triples (values of shear sj, n # $ 2 feature reflectivity zj, and height hj with 1 # j # n,wheren is the number of samples over the depth of the atmosphere). Each triple is extracted from a certain radar site’s elevation scan the necessary conditions for deep mesocyclonic range bin (the projected center of the range bin must fall rotation are that the vortex should be of storm scale into the composite grid cell). All elevation scans are con- (;2–10 km), have a reasonable vertical depth (;3 km), sidered. In regions of radar overlap, the sample shows have a sufficient duration, and meet a minimum strength contributions from multiple radars. The situation is analog 2 criterion (a rotational velocity of ;15 m s 1 or a vertical to that depicted in Fig. 6 with the orange patches now being 2 2 vorticity of ;10 2 s 1). Severity level 3 is established to interpreted as radar range bin data. The triples are sorted in meet these criteria by applying the respective thresholds increasing order of height and a rotation value z is calcu- on dmeso,equi, hmeso, yrot,max, and smax. Sufficient duration lated as a height–difference weighted mean, of a mesocyclone detected by the MCD can be tested by 2 considering the detection history and by comparison n 1 å s Dh with rotation track composites (see section 5). A statis- j j z 5 1 , (12) tical analysis of the mesocyclone detection algorithm is n21 å D provided in section 7. hj 1 5 : 1 sj 0 5 (sj11 sj), (13) 5. The DWD rotation and rotation track products D 5 2 hj hj11 hj . (14) The azimuthal shear composite products offer independent and additional visual insight. The pre- The azimuthal shear product (further referred to processing of azimuthal shear is inspired by the linear as rotation composite) is created for two altitudes: least squares derivative (LLSD) algorithm of the Na- The low-level rotation composite (ROT-LL) shows tional Severe Storms Laboratory (Smith and Elmore the mean shear between 0 and 3 km (AGL), while the 2004; Miller et al. 2013; Newman et al. 2013) in the sense midlevel rotation composite (ROT-ML) depicts the that a noise-suppressing extraction of azimuthal shear mean shear between 3 and 6 km (AGL). Both rotation from the elevation scan base data is attempted. The composites show positive cyclonic and negative anticy- analysis of shear derived from radial velocity data is a clonic shear. specific challenge, since derivatives are particularly The composite rotation track products are created by noisy as a result of the combination of variances. A accumulating the maximum shear so that in the operational single range bin with spurious velocity can cause a ‘‘hot setup, each grid cell shows the maximum (cyclonic) shear of spot’’ within the azimuthal shear composite. Thus, a the last 3 h (the accumulation time is configurable and can series of smoothing and averaging techniques is used to be set on demand for offline analyses). This product high- obtain a more robust final product. lights persistent, significant, and moving cyclonic vortex First, a smoothing 3 3 3 pixel window filter is applied to areas, which is typical for organized deep convection, such the radial velocity data. This filter essentially works iden- as supercells or bow echoes. A separate product for anti- tically to the one used for dual-PRF dealiasing error cor- cyclonic shear is conceivable, but experience shows that it rection with the exception that the central pixel’s radial has limited value. False signatures caused by significant velocity value is replaced by the phase-averaged mean of vertical shear near the surface, or outflow boundaries the neighboring eight pixels. In this way, single noisy pixels (Miller et al. 2013), can usually be distinguished by eye from are smoothed out, while regions where the radial velocities real rotation tracks using these rotation products (false change linearly with increasing range and azimuth are less signatures typically do not produce line or stripe-like pat- affected and thus emphasized. Such regions imply constant terns, as is observed for ‘‘real’’ rotation tracks). shear (as is typical for the core of mesocyclones). There- Any algorithm utilizing radar data suffers from the fore, the Laplacian filter smoothing mitigates single noisy uneven polar grid spacing of the base radar data. De- pixels while affecting vortices of constant shear less. terioration (loss of horizontal and vertical resolution) of

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TABLE 4. Severity metric. Each line represents a threshold thunderstorms followed from the west. They were as- condition. Threshold conditions are connected according to the sociated with a surface low that propagated eastward ^ _ following scheme using logical AND ( ) and OR ( ) operators: over the most southern part of Germany. t ^ t ^ (t _ t ). 1 2 3 4 The VIL track composite in Fig. 7 indicates severe Mesocyclone attribute, Severity level weather in southwestern Germany. High VIL values in 2 Threshold unit and threshold excess of 60 kg m 2 were measured. It shall be noted that condition operation 12345 the times given in Fig. 7 are reference times (start of . t1 dmeso, equi km 33555volume scan). The volume scan starts at approximately t2 hmeso km . 12368 23 40 s after the full minute and takes approximately 4 min, t3 smax 10 . 5 7 10 20 30 2 s 1 30 s to finish, so a time interval of approximately 4 h is 21 t4 yrot, max ms . 10 12 15 20 25 covered (1700:00–2055:00 UTC reference time corresponds to 1700:40–2059:30 UTC actual observation time). An accumulation time of 4 h rather than 3 h was chosen for this case study to show most complete tracks. the measurements of a single radar with increasing range Besides smaller signals three major supercells were is unavoidable. The network approach is better able detected by the MCD. These are also very visible in the to compensate for the loss in vertical sampling by com- rotation track composites (Fig. 8). One supercell moves bining all available radar measurements. However, directly over the radar at Feldberg, another on a parallel problems remain in composite border regions (the edge track displaced to the northeast, and the third supercell of the radar network domain). track can be seen close to the radar at Türkheim. All hail Rotation tracks are better defined in the central region and tornado reports were located on or close to the VIL of the composite and not too close to any of the radar sites, and rotation tracks. Most notably, two F3 tornadoes (see where vertical wind shear may cause high azimuthal shear Fig. 8) can be associated with supercells detected by the signals (‘‘hot spots’’) that are not related to rotation. The MCD, which could be tracked constantly for the pre- forecaster must be aware of these limitations to carefully vious 2 h before the tornadoes were observed. draw decisions in operational warning situations. Figure 9 shows the mesocyclone detections for the same time range as in Fig. 8. Each detection is repre- sented by a circle with a diameter corresponding to the 6. Case studies equivalent diameter. In Figs. 9a and 9b mesocyclone In the following subsections, two case studies are detections obtained when running the MCD in the de- presented to demonstrate the value of the network ap- fault network mode are depicted. From Fig. 9a one can proach. Furthermore, the potential of the MCD and see that up to six radar sites contributed to a detection. rotation composites to support forecasters in their The two detections with the largest number of features warning decisions is shown. These products are visual- show 22 and 25 detected rotation signatures, re- ized together with VIL track composites, which high- spectively. Figures 9b and 9c show the mesocyclone se- light cell tracks and give a general impression of the verity for the network and the single-site approach, severe weather potential. respectively. In particular, differences can be seen for 2 VIL values in excess of 10 kg m 2 indicate convection. the northern mesocyclone track. Besides eliminating For the most severe events, VIL can exceed 60 and ap- multiple simultaneous detections, it seems that the 2 proach 100 kg m 2. VIL and VIL track composites fol- MCD in network mode generates better severity esti- low the network algorithm approach, as described for mates. The combination of features detected by the ra- the rotation and rotation track composites. Analogous dar at Türkheim and the neighboring radar sites results to the rotation track composites, the VIL track com- in detections with severity levels 4 and 5. Single-site posites show a maximum value 3-h history in the oper- detections alone fail to generate the highest severity ational configuration. levels as a result of insufficient rotational strength or vertical extent. The radar at Türkheim alone, though a. Tornadic supercells in southern Germany on being close to the mesocyclone, is not able to capture the 13 May 2015 rotation in its full shape and characteristic. This can be Within a humid, unstable air mass, thunderstorms understood from restrictions in the scan geometry (cone developed in the afternoon and reached high severity of silence) and the fact that the strongest rotation over southeastern Bavaria, where high CAPE and shear within a mesocyclone may occur at higher altitude. values were present and dynamical forcing supported Figure 10 illustrates the benefit of the network ap- the lifting processes. In the evening marginally severe proach for the VIL and rotation track composites. The

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FIG. 7. VIL track composite and reports of the ESWD (Dotzek et al. 2009) visualized by NinJo for 1700–2055 UTC 13 May 2015. Severe wind reports (yellow rectangles surrounded by larger white rectangles), hail reports (green filled circles surrounded by white rectangles with rounded edges), and tornado reports (red circles framed by upside-down white triangles). Tornado strength (F scale) is labeled where a strength estimation based on damage survey was available. The radar sites Feldberg (F), Türkheim (T), Memmingen (M), and Isen (I) are indicated (white letters within white circles). effects of the blanking sector (area labeled ‘‘1’’) and the majority of smaller thunderstorms moving northeast). 2 cone of silence visible within the area marked by ellipse 2 VIL values reached up to 100 kg m 2. The aforemen- in Fig. 10a are mitigated in Fig. 10b. At far ranges the tioned hail observation (8-cm diameter) correlates with single-site VIL shows biased values [overestimation in the easterly end of the VIL track. Severe weather events, the case of strong vertical reflectivity gradients (Brown reported in the European Severe Weather Database andWood2000; Bellon and Zawadzki 2003)andun- (ESWD), are overlaid on the VIL track in Fig. 11b.The derestimation in the case of overshooting precipitation]. hail-producing potential of the single supercell is evident. From Figs. 10c and 10d, it can be seen that the (low level) The low- and midlevel rotation track composites rotation track composite shows less noise and shallow (Fig. 12) indicate regions of stronger and weaker rotation, rotation signals when using the network mode. A single the midlevel rotation being generally stronger (especially main rotation track with a bend toward the east becomes for the easterly part of the track). The low-level rotation visible in the encircled area of Fig. 10d, showing a char- composite shows some isolated pixels with high azimuthal acteristic ‘‘fishbone pattern’’ (an effect of the periodic shear values. However, these are most likely artifacts, scanning) for the whole track. related to the fact that elevation scan base data at low elevations suffer more from ‘‘impurities,’’ such as clutter b. A long-lived hail-producing supercell in northern contamination, than elevation scan data at higher eleva- Germany on 28 August 2016 tions. The mesocyclone was detected over the period On 28 August 2016, a midlevel trough was approaching from 1305 to 1650 UTC. Most of these detections are western Europe accompanied by a strong southwesterly associated with a mesocyclone base . 3km. flow. Germany was dominated by an unstable, humid, and Figure 13 shows the effect of the network approach on hot air mass. The first thunderstorms developed west of the MCD. In Fig. 13a the MCD detections are depicted Stuttgart in southwestern Germany and in Emsland in the with a color coding that indicates the number of radar northwest. In the course of the afternoon, severe thunder- sites that contributed to a given detection. For almost all storms occurred in almost all parts of northwestern Germany. detections there are contributions from at least two sites A single supercell showed a track of approximately 200-km and even for some detections from four sites. For an length in an easterly direction starting south of Hamburg. effective suppression of false detections, at least two Hail with diameters up to 8 cm was observed. features are needed for a successful mesocyclone object In Fig. 11 the VIL track of the single right-moving identification (see Table 3). Several MCD detections in supercell is visible as a broad line of red, violet, and Fig. 13a are composed of single features from single white extending from west to east (as opposed to the sites. If the MCD were used as a single-site algorithm

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FIG. 8. Rotation track products, mesocyclone detections, and severe weather tornado reports for 1700–2055 UTC 13 May 2015 visualized by NinJo. Overlaid ESWD tornado reports (upside-down white triangles), mesocyclone detections related to the time stamp 2055 UTC (current; ﬁlled triangles), and mesocyclone detections within the given time interval but prior to 2055 UTC (historic; open triangles). MCD detections of the highest severity level are particularly highlighted (thickly drawn violet triangles). For reasons of clarity, only mesocyclone detections with severity $ 2 are shown. (a) Rotation low-level track composite and (b) rotation midlevel track composite.

(treating the base data of all radar sites independently), MCD detection at 1410 UTC in Fig. 13b showing single- then these detections would be lost. For larger parts of feature contributions from the radar sites Boostedt, Rostock, its track, the mesocyclone is not adequately sampled Hannover, and Ummendorf is lost in Fig. 13c. Ellipse 3 in by a single radar alone, since it has a higher base and is at Fig. 13c highlights an area where again many detections some distance from the neighboring radars (approxi- are lost when the MCD is operating in single-site mode. mately 80–200 km for the easterly part of the track). Figures 13b and 13c show the detections obtained in the network and the single-site mode, respectively. Here, the 7. Statistical analysis color coding indicates the severity level. Ellipse 1 in Fig. 13c a. Comparison of MCD statistics with previous marks a region without any MCD single-site detections. The studies early detections visible in Fig. 13b are lost in Fig. 13c.Fur- thermore, in Fig. 13c there is a double detection of the same In this subsection mesocyclone detection statistics are mesocyclone object within the area marked by ellipse 2. The presented and compared with previous studies. The

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FIG. 9. Map of mesocyclone detections for 1700–2055 UTC 13 May 2015 (cf. Fig. 8). Diameters of the circles correspond to the equivalent diameters of the detected mesocyclones. (a) MCD detections in the network approach; color coding shows the number of radar sites that contributed to detection. (b) MCD detections in the network approach; color coding shows the severity. Tracks of the tornadic supercells show mesocyclone detections with the highest severity. (c) MCD run on radar base data from single sites (single-site approach). Ellipse 1 marks a region where multiple simultaneous detections (single mesocyclone objects ‘‘seen’’ by multiple radars) with apparently underestimated severity can be seen. Ellipse 2 marks regions where there are several multiple detections as well.

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FIG. 10. VIL track and rotation low-level track composites produced in single-site and network modes for 1700–2055 UTC 13 May 2015 (an accumulation period of 4 h was chosen to show most complete tracks). (a) VIL track product for the radar site Feldberg (FBG). A blanking sector is visible in the southeastern direction. (b) VIL track composite using data from all radar sites. (c) Rotation low-level product for the radar site Türkheim (TUR). (d) Rotation low-level composite using data from all radar sites. Regions of interest are indicated (encircled areas; see text for detailed explanations). characteristics of mesocyclones detected by the MCD are Dotzek et al. 2005). In Wapler et al. (2016),theoccur- investigated in Wapler et al. (2016) based on a 3-yr rence of mesocyclone detections for hailstorm events was analysis (April–September 2013–15). No restriction on investigated. This analysis revealed that about half of all the number of features per mesocyclone object was ap- hailstorms in Germany are associated with a mesocyclone plied at that time. The same is true for the analysis pre- detected by the MCD during the time of reported hail. sented in Bellon and Zawadzki (2003), who studied However, newer studies that analyzed the entire life cycle mesocyclones in southern Quebec, Canada, using a 9-yr of hailstorms showed that approximately three-quarters dataset from one radar. In Wapler et al. (2016),charac- of all hail-producing cells in central Europe show rota- teristics of the MCD detections are compared to the re- tional characteristics (Wapler 2017). sults given in Bellon and Zawadzki (2003). In addition to annual and diurnal cycles, the frequency The annual and diurnal cycles of mesocyclone de- plots for the mesocyclone attributes hmeso,top, hmeso,base , hmeso, tections as obtained by the MCD show typical (broad) dmeso, and the maximum and mean shear and moment (smax, maxima in June–August and for 1600–1700 UTC, smean, lmax, lmean), as well as VIL, echo-top height hecho top, respectively (Wapler et al. 2016). It was found that for all and VILdensity are presented in Wapler et al. (2016). six strong tornadoes (F2) in the years 2012–14 within The depth hmeso of 85% of the detected mesocyclones Germany, a mesocyclone was detected by the MCD well is below 3.5 km. Because of the thresholds applied in the before the tornado occurrence. Strong tornadoes were detection algorithm, the minimum mesocyclone di- selected because, in the case of weaker tornadoes ranked ameter dmeso is 3 km (at least three adjacent pattern as F0 or F1 on the Fujita scale, the possibility of non- vectors are required to form a feature). Half of the mesocyclonic origin is high (Brooks and Dotzek 2008; mesocyclones have a diameter between 3 and 6 km.

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FIG. 11. (a) VIL track composite for 1305–1600 UTC 28 Aug 2016. Radar site Boostedt is indicated (black circle with white ‘‘B’’). Directions to the neighboring radar sites Hannover (H), Ummendorf (U), and Rostock (R) are shown (arrows). (b) As in (a), but for additional severe weather reports archived in the ESWD. Severe wind reports (small yellow rectangles framed by larger white rectangles), heavy precipitation reports (blue dots framed by white circles for better visibility), and hail reports (green dots framed by white rectangles with rounded edges).

Two-thirds of all mesocyclones have a maximum shear detections of the 4-yr period 2013–16 (April–September) 2 2 between 4 and 8 m s 1 km 1. were analyzed. Mesocyclone objects were restricted to be These shape and rotational characteristics of the composed of at least two features. MCD mesocyclone detections are in general agreement The severity criteria are the same as described in with those presented in Bellon and Zawadzki (2003). section 4, except that the rotational velocity criterion is not used—this attribute is not available for all archived b. Comparison of the MCD network with the MCD mesocyclone detections. single-site approach Figure 14a shows the frequency of mesocyclone de- For a further investigation comparing the single-site and tections as function of the severity level for the default network approaches of the MCD, archived mesocyclone network and the single-site approach.

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FIG. 12. (a) Rotation low-level track composite, and (b) rotation midlevel track composite with overlaid mesocyclone detections for 1305–1600 UTC 28 Aug 2016.

Approximately 10%–15% more mesocyclone de- the accuracy of the detected mesocyclones properties tections are gained when using the network mode. This (e.g., the vertical extension cannot be measured gain is roughly evenly distributed across severity levels accurately), but a detection may still be accom- 1–4. For severity level 5, no detections were gained plished. On the other hand, at a larger distance from a using the network approach, since mesocyclones de- given radar site, a mesocyclone may be not optimally tected at this level have a depth of at least 8 km, so scanned by this radar alone (as a result of the de- multiple features are very likely detected even in sin- creasing resolution and the increasing beam height), gle-site mode. so only a single feature or no feature is detected and Figure 14b shows the spatial distribution of all meso- the whole detection is lost in single-site mode. Thus, it cyclone detections for the years 2013–16 that are is plausible that the detections gained in network detected only within the network approach. Con- mode are fairly uniformly distributed over Germany. cerning the single-site mode, limitations of the scan Figure 14c shows the frequency of the gained meso- geometryintheareaclosetoaradarsitewillaffect cyclone detections as function of the distance to the

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FIG. 13. Map of mesocyclone detections for 1305–1600 UTC 28 Aug 2016. (cf. Fig. 12). Diameters of the circles correspond to the equivalent diameters of the detected mesocyclones. (a) MCD detections in the network approach; color coding shows the number of radar sites that contributed to a detection. (b) MCD detections in the network approach; color coding shows the severity. (c) MCD run on radar base data from the sites Boostedt, Rostock, Ummendorf, and Hannover (single-site approach). Numbered black ellipses mark areas of interest (see detailed description in the text). nearest radar site. The frequency histogram has a the mean nearest-neighbor distance within the DWD linearly rising slope as is expected from a spatially radar network, which is 140 km. Applying the MCD in uniform distribution of the additional detections. The network mode increases the number of detections decrease at distances larger than 65–70 km is due to particularly for weak meocyclones and therefore is diminishing radar overlap at the radar network bor- likely to extend the lead time in severe weather der region. The peak at around 70 km is in line with warning operation.

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For cell lifetime studies, tracks of storm cells as de- The quality assurance successfully removes dual-PRF tected by the reflectivity-based cell detection algorithm dealiasing artifacts while not eliminating mesocyclonic Konvektive Entwicklung in Radarprodukten (KONRAD; vortices. The MCD with its severity metric shows a good convective development in radar products; Lang 2001; correlation with the rotation tracks. Wapler et al. 2012) were investigated. Only those storms Because of the dense radar network of DWD, the that show at least one associated mesocyclone de- MCD shows significant additional detections in network tection are considered. In Figs. 15a and 15b,absolute mode. Therefore, the tracks of mesocyclone detections and relative numbers of KONRAD tracks with asso- become more complete and a future tracking and now- ciated mesocyclone detections are shown as a function casting extension of the MCD will benefit from the of the KONRAD track duration (i.e., the estimated network approach. In network mode, there are more cell lifetime). A relative gain of 10%–15% in the samples available for a given mesocyclone detection to number of ‘‘mesocyclonic’’ KONRAD tracks can be calculate the mesocyclone properties. This leads to an deduced for the network approach independent of cell improvement in severity estimation. Also, the rotation lifetime. tracks are improved using the network approach as Figure 15c shows the mesocyclone fraction, that a result of better suppression of shear artifacts and is, the percentage of the KONRAD lifetime with shallow rotation. attributed mesocyclone detections. The number of The shape and rotational characteristics of mesocy- KONRAD tracks with very low mesocyclone fraction clones over central Europe detected by the presented decreases, while the number of KONRAD tracks with MCD confirm the results reported in Bellon and significant mesocyclone fraction increases for the net- Zawadzki (2003) for Quebec. An investigation of a cor- work mode. Figure 15d depicts the mean time between relation between a reflectivity-based cell detection successive mesocyclone detections along a given (KONRAD) and the MCD revealed that KONRAD KONRAD track. For the MCD in the standard net- cells with an additional detected mesocyclone show a work mode, the mean time decreases; that is, mesocy- longer lifetime on average, whereby the lifetime in- clone detections attributed to a KONRAD track are creases with the severity of the mesocyclone detection. more closely spaced. Both findings suggest an im- This finding is in line with mesocyclonic rotation being provement in the continuity of mesocyclone detections known to occur in highly organized, long-lived storms for the network approach, which is also demonstrated and confirms the practical significance of the MCD. by the case studies (section 6). Further studies suggest a correlation between the oc- Figure 16 shows the lifetime frequency distributions currence of hail-producing cells and the presence of of mesocyclonic KONRAD cells. As the severity level mesocyclonic rotation (as detected by the MCD). Fu- of the associated mesocyclone detections increases, ture cell lifetime studies will benefit from the detection the frequency distributions become flatter; from of rotational cell characteristics. all detections attributed to a given KONRAD track, A rigorous statistical analysis of the performance of the maximum severity was chosen. Thus, KONRAD the MCD requires a sufficiently large radar database cells with associated mesocyclone detection show a of convective storms that are classified into meso- longer lifetime on average: the higher the mesocyclone cyclonic and nonmesocyclonic storm types (as well as severity, the longer the cell’s lifetime. The gain of further subdivisions; e.g., tornadic and nontornadic additional mesocyclone detections for the network supercells). Using a recently introduced procedure, approach is distributed rather equally among the forecasters at DWD now regularly classify current lifetimes. weather phenomena so that a ‘‘case database with Recent life cycle studies with a meteorological rather categorization’’ can gradually build up. However, the than an algorithmic aspect can be found in Wapler categorization of cases, done by human experts, is (2017), where the life cycles of hailstorms, including subjective to a certain degree and so are the derived possible mesocyclone occurrence, are investigated. performance measures. Therefore, a meaningful statistical analysis should have a comparative character (comparing performances of algorithms being applied 8. Summary and discussion to the same database and using the same criteria for In this paper, the operational mesocyclone detection hits and misses). algorithm (MCD) and the rotation composite algorithm A proper setting for an algorithm intercomparison of DWD were presented. These algorithms follow a study can be found within WMO’s World Weather Re- network approach and process quality-controlled Doppler search Programme as the example of the Sydney 2000 wind data. Forecast Demonstration Project (Keenan et al. 2001)

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FIG. 14. (a) Frequency of mesocyclone detections as a function of the severity level for the standard network and the single-site approach. MCD detections for 2013–16 (April–September) are analyzed. (top) Absolute numbers. (bottom) Relative frequencies. (b) Map of the additional mesocyclone detections that are gained when using the network approach. These detections are composed of single features from at least two neighboring radar sites. (c) Frequency of additionally gained mesocyclone detections in network mode as a function of the distance to the nearest radar. Linear ﬁt for distances below 65 km (dashed line).

shows (radar-based nowcasting played a major role the network approach (Werner 2017). A generic within the project). In Sydney 2000, participants ran tracking module will be available for both cell and their own algorithms, properly adjusted to the avail- mesocyclone detection algorithms so that tracking able data (an important aspect to eliminate bias) on a and nowcasting of 3D cell objects with detected re- common database. A mesocyclone detection algorithm ﬂectivity and rotation characteristics will be possible. intercomparison may well be feasible in the future The tracking of MCD objects opens new possibilities within such a forecast demonstration project. concerning the detection of weak mesocyclones. The Quality assurance issues to be tackled by future devel- thresholds as used in the severity calculation may be opment include a range correction of azimuthal shear so further lowered for the purpose of early detection. The that rotation tracks and mesocyclone detections will be resulting increase in false alarms can be reduced by improved at the composite border regions. Also, azi- requesting that a mesocyclone detected with low muthal shear data in overlap areas (of different radar thresholds must be part of a track with a certain mini- sites) naturally showing mixed resolution will be equalized mum duration. by the range correction so that these data become better In conclusion, the mesocyclone detection and rota- comparable (Newman et al. 2013) and that the MCD and tion products provide a new perspective at looking at rotation composites are improved. severe convective storms in Germany and adjacent Inthenearfuture,POLARAwillincludea3D European countries, and provide valuable information reﬂectivity-based cell detection algorithm following to improve the weather and warning service of DWD.

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FIG. 15. (a) Frequency of KONRAD tracks associated with at least one mesocyclone detection as a function of the KONRAD track duration (i.e., the cell lifetime). (b) As in (a), but for the gain of the network approach relative to the single-site approach. (c),(d) Analysis of KONRAD tracks associated with a mesocyclone detection. Only KONRAD tracks with a duration of at least 15 min and with at least one attributed mesocyclone detection are investigated. (c) Histogram of the mesocyclone fraction, i.e., the fraction of the KONRAD track where mesocyclone detections could be associated. (d) Mean time between successive mesocyclone detections. Smallest possible time distance is 5 min (as determined by the volume scan interval).

The mesocyclone detections are integrated in the anonymous reviewers for the very valuable comments NowCastMIX system (James et al. 2013), which pro- and recommendations. vides basic information for AutoWARN (Reichert 2013), the operational warning decision support system APPENDIX A of DWD. Velocity Extension by Dual-PRF Dealiasing Acknowledgments. The support offered by other Technique members of the radar meteorology R&D team at DWD is greatly appreciated. An evaluation of all DWD radar– In the dual-PRF scan mode, the radar data are collected based algorithms and products mentioned in this paper with azimuthally alternating PRFs on 18 azimuthally spaced at the testbed organized by the European Severe Storms rays (Dazhang et al. 1984). The indices 1 and 2 of the Laboratory (ESSL) in Wiener-Neustadt proved very physical quantities given below relate to these two PRFs. useful. We are very grateful to Pieter Groenemeijer for For the lowermost six elevations within DWD’s volume the many fruitful discussions and recommendations, in scan, the PRFs are f1 5 800 Hz and f2 5 600 Hz, and the particular concerning the estimation of the mesocy- wavelength for the DWD radar systems is approxi- clone severity. Furthermore, this study has beneﬁted mately 5.3 cm. The corresponding maximum unambiguous 21 21 from the authors’ discussions with members of the velocities are yNyq,1 5 10.6 m s and yNyq,2 5 7.95 m s . DWD forecasting department concerning the in- The dual-PRF dealiasing technique relies on the basic as- terpretation of the rotation and rotation track com- sumption that the velocities (of azimuthally adjacent pixels) posites in particular. Last but not least, we thank the to be measured are identical. If this assumption is fulﬁlled,

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range are required. Thus, a dealiasing algorithm was developed running within POLARA at DWD’s Central Ofﬁce, where the complete datasets are gath- y ered. Then, (i21,j) is replaced by a phase-averaged mean calculated within [2yNyq,i21, 1 yNyq,i21]fromthe y 2 # # 1 6¼ six neighbor values (k,l) with i 1 k i 1, k i and j 2 1 # l # j 1 1. These six neighbor values with the given indices are related to the same maximum unambiguous velocity yNyq,i21 5 yNyq,i11 6¼ yNyq,i.

APPENDIX B

Complete List of the Properties of Mesocyclone Detections An overview is given below of all calculated attributes

FIG. 16. Frequency distributions of KONRAD cell lifetime for the mesocyclone objects detected by the MCD (see without (blue curve) and with associated mesocyclone detection also Table 2). (colors indicate the maximum mesocyclone severity). a. Geographical coordinates and shape attributes y then an estimate e with related extended maximum un- A digital elevation model with 1-km resolution is used y ambiguous velocity Nyq,e can be derived from the measured for height above ground layer (AGL) calculations. velocities y1 and y2, d Latitude and longitude center coordinates clat and clon (8), f y 2 f y l f f y 5 1 2 2 1 # y 5 1 2 . (A1) respectively, are calculated as the shear weighted location e 2 Nyq,e 2 f1 f2 4 f1 f2 of the lowest 3 km (or less if the whole mesocyclone does not extend over 3 km) of the 3D mesocyclone object. y ’ 21 Inserting numbers into Eq. (A1) yields Nyq,e 32 m s . Here, all pixels and their shear values within the 3D The dual-PRF dealiasing is performed at the radar site in mesocyclone object region are evaluated. the radar system’s signal processor in real time. Introducing d The mesocyclone base hmeso,base and top hmeso,top (km) i as azimuth and j as the range index, Eq. (A1) becomes are calculated as the height (AGL) of the lowest and y 2 y highest 2D features, respectively. fi21 (i,j) fi (i21,j) y 5 . (A2) d The mesocyclone depth hmeso (km) is defined as the e,(i,j) f 2 f i21 i difference between the mesocyclone top and base The estimate as given by Eq. (A2) is not used directly, heights. d since both measured velocities have errors that contribute For the mesocyclone diameter dmeso (km), the di- y ameter of the largest 2D feature is used, defined by to the error in e,(i,j). Instead, one analyses possible esti- y0 the maximum of the estimates of range and azimuth mates corr,(i,j)(n), which represent possible aliasing correc- y extensions as given in Zrnic´ et al. (1985). tions of the originally measured value (i,j) and are given by d The mesocyclone equivalent diameter dmeso,equi (km) y is calculated as the diameter of the circle that y0 (n) 5 y 6 2n y , n # Nyq,e. (A3) corr,(i,j) (i,j) Nyq,i y covers the same area as the group of pattern vectors Nyq,i composing the largest 2D feature. The term dmeso,equi Here, n is an integer confined by the ratio of the ex- is used to make elongated features more comparable. tended maximum unambiguous velocity to the maximum unambiguous velocity of the given ray. Minimizing b. Doppler velocity attributes jy 2 y j 5 jy 2 y 7 y j e,(i,j)(n) corr,(i,j) e,(i,j) (i,j) 2n Nyq,i with respect Doppler velocity attributes are evaluated by consid- to n yields nmin and thus the sought for correction is ering all pattern vectors that belong to the 3D mesocyclone y 5 y0 5 y 1 y object. Each 1D pattern vector has an azimuthal shear and a corr,(i,j) corr,(i,j)(nmin) (i,j) 2nmin Nyq,i. (A4) specific angular momentum value. The maximum and mean y This procedure will result in data loss if (i21,j) is not values are the maximum and the arithmetic mean of all the available, since two velocity estimates at the same pattern vectors, respectively. Shear values are given in units of

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