Radar-based hail detection

Atmospheric Research 144 (2014) 175–185

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Radar-based hail detection Kateřina Skripniková a,b,⁎, Daniela Řezáčová b a b

Charles University in Prague, Faculty of Science, Department of Physical Geography and Geoecology, Albertov 6, 128 43 Prague, Czech Republic Institute of Atmospheric Physics, ASCR Boční II 1401, 141 31 Prague, Czech Republic

a r t i c l e

i n f o

Article history: Received 21 November 2012 Received in revised form 29 May 2013 Accepted 4 June 2013 Available online 13 June 2013 Keywords: Hail detection Weather radar Hail damage risk

a b s t r a c t Damaging hailstorms are rare but are significant meteorological phenomena from the point of view of economic losses in central Europe. Because of the high spatial and temporal variability of hail, the proper detection of hail occurrences is almost impossible using ground station reports alone. An alternate approach uses information from weather radars. Several algorithms that use single-polarisation radar data have been developed for hail detection. In the present study, seven algorithms were tested on well documented recent hail events from Czechia and southwest Germany from 2002 to 2011. The study aimed to find the optimal threshold values for the applications of these techniques over the Czech territory and for evaluating the climatology of hail events. The results showed that the Waldvogel technique and the NEXRAD severe hail algorithm were the most accurate methods for hail detection over the area of interest. A combined criterion was proposed based on a combination of previously tested techniques. The precision of this “combi-criterion” was demonstrated for a severe hail event. The abilities of the tested criteria to provide information about a hail-fall area distribution and hail damage risk over the Czech territory were shown and discussed. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The occurrence of severe hail in Czechia is rare, but these are significant meteorological phenomena from the point of view of damage to agriculture and property. Hail events are limited in time and space, and the ground observation network can provide only partially complete information about the hail spatial distribution. The difficulty of determining the hail spatial distribution based on ground station data was expressed in the Climate atlas of Czechia (2007), which presented a map of the average annual number of days with hail for the period from 1981 to 2000. In this work we are interested in large hail, which can cause significant damage. The hail dimension implicitly comes out from the data about hail occurrence used in this study. Experimental or operational hailpad networks in some European countries provide more detailed information about ⁎ Corresponding author at: Institute of Atmospheric Physics, ASCR Boční II 1401, 141 31 Prague, Czech Republic. Tel.: +420 737 289 021. E-mail address: [email protected] (K. Skripniková). 0169-8095/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.atmosres.2013.06.002

hail on the ground (Manzato, 2012; Berthet et al., 2011; Pocakal, 2011; Sioutas et al., 2009). For example, four hailpad networks operating in the most hail prone regions of France use more than 1000 hailpad stations (Berthet et al., 2011) and the studies of Giaiotti et al. (2001, 2003) demonstrate the potential of ground based networks in the Italian plain of Friuli Venezia Giulia. However, there is currently no hailpad network in Czechia. To obtain information about the hail risk distribution over the Czech territory, it is useful to use weather radar data, possibly in combination with aerological or satellite data. The radar data provide information with high temporal and spatial resolution. There are two C-band single-polarisation radars that have been operating in Czechia since 2000 (Novak, 2007). Single-polarisation weather radar cannot distinguish among different types of hydrometeors, but some features in the reflectivity data, including high reflectivity occurrences at specific levels, can represent physical processes that are related to hail growth. Several methods for hail detection with single-polarisation weather radar data were developed and tested in different parts of the

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world. Some methods use threshold values for a hail-related quantity, such as reflectivity in low-level CAPPI (Geotis, 1963), vertically integrated liquid water (Amburn and Wolf, 1997) or the height difference between the zero isotherm and the highest level of the 45 dBZ reflectivity (Waldvogel et al., 1979). Other methods transform radar-based quantities into probability values, such as the Hail Detection Algorithm (Witt et al., 1998) and the Probability of Hail (Delobbe and Holleman, 2006). Some hail detection algorithms are based solely on radar measurement data (Geotis, 1963; Amburn and Wolf, 1997). Several algorithms make use of radar measurements together with other meteorological information; for example, aerological data are often used (Waldvogel et al., 1979; Witt et al., 1998). Auer (1994) and Hardaker and Auer (1994) proposed a method that combines radar reflectivity data with infrared cloud-top temperatures from satellite imagery. Some more recent studies deal with radar-based identification of hail. Lopez and Sanchez (2009) calculated a number of variables derived from radar parameters, classified them by means of logistic regression and linear discriminant analysis, and combined selected variables to develop a new discriminating tool. Both statistical models selected mostly the traditional radar parameters for hail identification such as VIL, maximum reflectivity, height of the maximum reflectivity, maximum reflectivity change rate, storm top, and the tilt of the storm. The variable with the greatest weight in the final function was in both cases VIL. Makitov (2007) dealt with the algorithm for separating hail and rain parts of radar echo, which is needed to improve the accuracy of radar-based estimation of hail kinetic energy. He proposed an algorithm based on the empirical relationship between hail probability and the altitude of the 45 dBZ contour above the level of zero isotherm. Mallafre et al. (2009) considered hail identification techniques for Ebro valley region in Spain. They did not found a significant difference between the various methods, however kinetic energy flux was recognised to be the best parameter for distinguishing between hail and no-hail precipitation in the studied area. The most recent studies use data from dual-polarisation radars, which become widely used (e.g. Chandrasekar et al., 2013; Kaltenboeck and Ryzhkov, 2013). In the present study, seven hail detection methods were selected according to their data availability and after considering their simplicity of operational use. The selected methods were converted into hail criteria using appropriate threshold values, and those methods with the best capabilities in the studied areas were used to estimate a hail risk distribution over the Czech territory. The present study addresses the capabilities of selected hail detection methods in southwest Germany and Czechia. In both areas, data from C-band Doppler radars were used. In Czechia, two radars, which are operated by the Czech Hydro-Meteorological Institute (CHMI), cover the territory with measurements, and a merged product of radar reflectivity is provided to users (Novak, 2007). In Germany, radar data from the Institute for Meteorology and Climate Research (IMK) of the Karlsruhe Institute of Technology were used (Kunz and Puskeiler, 2010).

The study has the following sections. In the second section, the selected hail detection algorithms and input data are described. The third section addresses the sensitivity tests of the hail detection criteria and presents the test results; this section includes the application of criteria to several hail events in Germany (Section 3.1) and Czechia (Section 3.2). In the fourth section a new combi-criterion is defined which combines the information of several basic criteria. The capabilities of these criteria are demonstrated through the analysis of a severe hail event in 2010 (Section 4.1), and the hail risk over the Czech territory is considered in Section 4.2. The summary of results and outlook for future work are included in Section 5. 2. Hail detection algorithms and input data Seven methods that use radar data for hail detection were tested. Data availability was considered when choosing the methods and adjusting the algorithms. CAPPI data from single-polarisation C-band radars were available for the days with several established hail events, and sounding data from Prague and Stuttgart were also accessible. The tested hail detection techniques can be described as follows. CAPPI method: a simple method that aims to distinguish hail from rain and is based on a plan-position indicator of the radar reflectivity at a constant altitude (CAPPI). Holleman et al. (2000) tested this method and used a CAPPI of 0.8 km. To distinguish rain from hail, Schuster et al. (2006) applied the CAPPI reflectivity at an altitude of 1.5 km with a threshold reflectivity value of 55 dBZ. The same threshold was proposed by Geotis (1963). Mason (1971) reported that if the 55 dBZ value represented rain, then it would imply improbably high rainfall rate values. In this study, we applied CAPPI values of 2 km. This level was selected to be high enough to consider a typical range of the altitudes of Czechia and the altitudes of the radar sites. For instance, the mean height of the zero isotherm in summer months 2007–2011 as detected by the sounding station Prague-Libus is 3100 m a.s.l. ZMAX method: this method is an extension of the CAPPI method. The ZMAX method uses the maximum radar reflectivity in a vertical column (Zmax) instead of the reflectivity at a fixed altitude. The ZMAX method as a hail warning product is present in the Rainbow processing software of Gematronic radars (Holleman, 2001). A threshold value of 55 dBZ is used (Kunz and Puskeiler, 2010). VIL method: the vertically integrated liquid water content (VIL) is the basis of this method. Greene and Clark (1972) introduced VIL, which converts three-dimensional radar data to a two-dimensional display via the conversion of radar reflectivity to the liquid-water content and subsequent vertical integration. The VIL can be determined by the following equation (Amburn and Wolf, 1997): −6 

VIL ¼ ∑3:44  10


4=7 Zi þ Ziþ1 =2 Δh;

ð1Þ

where Zi and Zi + 1 are radar reflectivity values at the lower and upper portions of the sampled layer, respectively, and Δh is the vertical thickness of the layer in metres. Although VIL was designed to show the rainfall potential, high values of VIL correlate well with the occurrence of hail. There are no obvious VIL values to use as threshold values for hail detection. Amburn

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and Wolf (1997) mention that storms in colder air masses can produce hail when VIL values are lower (25–35 kg/m2) than storms in warmer air masses (50–60 kg/m2). It is shown by Giaiotti et al. (2003) that in the plain of Friuli Venezia Giulia even small hailstones can succeed in reaching the ground according to the colder boundary layer in April and May. This can explain the lower VIL values at hail in colder air masses. Kitzmiller et al. (1995) found different maximum values of VIL in severe summer storms for regions of the United States: Florida (50 kg/m2), the Great Plains (30 kg/m2) and the Northeast (20 kg/m2). Meteorologists of the United States National Weather Service used the VIL of the day for warning purposes. The VIL of the day is found according to the first hail occurrence in a day (Lenning and Fuelberg, 1998). VIL density method: to improve the VIL based warning method for severe hail, Amburn and Wolf (1997) proposed VIL density, which is defined as the VIL value divided by the value of the radar echo top height. VIL density indicates storms with high reflectivity relative to the storm height. For hail detection, they suggested a VIL density threshold of 3.5 g/m3. Waldvogel method: the aforementioned methods use radar reflectivity data alone. Other methods, such as the Waldvogel method, make use of additional data. For example, information about the vertical temperature profile from atmospheric sounding can be added. Waldvogel et al. (1979) proposed a hail criterion which uses the zero isotherm height. The Waldvogel method applies the maximum altitude, H45, at which a reflectivity of 45 dBZ is found and compares it with the zero isotherm height, H0. The presence of hail is likely if H 45 ≥H 0 þ 1:4 km:

ð2Þ

The Waldvogel technique was originally examined with data from X-band radar (Waldvogel et al., 1979). Because we used C-band radar data, we aimed to find not only the best threshold value for the height difference between H45 and H0 but also the best value for the reflectivity parameter. We tested values from 41 dBZ to 60 dBZ and determined the corresponding height levels for the threshold height difference. Witt et al. (1998) developed a Hail Detection Algorithm (HDA) for the network of WSR-88D radars in the United States. The HDA contains two separate components, one for detecting hail of any size and one for detecting severe hail. The first part of the HDA is based on the Waldvogel criteria (Waldvogel et al., 1979). The maximum height of the 45 dBZ reflectivity above the zero isotherm level is converted into a probability of hail of any size. Height differences of 1.6 km and 5.5 km correspond to probabilities of 0% and 100%, respectively. The HDA is used in the CHMI to determine the probability of a hail occurrence. The HDA is then termed HAIL PROB, and the zero isotherm height is identified from a nearby aerological sounding (Rezacova et al., 2007). The second part of the HDA attempts to estimate the probability of severe hail by designing a Severe Hail Index (SHI). A warning threshold for the SHI is calculated from the height of the freezing level, and the probability of severe hail is determined from the SHI value and the warning threshold (Witt et al., 1998). Originally, the SHI was calculated by using outputs from the Storm Cell Identification and Tracking (SCIT) algorithm (Johnson et al., 1998). The SCIT detects storm cells, thus solving the problem associated with hail cores that are

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stretched across the grid boundary. We did not use a cell identification algorithm in the present study. SHI method: SHI is based on the semi-empirical relationship between the kinetic energy flux of the hailstones, Ė, and the radar reflectivity (Waldvogel et al., 1978a,b): Ė ¼ 5  10

−6

0:084Z

 10

:

ð3Þ

The SHI value is calculated by vertically integrating the kinetic energy flux weighted by reflectivity-based W(Z) and temperature-base WT(H) weighting functions (Witt et al., 1998). HT

SHI ¼ 0:1 ∫ W T ðH Þ W ðZ Þ E_ dH;

ð4Þ

H0

where H0 is the melting level height, and HT is the height of the top of storm cell. The weighting functions (Witt et al., 1998) assign weights to the values between 0 °C and − 20 °C for temperature and between 40 dBZ and 50 dBZ for reflectivity. The weighting function for reflectivity was used by Federer et al. (1986) when calculating the flux of hail kinetic energy but with higher reflectivity threshold values of 55 and 65 dBZ. The SHI is primarily sensitive to high reflectivity values at temperatures near − 20 °C or colder, where most hail growth occurs. During the initial testing of SHI, Witt et al. (1998) found that the SHI values are close to 300 J/(m.s) for hail with diameters of 19 mm and greater. The reflectivity-based weighting function W(Z) is used to define a transition zone between rain and hail reflectivity. The default values for this algorithm were set to 40 dBZ and 50 dBZ. Witt et al. (1998) noted that the default values cannot be treated as fixed. Because they are lower than those used by Federer et al. (1986), we also tested values of 45 dBZ and 55 dBZ. POSH method: the Probability of Severe Hail (POSH) is determined from the SHI and the warning threshold value WT. The WT value is calculated from the height of the freezing level by using an empirical relationship (Witt et al., 1998): WT ¼ 57:5H 0 −121; if WTb20 then WT ¼ 20:

ð5Þ

The POSH value is determined by using an empirical relationship (Witt et al., 1998):  POSH ¼ 29 ln

 SHI þ 50: WT

ð6Þ

POSH is given in %, negative POSH values are set to 0, and POSH values larger than 100 are set to 100. The hail detection methods are based on various properties of clouds and cloud environment, which should indicate the hail occurrence. The CAPPI and ZMAX methods are looking for the high reflectivity values, which should represent highly reflecting targets, possibly hail. The VIL and VILdensity methods look for the areas with high liquid water content that might produce supercooled droplets essential for the hail growth. In the Waldvogel method, elevated high reflectivity reflects strong updraft, which is able to hold the highly reflecting targets in the height. When the level of zero isotherm is used in the methods, the thermodynamic properties of the environment are represented, especially the potential supercool water supply and the

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vertical extent of melting layer. The POSH algorithm examines the area above 0 °C isotherm, where the hail formation occurs. The highest emphasis is given to the area above the −20 °C isotherm. And only the reflectivity values higher than 40 dBZ, and with most importance higher than 50 dBZ, are considered. Data from C-band single polarisation radars were used for the calculations. For Czechia, merged pseudo-CAPPI data from the two CZRAD radars were used (Novak, 2007). German radar data from radar in Karlsruhe provided CAPPI data (Kunz and Puskeiler, 2010). For both areas, the radar data had a horizontal resolution of 1 × 1 km, a CAPPI vertical resolution of 500 m and a time step 5 min. The areas covered by the radar data are shown in Fig. 1. If additional atmospheric sounding data were needed, then the data from the Prague-Libus station in Czechia and from the Stuttgart-Schnarrenberg station in Germany were used. In all cases, the data from the noon sounding were used for the entire day and the entire area of interest. 3. Sensitivity tests The seven methods, i.e., CAPPI, Zmax, VIL, VILdensity, Waldvogel, SHI and POSH, were tested to determine their optimal thresholds for hail detection. The identification of whether the radar pixel related value exceeded the threshold transformed the method into a YES/NO criterion for distinguishing events with and without hail. We primarily searched for threshold values in the literature, which provided an initial list of potential threshold values. The threshold range was determined according to several documented hail events in Czechia and Germany. We searched for thresholds when at least

one radar pixel in the area of hail confirmed the occurrence of hail. Two types of sensitivity tests were made according to the data that were available in each of the studied areas (Czechia and SW Germany). 3.1. German hail events The verification with German data was performed using information from an insurance company in Baden-Württemberg and radar information from IMK Karlsruhe. The area of interest was selected around Stuttgart. This location is halfway between the radar location and the radar range boundary and is not shaded by mountains. Sounding data were obtained from the Stuttgart-Schnarrenberg station, and the insurance data were expected to be most accurate here, as they cover a densely populated area. From the information about hail damages in Baden-Württemberg, 25 days from 2002 to 2010 were selected according to the amounts paid for hail damages by an insurance company along with high reflectivity occurrences in the area of interest. Information about hail damage in zip-code zones was available for these 25 days. The area of interest around Stuttgart contains 239 zip-code zones with their average area of 20 km2. The information about hail damage indicated the loss amount for each individual zip-code zone for the entire day; however, more detailed time indications were not available. The maximum daily values of the tested hail methods were computed over the area of interest for each of the 25 selected days. Various thresholds were then applied to distinguish

Fig. 1. Radar ranges of the employed radars. Left: radar in Karlsruhe, southwest Germany (www.radar-info.de). Right: CZRAD network in Czechia, radar Brdy-Praha and radar Skalky, maximum radar ranges (circles) and ranges for precipitation intensity assessed up to a height of 1500 m above the terrain (www.chmi.cz).

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between hail and no hail radar pixels. The presence of a hail-indicating pixel in zip-code zones with hail damage losses was considered. A hail event observed was defined as follows. In the territory of interest, the radar pixels were assigned to the zip-code areas. A pixel was said to be a hail pixel, when more than 3 claims, each with at least 100€ of hail damage, were found in the corresponding zip-code area on a date. Detected hail pixel was recognised when a hail detection algorithm resulted in a value higher than the tested threshold at least once in a day. Pixels were sorted to compile a contingency table according to the following definitions: Hit

At least one pixel meeting the criterion in a zip-code zone with hail damage on a given day. Miss No pixel meeting the criterion within a zip-code zone with hail damage. False alarm At least one pixel meeting the criterion in a zip-code zone without hail damage. Three traditional verification scores were calculated from the contingency table: probability of detection (POD) = hit / (hit + miss), false alarm rate (FAR) = false alarm /

179

(hit + false alarm), and critical success index (CSI) = hit / (hit + miss + false alarm). Fig. 2 shows the POD, FAR, and CSI values for the individual hail detection methods as a function of the corresponding threshold. For all methods, the POD decreases monotonically with an increasing threshold. The increasing threshold causes decreasing FAR values with the exception of POSH, where the FAR starts to increase again for very high threshold values. The most useful measure is the CSI behaviour. All of the CSI curves show maxima at a certain threshold value. The position of the CSI maximum was indicative of how to modify the threshold value. The highest CSI value (0.336) was obtained for the POSH method with reflectivity thresholds that were shifted to 45 dBZ and 55 dBZ and with a threshold of 50% (Fig. 2). The differences among the highest CSI values for SHI, POSH 40–50, and Waldvogel 56 criteria were very small. The CSI values for the Waldvogel method with various reflectivity factors and height difference thresholds are shown in Fig. 3. They clearly indicate the threshold region with the highest CSI values; the absolute maximum CSI of 0.323 appeared for 56 dBZ and a level difference of 3500 m.

Fig. 2. Verification with German data. The scores of POD, FAR and CSI for the tested hail detection methods as a function of the corresponding threshold value. The range of reflectivity, which was used for the reflectivity weighting function, is indicated at the top of SHI and POSH subpanels. Similarly, the threshold reflectivity, applied in the Waldvogel method, is indicated at the top of the Waldvogel subpanels.

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Fig. 3. CSI values obtained from testing the Waldvogel method as a function of the threshold reflectivity (horizontal axis) and height difference values (vertical axis). Based on the verification using German data. Table 1 Hail events in Czechia included in the verification. The fifth column gives the total number of pixels (time window of 4 h, space window of 40 × 40 km) with column maximum reflectivity, Zmax ≥ 55 dBZ (58 dBZ). The sixth column indicates the main source of information about hail-fall: torn — CHMI tornado webpage (www.chmi.cz/torn); news — newspaper; MB — Meteorological Bulletin; chmi — CHMI significant weather webpage (old.chmi.cz/meteo/om/prubeh/ vyzpoc/); bourky — thunderstorm webpage (www.bourky.com); ins — insurance claims; eye-w — eye-witness; ESWD — European Severe Weather Database (www.essl.org/ESWD). Date, time (UTC)

Location

Size information

CAPE [J/kg]

Zmax ≥ 55 dBZ (58 dBZ)

Source

23.6.2002, 14:00 10.7.2002, 15:00 22.7.2003, 17:00 23.7.2003, 09:00 23.5.2005, 15:00 30.5.2005, 14:00 30.7.2005, 16:00 21.6.2006, 15:00 25.6.2006, 15:00 12.7.2006, 15:00 14.5.2007, 15:00 25.5.2007, 12:00 21.6.2007, 14:00 23.8.2007, 16:00 1.6.2008, 16:00 25.6.2008, 15:00 3.7.2008, 19:00 9.6.2009, 22:00 2.8.2009, 13:00 12.6.2010, 16:00 15.8.2010, 18:00 22.6.2011, 17:00 7.7.2011, 13:00 19.8.2011, 13:00 24.8.2011, 16:00

Brno Klatovy region Otrokovice Karlovy vary reg. Pelhřimov Praha Soběslav Central Bohemia Strakonice Vodňany region Liberec region Sušice region Kroměříž Písek Praha-east Praha-northeast Počátky Znojmo region Milevsko Vysočina region Praha Mladá Boleslav Ostrava-Poruba Plzeň Vysočina region

Max 6 cm in diameter 15 cm circumference Not specified 3–5 cm in diam., 30 cm layer 5–20 cm layer Car damages Not specified Not specified Over 2 cm in diameter 2 cm in diameter 3–5 cm in diameter Max 2–3 cm in diameter Not specified 1 cm in diam., notable layer 1–2 cm in diameter Not specified Not specified 3 cm in diam., 25 cm layer 2–3 cm in diameter 3 cm in diameter 3 cm in diameter Max 4 cm in diameter 3–4 cm in diameter 3 cm in diameter Max 5 cm in diameter

3441 3622 1545 2008 933 2934 609 2484 2958 1420 534 1053 665 485 3690 1219 3255 1709 438 952 2004 1162 91 2559 1694

1069 (259) 1566 (592) 776 (304) 502 (182) 835 (145) 1392 (496) 1907 (1061) 1682 (466) 1479 (634) 720 (120) 941 (376) 343 (63) 2205 (694) 787 (287) 161 (13) 217 (5) 261 (95) 289 (129) 1048 (477) 522 (188) 620 (273) 229 (24) 167 (47) 94 (15) 726 (200)

torn torn torn news MB ins ins ins MB torn chmi torn chmi torn chmi chmi bourky torn eye-w news news ESWD ESWD bourky ESWD

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Table 2 Threshold values for hail detection by the tested methods as found in the literature and resulting from the verification of German and Czech data. See Section 2 for descriptions of the methods and thresholds. Method

Literature

SW Germany — Stuttgart area

Czechia

CAPPI Zmax VIL VILdensity SHI (40–50 dBZ) SHI (45–55 dBZ) POSH (40–50 dBZ) POSH (45–55 dBZ) Waldvogel (45 dBZ) Waldvogel (>45 dBZ) Combi-criterion SHI (40–50 dBZ) POSH (45–55 dBZ) Waldvogel

55 dBZ 55 dBZ 43 kg/m2 3.5 g/m3

58 dBZ 60 dBZ 45 kg/m2 3.2 g/m3 100 J/(m.s) 100 J/(m.s) 50% 50% 7000 m 3500 m for 56 dBZ

55 dBZ 57 dBZ 34 kg/m2 2.1 g/m3 60 J/(m.s) 50 J/(m.s) 40% 30% 7000 m 3000 m for 54 dBZ

60 J/(m.s) 50% 5500 m for 54 dBZ

60 J/(m.s) 30% 5500 m for 52 dBZ

50% 5500 m

3.2. Czech events Two well-documented hail events from Czechia were discussed in a preliminary study on radar-based hail detection methods (Skripnikova and Rezacova, 2010). In this study, five methods for hail detection were shown to have capabilities for detecting hail in the Czech territory. The hail event database was then enlarged to allow a more thorough verification. Information about recent hail events was collected from a variety of sources (including newspaper articles, insurance reports, and eye-witnesses). The occurrence of hail-fall during the 25 studied days was undisputed (Table 1). The hail-fall event reports contained information about the time, location, hailstone size, and extent of hail damage. The reports were

obtained from reliable sources; in most cases, the event was confirmed by at least two sources. A total of 10 methods were tested (Table 2, first column), including 2 options for the Waldvogel technique, SHI and POSH. Each method was applied with 6 threshold values. Three quantities were studied for all tested methods and thresholds: the SUMPIX gave the total number of pixels which met the criterion, the COVER expressed the number of pixels where the criterion was met in at least one term, and the NUMTERM represented the number of terms when at least one pixel met the criterion. The three quantities were calculated for each hail event, time window of 4 h, and space window of 40 × 40 km. The COVER, SUMPIX and NUMTERM values were then summed for all 25 reported hail events to obtain three global characteristics for each method and threshold.

Fig. 4. The COVER, SUMPIX and NUMTERM (see Section 3.2 for explanation) sums over the 25 reported hail events. The horizontal axis indicates the methods and the threshold values which correspond to the optimal selected criteria.

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Fig. 5. Combi-criterion and its components detecting hail on 15 August 2010, 1600–1955 UTC.

We studied all sets of global SUMPIX, COVER and NUMTERM values corresponding to the 10 methods and all threshold combinations. The 6 sets with minimum variance and minimum mean absolute deviations were found for the global SUMPIX, COVER and NUMTERM values, indicating the threshold range from which the final threshold values were subjectively selected. Fig. 4 shows the global COVER, SUMPIX and NUMTERM values for the final threshold selection. These threshold values were suggested as an optimal selection for use over the Czech territory. The similar behaviours for the COVER, SUMPIX and NUMTERM values based on their minimum variability supported the selection.

4. The definition of combined criterion All of the tested methods were capable of detecting hail in the studied regions. Three of the methods were selected to form a new combi-criterion. The methods were selected according to the highest CSI values from the verification of the German data. The combi-criterion was defined by requiring that at least 1 of 3 basic criteria were met for the detection of a hail occurrence. Although the criteria were highly correlated, the combi-criterion had a slightly higher CSI than the single criteria. By testing many combinations of thresholds for the selected methods, the optimal threshold combination was

Fig. 6. Average annual number of days with hail in the Czech territory (May–August of 2007–2011) based on the combi-criterion. The omitted areas indicate the 15 km range around the radars, where the radar data were not reliable.

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Fig. 7. Relative coverage of the Czech territory (vertical axis) for the ranges of hail days per year (horizontal axis). The minimum, maximum, mean, median and variance values are shown in the legend.

found according to the highest CSI (0.344) when testing German data. To consider the uncertainty of the combined method, the combination of thresholds for the combi-criterion was tested also by using 20 randomly selected hail events from the total number of 25. This was repeated 60 times. In most cases the combination with the highest CSI was the same as when testing the 25 events altogether and the mean highest CSI value was 0.35. Because there was not sharp change in the CSI when the threshold values were shifted, the construction of the combi-criterion for Czechia was kept the same as for the German data but with modified thresholds. The original combi-criterion appeared to be too strict with the Czech hail events. In addition, the optimal thresholds for the single methods were higher for the German data than for the Czech data (see Table 2). Based on these findings, the thresholds for the combi-criterion in the Czech territory were subjectively adjusted. The aim was to find a combination of thresholds, which composes combi-criterion detecting well the Czech hail events. The number of hail pixels detected by the combicriterion was compared for the Czech and German events. The combination giving the most similar number of hail pixels was selected. The three methods forming the combi-criterion consists of the Waldvogel criterion with a reflectivity threshold higher than 45 dBZ, the SHI criterion with reflectivity thresholds of 40 and 50 dBZ and the POSH criterion with reflectivity thresholds of 45 and 55 dBZ (Table 2).

Table 3 Frequency of hail days (at least one pixel detected by the combi-criterion over the whole day) in May, June, July and August (period 2007–2011). Hail days 2007–2011

V

VI

VII

VIII

Absolute frequency Relative frequency

9.2 0.30

11.0 0.37

10.4 0.34

8.4 0.27

4.1. Severe hail event on 15 August 2010 A severe hail event occurred on 15 August 2010. A low-pressure area was moving northward through central Bohemia (western Czechia). An associated cold front propagated from the southwest in the afternoon and triggered pronounced convective activity. In the evening, a storm with marked supercellular features developed. The system moved from southern Bohemia to the north and reached the densely populated area of Prague at 1900 UTC. Severe hail-fall affected the southern part of Prague, where hailstones of approximately 3 cm in diameter caused several injuries and severe damage to roofs, cars and trees. The combi-criterion was calculated for this case, and the locations of the components are depicted in Fig. 5. The combi-criterion represents the severe hail impact in this case. 4.2. Radar-based hail risk over Czechia The hail criteria values were determined from the Czech radar data for the summer months (May–August) of 2007–2011. A hail day in a pixel was defined using the combi-criterion. If at any time in a day the combi-criterion indicated hail in a pixel, then the day was counted as a hail day in that pixel. From the number of hail days in each pixel, a map of the average annual number of days with hail was constructed (Fig. 6). The map showed values up to 1 day with hail per year and confirmed that large hail represents a rare event over the Czech territory. The use of merged CAPPI data from two Czech radars showed a change in the criteria values in the area behind the range of the radar Skalky (western Czechia). This change was reflected in the performance of all single methods. By comparing the frequencies of daily maximum reflectivity values in the different zones according to the radar ranges, shifted thresholds were found for the study area.

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Fig. 8. Diurnal distribution of the relative frequency (%) of hail pixels as indicated by the combi-criterion during summer seasons 2007–2011.

The map of the average annual number of hail days (Fig. 6) was transformed into a histogram (Fig. 7). The histogram indicates the relative area coverage by the number of average annual hail days. Most of the Czech territory has fewer than 0.25 hail days per year based on the results of the combicriterion. The seasonal and diurnal distributions of hail pixels were examined. The seasonal distribution of hail days is shown in Table 3. A day was considered to be a hail day when at least one pixel was detected as hail pixel over the whole day. The results show even values for May, June and July and slightly lower hail day occurrence in August. The histogram in Fig. 8 shows the relative diurnal distribution of hail pixels as obtained from the data available. From the total number of 4256 detected hail pixels nearly 25% refer to the interval of 14–16 UTC. Minimal number of hail pixels was found at the interval 6–8 UTC.

5. Conclusion Several methods for hail detection using single-polarisation radar data were tested with the intention of determining the hail risk distribution and hail climatology in the Czech territory. Records of hail occurrences from southwest Germany and Czechia together with the corresponding radar data were used to find the optimal parameters of the detection methods. A verification based on German data was performed using information about hail damage to buildings, and traditional verification scores (POD, FAR and CSI) were calculated from the contingency table. For the Czech territory, thresholds were selected which indicated the number of hail-impacted pixels and the hail occurrence times in a similar way for all methods. From the verification, optimal thresholds emerged which transformed the hail detection methods into hail criteria. Three of the optimised criteria were used to create a new combi-criterion. The combi-criterion detected hail when at

least one of the criteria based on the Waldvogel method, SHI and POSH indicated a hail occurrence. According to the data used for the verification, we principally detected large hail (at least 2 cm in diameter). The criteria performed well in cases of severe hail-falls. The area distribution of the hail risk based on the hail combi-criterion differed locally from the hail distribution based on ground observations and topography (Climate atlas of Czechia, 2007). It is believed that the variations in the area distribution reflected differences between all hail cases (from 0.5 cm in diameter) and severe hail cases. A map of the average annual number of hail days was constructed that showed values up to 1 hail day per year. The map confirmed that large hail represents a rare event in the Czech territory. A future study will concentrate on gaining information about additional hail events to enlarge the verification data set. This information will make the statistical results more significant. Because the radars in the Czech Republic will be replaced by dual polarisation radars in the future, we propose that future hail detection techniques will be transformed to exploit the potential of the polarisation data. Acknowledgements This work was supported by GACR P209/11/2045, COST CZ LD11044 and SVV 267-202. The Czech radar data were provided by the Czech Hydro-Meteorological Institute. The authors wish to acknowledge the Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology for supplying the German data and for their assistance in data processing. References Amburn, S.A., Wolf, P.L., 1997. VIL density as a hail indicator. Weather. Forecast. 12, 473–478. Auer, A.H., 1994. Hail recognition through the combined use of radar reflectivity and cloud-top temperatures. Mon. Weather Rev. 122, 2218–2221.

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