1. Introduction
Hail is one of the major weather hazards that impacts agriculture and transportation, as well as causing considerable damage to homes and vehicles. Surface hail occurrence and size observations are collected in limited regions and time scales with various approaches (Zhang et al. 2008; Changnon et al. 2009; Punge and Kunz 2016). The lack of consistent, global surface observation networks for hail has limited the study of regional variations in severe hailstorm properties and climatological behavior. As an alternative, remote sensing from satellites is capable of global observation. Spaceborne observations such as passive microwave (Cecil 2009; Cecil and Blankenship 2012; Ferraro et al. 2015) and visible and infrared measurements (Bauer-Messmer and Waldvogel 1997; Ravinder et al. 2013; Merino et al. 2014) can be exploited to get a more comprehensive mapping of hail occurrence. In the current literature, passive channels are utilized in different applications. Visible and infrared satellite imagery from geostationary satellites has potential for the detection and nowcasting of hailstorms in particular regions (Bauer-Messmer and Waldvogel 1997; Liu et al. 2009; Ravinder et al. 2013; Merino et al. 2014; Melcón et al. 2016). Meanwhile, by using passive microwave sensors on low-Earth-orbit satellites, algorithms for hailstorm identification have been developed and applied to constructing global proxy hail climatological descriptions (Cecil 2009; Cecil and Blankenship 2012; Ferraro et al. 2015).
In theory, visible and infrared channels might detect potential hail occurrence according to indirect relationships between low brightness temperature (TB) or temperature difference near cloud top and the presence of strong updrafts and hail lower in the cloud. Regional differences in hailstorm characteristics make it difficult to apply such indirect relationships globally, however. Melcón et al. (2016) found different characteristics of cloud-top TB between the south of France and the middle Ebro valley in Spain. For this reason, techniques that identify hailfall on the basis of infrared TB probably need to be adapted to each specific study region. Spaceborne passive microwave sensors detect upwelling radiation from the surface, which is scattered by graupel and hail particles in convective clouds, resulting in TB depressions. The measured radiation reaching the sensor depends on column-integrated scattering and emission effects, such that a deep layer of graupel or small hail might not be distinguished from a shallower layer of large hail. The Precipitation Radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite (Kummerow et al. 1998) has been used extensively in the study of tropical and subtropical convection (Nesbitt and Zipser 2000; Cecil et al. 2005; Zipser et al. 2006; Liu et al. 2008; Cecil 2009; Jiang et al. 2011). The PR could detect radar reflectivity with 250-m range resolution, thus providing detailed information about the vertical structure of storms. The dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement (GPM) mission Core Observatory (Hou et al. 2014) extends such measurements to ±65° latitude. This motivates us to examine spaceborne radar detection of hailstorms to better understand the global hail distribution.
Studies using ground-based, single-polarization radar reflectivity in particular regions have established good relationships with hail occurrence (Waldvogel et al. 1979; Auer 1994; Witt et al. 1998; Donavon and Jungbluth 2007; Skripnikova and Rezacova 2014; Kunz and Kugel 2015). Waldvogel et al. (1979) used the presence of 45-dBZ echo 1.5 km above the freezing level to detect hail. Holleman et al. (2000) compared five different criteria for hail detection that are based on reflectivity and found the Waldvogel criterion (Waldvogel et al. 1979) to be the most appropriate, having its maximum critical success index (CSI) after being adjusted to 50 dBZ between 3 and 5 km above the freezing level. The 3–5-km height above the freezing level is consistent with the well-accepted hail-growth zone between −10° and −30°C (Miller et al. 1988). Similar algorithms using single-polarization radar reflectivity are also found to be efficient in detecting severe surface hailstones in China (Guo et al. 2015) and in southeastern Germany (Kunz and Kugel 2015). The most effective thresholds for hail identification do vary some in the studies from different regions.
Ground-based radars typically have limited vertical resolution (~1 km) as compared with the spaceborne radars used in this study. Ground-based radars used for hail detection also typically have longer wavelengths (several centimeters for S band and C band) than does the Ku-band (2 cm) and higher-frequency spaceborne radars. With 16 years of observations from TRMM and continuing observations from GPM, we seek here to define relationships between hail occurrence and vertical characteristics of Ku-band reflectivity. A related study by Mroz et al. (2017) uses GPM Core Observatory measurements together with ground-based dual-polarization radar signatures of hail. A key distinction between that study and this one is that the Mroz et al. (2017) hail signatures include the presence of hail aloft, with no minimum hail-size requirement. Our study uses reports of large hail (>19 mm) that reaches the surface.
This paper will focus on the ability to detect storms producing large hail that reaches the surface by using spaceborne precipitation radar and passive microwave brightness temperature observations together with surface reports of hail from the southeastern and south-central United States. After defining criteria for hailstorm detection, we examine the application of constructing a global proxy hail climatological description from TRMM and GPM observations. We discuss discrepancies between results that are based on radar reflectivity criteria and microwave TB criteria. We recognize that empirical relationships developed from cases in one region may not be equally suitable elsewhere but believe that they allow credible identification of potential hailstorms as used here.
2. Data and method
To validate potential hail detections using satellite observations, ground-based reports of large hail over the United States are utilized. The hail observations maintained and updated by the National Climatic Data Center (now part of the National Centers for Environmental Information) for the publication Storm Data (Schaefer et al. 2004; Allen and Tippett 2015) are matched with TRMM satellite observations in the southeastern and south-central United States. The hail diameters are listed in Storm Data with 0.25-in. (6 mm) precision, but in reality certain sizes are preferentially reported on the basis of the National Weather Service’s minimum thresholds for severe weather [0.75-in. (19 mm) diameter before 2010, or 1 in. (25 mm) since 2010] and the sizes of common objects [e.g., 1.75-in. (44 mm) golf balls, 2.75-in. (70 mm) baseballs, and 4.5-in. (114 mm) softballs]. We focus on the hailstorms that produced hail of at least 19 mm in diameter; almost all hail reports in Storm Data are at least that size. We further stratify the reports into three size ranges: 0.75–1.0 in. (19–25 mm), 1.25–2.0 in. (32–51 mm), and >2.0 in. (>51 mm).
The satellite observations used in this study are from the TRMM precipitation-feature (PF) database (Liu et al. 2008). Using an event-based analysis method, the TRMM PF database provides an efficient approach for studying properties of convection, such as that in thunderstorms (Cecil et al. 2005) and hurricanes (Jiang et al. 2011). A PF is defined by grouping all contiguous pixels that have nonzero near-surface rainfall detected by the TRMM Precipitation Radar. The properties of each PF are summarized using collocated observations from the PR, TRMM Microwave Imager (TMI), Lightning Image Sensor, and Visible and Infrared Scanner. Because of the coverage of TRMM’s orbit (35° inclination) and ground hail reports, only hail reports and PFs over the southeastern and south-central United States (30.5°–36°N, 105°–81.5°E) are used to develop and validate the hail-detection method. The years 1998–2013 are used.
In this study, we focus on using the temperature at the maximum height attained by a given radar reflectivity value (T_MAXHT), as well as the minimum polarization-corrected temperatures (PCT; Spencer et al. 1989) at 85 GHz (MIN85PCT) and 37 GHz (MIN37PCT) in the level-2 data of the PF database. For hail-detection algorithms using single-polarization radar reflectivity in the literature, there are typically two approaches. One is based on vertical distance from high radar echoes relative to the freezing-level height (Waldvogel et al. 1979), and another is to use the temperature with high radar echoes (Auer 1994). Because hail growth mostly occurs with supercooled liquid water in temperatures from −10° to −30°C, it is reasonable to relate the surface hail with high radar reflectivity values at these temperatures. Here, we utilize temperatures of radar echo tops to develop thresholds to reduce the areal discrepancy, especially the discrepancy between the midlatitudes and tropics. The T_MAXHT values from 20 to 60 dBZ in 1-dB intervals are calculated by combining temperature profiles from the ERA-Interim reanalysis (Dee et al. 2011) with the maximum reflectivity profile of each PF. Note that these temperature profiles provide only a rough approximation of the echo-top temperatures, since the reanalysis does not depict the in-storm conditions.
The first step in developing the hail-detection criteria is to collocate the hail reports with TRMM PFs. During collocation, TRMM PFs within 1 h and 1° range from each hail report are selected, following the method used in Cecil (2009) and Ni et al. (2016). Then, if there are multiple PFs associated with a single hail report, the PF with the minimum MIN37PCT is chosen to be the hail PF. It is also possible that a single hail PF could be initially collocated with multiple hail reports. In this case, the hail report with the maximum hail size is used to build a one-to-one association between a hail PF and a storm report. The PFs that are in the selected domain but are not collocated with any hail report are referred to as nonhail PFs. An example of a squall line with five collocated hail reports is shown in Fig. 1. The overpass time of TRMM is 0147 UTC 28 November 2005. Several pixels with PCT depressions are found near the hail-report locations. The large, contiguous precipitation area is treated as a single hail PF, and it is assigned the largest hail size (1.75 in.) from those five reports within 1 h. The minimum values of PCT and maximum values of radar reflectivity (at each vertical level) anywhere inside the contiguous precipitation area are assigned as this hail PF’s properties. The MIN37PCT is 198 K. A cross section (Fig. 1c) is shown along the convective line. Two deep convective areas are found with 40-dBZ echo-top height around 10 km. After the collocation of 16 years of TRMM PFs with U.S. hail reports, 2231 hail PFs are defined. The numbers of collocated hail PFs in different hail-size ranges are listed in Table 1. The mean values of T_MAXHT40 and of microwave PCT do depict increasing convective vigor (colder echo tops and greater PCT depressions) for increasing hail sizes.
Example of one hail PF at 0147 UTC 28 Nov 2005: (a) TMI 37-GHz PCT, (b) PR near-surface reflectivity, and (c) a cross section of selected convective cells. The five collocated hail reports from Storm Data are marked with times signs in (a) and (b). In (c), the thick dashed and solid lines are for the 37- and 85-GHz PCTs, respectively.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
Number of hail PFs, mean temperature at 40-dBZ echo top, and mean minimum 37- and 85-GHz PCT for different hail-size ranges in the southeastern and south-central United States from 1998 to 2013. Standard deviations are shown in parentheses.
The GPM Core Observatory satellite was launched in 2014, with coverage to 65° (Hou et al. 2014). Its instrument suite provides analogs to the key TRMM measurements that are used here. To be specific, the GPM Ku-band precipitation radar has a footprint and a resolution close to those of the TRMM PR, and the GPM Microwave Imager includes 89- and 36.5-GHz channels with footprint sizes similar to 85 and 37 GHz on TMI. A GPM PF database has been constructed using the same procedures as the TRMM PF database. In the discussion of the global hail distribution, we use the GPM PF database that is constructed from version-4 GPM products from March 2014 to February 2017. Using the same collocation method, 237 surface hail reports have been collocated with three years of GPM PFs over the whole continental United States. Here, we use these reports to validate the regional variation of the hail-detection method by using TRMM.
3. Results
a. Detection of hail with precipitation radar reflectivity
The mean values of T_MAXHT40 are calculated for different hail-size ranges in Table 1. The smallest hail category (up to 1-in. or 25-mm diameter) has a 40-dBZ echo reaching up to the −18°C level in the mean. The mean 40-dBZ echo top for PFs with 1.25–2.0-in. (32–51 mm) diameter hail is −24°C, with a −32°C mean for larger hail. The fraction of TRMM satellite observations satisfying those criteria is mapped in Fig. 2. This gives credible distributions of potential large hailstorms, highlighting regions that have been identified in other studies as producing abundant lightning and/or hail. Using thresholds with colder 40-dBZ echo-top temperatures (Fig. 2c), the potential for large hail is identified over regions that are similar to where the most intense thunderstorms are known to occur (Zipser et al. 2006).
Fraction of TRMM overpasses from 1998 to 2013 for each 1° × 1° grid box that have a PF satisfying the 40-dBZ echo-top temperature criteria listed in Table 1, representing the three hail-size ranges.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
Next, we aim to determine optimum criteria for detecting storms that produce large hail capable of reaching the surface. Skill scores are calculated using a range of combinations of radar reflectivity and temperature. To conduct this calculation, contingency tables are constructed using the number of hail PFs and nonhail PFs that meet specific criteria (hits a and false alarms b) or that fail to meet those criteria (misses c and correct nonevents d). Four skill scores are utilized (Heinselman and Ryzhkov 2006). They are the probability [Prob = a/(a + b), where 1 is perfect], miss rate [MS = c/(a + c), where 0 is perfect], critical success index [CSI = a/(a + b + c), where 1 is perfect], and Heidke skill score {HSS = 2(ad − bc)/[(a + c)(c + d) + (a + b)(b + d)], where 1 is perfect}. The CSI combines the characteristics of Prob and MS. The HSS contains all of the information in the contingency table.
Skill scores for combinations of reflectivity and temperature are shown with color fills in Fig. 3. For most reflectivity or T_MAXHT values, the Prob and MS are monotonic (Figs. 3a,b), but Prob has a nonmonotonic area between 28 and 40 dBZ and below −55°C (Fig. 3a). The high Prob for those combinations of high reflectivity and very cold echo tops likely results from a small number of PFs with faulty reflectivity measurements, or faulty assignment of temperature profiles. Very few storms loft enough graupel or hail so high in the troposphere to produce such values, and therefore a small number of artifacts could skew the statistics there. Combining the performance of Prob and MS, CSI is found to have its maximum score (0.24) for T_MAXHT44 below −22°C (Fig. 3c). The maximum HSS (0.37) also results in the same criteria (44 dBZ below −22°C; Fig. 3d), which are somewhat similar to criteria established from ground-based radar studies (Waldvogel et al. 1979; Cintineo et al. 2012) and GPM Ku-band reflectivity (Mroz et al. 2017). Although 44 dBZ at −22°C have been picked as the best criteria, all high reflectivity values in the mixed-phase temperature range have high CSI and HSS scores, which means that those criteria would probably be just as good as indicators of surface hail. Also, we acknowledge there may be regional differences in the true relationships between such measurements and hail occurrence. To validate this to some extent, 237 collocated GPM hail events have been analyzed similarly and are shown as contours in Fig. 3. The results from GPM are consistent with those from TRMM, which suggests that there is not a large difference in the hail-detection criteria between the TRMM subtropical region and the midlatitudes over the United States. Because of a lack of surface hail reports, it is difficult to validate these criteria over the tropics, however. Further validation in the tropics is needed in the future.
(a) Prob, (b) MS, (c) CSI, and (d) HSS for different radar reflectivity and echo-top temperature combinations. The scores are calculated in 1-dBZ and 1°C intervals. The white dots are the points with maximum CSI and HSS. The results derived using TRMM hail PFs are shown with color fill, and those derived using GPM hail PFs are shown with contours.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
With this caveat in mind, the criteria of 44 dBZ at −22°C obtained from U.S. hail PFs in Fig. 3 are applied to satellite observations globally in Fig. 4. The global distribution of PFs with T_MAXHT44 of less than −22°C is shown in Fig. 4. Figure 4a uses 16 years of TRMM data for the tropics and subtropics; Fig. 4b uses 2 years of GPM Ku-band radar data extending through the midlatitudes. Surface air temperature > 10°C is used to exclude potential winter snowstorms with solid precipitation (Liu 2008). Some of the differences between Figs. 4a and 4b undoubtedly are due to the different set of years used in each, and the less robust sample size in Fig. 4b. The largest concentration of hailstorms is indicated in central Africa, with other hot spots in the central and southeastern United States and in Mexico, Argentina, Bangladesh, and Pakistan. In midlatitude regions (Fig. 4b), there are fewer storms satisfying these criteria than in tropical and subtropical regions but there are considerable concentrations in Europe, eastern Eurasia, and central North America. There are some scattered storms across Russia. Similar geographical distribution characteristics are also found in the results derived from DPR profiles (Mroz et al. 2017).
(a) Fraction of TRMM overpasses from 1998 to 2013 for each 5° × 5° grid box that has a PF satisfying the 44-dBZ echo-top temperature criterion of −22°C. (b) As in (a), but for GPM overpasses from Mar 2014 to Feb 2017, and with the restriction that the surface air temperature is greater than 10°C. (c) Locations of individual events satisfying these criteria from GPM, color coded by season. The requirement of surface air temperature > 10°C reduces artifacts from surface snow and ice cover.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
The seasonality of PFs satisfying these criteria (Fig. 4c) generally conforms to expectations, with mid- and high-latitude events occurring almost exclusively during summer and subtropical events mostly mixed among the spring and summer months. Note that a few hail PFs are found in local winter in midlatitude regions. For example, several hail PFs are located in the Mediterranean Sea. Vulpiani et al. (2015) discussed a winter convective storm with reported hail in the Mediterranean Sea, with a freezing-level height slightly above 2 km. Detailed seasonal hail maps that are based on DPR profiles also found that the central months of hail occurrence in parts of the Mediterranean area are in winter (Mroz et al. 2017). The physical processes in these hail-bearing winter storms would be an interesting topic to investigate in the future.
In comparison with the global hail frequency derived from AMSR-E 36-GHz measurements by Cecil and Blankenship (2012), Fig. 4b suggests more frequent hailstorms virtually everywhere. Cecil and Blankenship (2012) consciously chose to err toward a higher probability, at the expense of missing a greater fraction of storms. The criteria used here do have lower probability, even though they were selected to maximize the CSI and HSS [Figs. 3 and 6 (described in more detail below)]. Another reason for differences with the AMSR-E results is that the AMSR-E observes near 0130 and 1330 local time and misses the typical afternoon peak of hail events.
The hotspots in the geographical distribution of hail in Fig. 4 are consistent with the surface hail reports in the literature to some extent, recognizing that there are considerable questions about inconsistent surface hail databases. Frisby and Sansom (1967) first reviewed hail occurrence in tropical regions. Their station-based results showed that in central Africa the annual hail days could reach 5 days per year, whereas in northern India the maximum hail frequency was approximately 1 day per year. As shown in Fig. 4, the ratio of hail PF fractions between central Africa and northern India is around 5, which is close to Frisby and Sansom’s results. In the subtropics, Martins et al. (2017) and Schuster et al. (2005) reported considerable large hailstones in Brazil and southeastern Australia, which are also found in Fig. 4. In the United States, the distribution center of hail PF fraction was consistent with surface hail reports (Allen and Tippett 2015). In China, although hail reports from weather stations include small-size hail (Xie et al. 2010; Ni et al. 2016), the distribution pattern of hail frequency in low elevations is similar to the results in Fig. 4b, with the local maximum frequency in the northeast of China and part of southwestern China (Zhang et al. 2008). In Europe (Punge and Kunz 2016), the areas most affected by hailfalls include southern France, northeastern Spain, and northwestern Italy, which are shown with relatively high hail occurrences in Fig. 4b.
b. Hail detection with passive microwave brightness temperature
By using TB observations from spaceborne passive microwave sensors, multiple algorithms have been constructed to derive global hailstorm maps. Cecil (2009) and Cecil and Blankenship (2012) computed the fraction of cases with a given PCT value that also have corresponding hail reports and used that fraction to weight PCT-based estimates of hailstorm likelihood from TRMM and AMSR-E measurements. Ferraro et al. (2015) developed a prototype AMSU-based hail-detection algorithm, in which average TBs are calculated as a function of hail size and then the number of storms with TB below those thresholds are counted. Here, a method that is similar to that used by Ferraro et al. (2015) is adapted for TRMM measurements.
The global distribution of TRMM PFs with MIN37PCT and MIN85PCT colder than the average PCT for different hail sizes (Table 1) is shown in Fig. 5. These distributions are roughly consistent with Ferraro et al.’s results, with large concentrations in central Africa, Paraguay, the “Maritime Continent,” the Amazon region, and northwestern South America. The distribution that is based on the largest hail size (>2 in., or 51 mm) has similar spatial patterns but with many fewer numbers. Results using the smaller hail (≤1 in., or 25 mm) thresholds show considerable amounts over the Maritime Continent and the Amazon that are not found in the results of the reflectivity-based algorithm in Fig. 4.
As in Fig. 2, but satisfying the 37- and 85-GHz PCT criteria for different hail-size ranges in Table 1.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
As an alternative, we consider both the CSI and HSS to create different, optimal detection criteria from 37- and 85-GHz PCT. Similar to the radar reflectivity hail-detection assessment, the performances of passive microwave PCT at two channels for hail detection are examined together, with 1-K intervals in the PCT values. When PCT values are higher, they indicate relatively less ice scattering in the system; the Prob decreases, and the MS decreases (color fill in Figs. 6a and 6b). CSI/HSS scores are maximized around 230-K PCT at 37 GHz and 210-K PCT at 85 GHz in Figs. 6c and 6d. Note that the maximum CSI and HSS values are not very sensitive to MIN85PCT. When MIN37PCT values are less than 230 K, the MIN85PCT values are nearly always less than 180 K (shown later). Storms with low PCT values, such as 37-GHz PCT lower than 180 K, have also been shown to be more likely to produce large hailstones (Cecil 2009). The PFs with 180 K at 37 GHz are the coldest 0.01% among all samples (Zipser et al. 2006), which suggests the strongest convective systems. This criterion also has high MS values (~0.9 in Fig. 6b), however. Although 230 K at 37 GHz only ranks at 0.1% among overall PFs, it does have higher CSI and HSS and lower MS than does 180 K (Fig. 6). The results using 237 GPM collocated hail reports (contours in Fig. 6) basically confirm what has been found with TRMM. Taking all of the factors into consideration and to be consistent with the reflectivity method, 230 K at 37 GHz will be taken as the PCT criterion in the following discussion.
As in Fig. 3, but for minimum 37-GHz PCT and minimum 85-GHz PCT. The skill scores are calculated in 1-K intervals for both 37 and 85 GHz. The results derived using TRMM hail PFs are shown with color fill, and those derived using GPM hail PFs are shown with contours.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
The PCT criterion with optimum CSI (MIN37PCT < 230 K) is applied to TRMM and GPM PFs in Fig. 7. The major hot spots of hail PFs are similar to those in Fig. 5c; the threshold is similar to that taken from the mean value associated with the largest hail. There are more PFs as identified with these PCTs in tropical regions, like the Maritime Continent, than in the radar-based Fig. 4.
As in Fig. 4, but the threshold is based on the PCT criterion with minimum 37-GHz PCT of < 230 K.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
Overshooting cloud tops defined using infrared observations are sometimes considered as one proxy for hailstorms (Punge et al. 2014). Using different definitions of the tropopause, overshooting deep convection (Liu and Liu 2016) showed some discrepant results with Figs. 4c and 7c. Such as in the North China Plain, there are considerable hail PFs according to the reflectivity algorithm, but few overshooting tops are found in this region (Liu and Liu 2016). Dworak et al. (2012) found regional discrepancies in the frequency of overshooting tops with severe-weather reports. In terms of the rapid drop of tropopause height in midlatitudes and its seasonal variations (Hoinka 1999), the convective structure of hailstorms could be affected by local tropopause height, and hence the relationships between hailstorms and overshooting tops could vary by season and from region to region.
c. Differences in hail detection by using passive microwave brightness temperature and radar reflectivity
The global proxy hail distributions shown in Fig. 4 (reflectivity based) and Fig. 7 (PCT based) are broadly consistent in identifying regions of potential high hail frequency like central Africa and the subtropical Americas. Differences are also obvious over the Maritime Continent and tropical South America regions. Figure 8 allows a comparison of results from the 37-GHz PCT-based (Fig. 8a) and radar reflectivity-based (Fig. 8b) thresholds, as well as differences between the two (Fig. 8c). First, a normalization is employed, since the different false-alarm rates and miss rates associated with the two thresholds would produce different total storm counts, even if the spatial patterns were identical. Figures 8a and 8b are constructed such that the grid values in each map sum to a value of 100%. If the total number of PFs satisfying the thresholds is proportional to the number of hailstorms, then the value for an individual grid box would be the fraction of all hailstorms that occur in that grid box.
Percentage of all TRMM PFs that satisfy the (a) minimum 37 GHz of < 230 K and (b) temperature at 44-dBZ with echo top less than −22°C thresholds, as they are distributed among 1° × 1° grid boxes. The total from all grid boxes sums to 100%. (c) Difference between (a) and (b).
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
The PCT-based thresholds yield higher percentages in equatorial regions such as west-central Africa, the Maritime Continent, and northwestern South America, similar to the unscaled 36-GHz-based distribution in Fig. 6b of Cecil and Blankenship (2012). The reflectivity-based thresholds also show a strong maximum in west-central Africa but identify many more storms in the subtropics than in the deep tropics. The percentage difference between results from PCT-based thresholds and reflectivity-based thresholds in Fig. 8c highlights the regional distinctions. PCT-based thresholds overestimate hail occurrence over the Maritime Continent and the tropical South America relative to the reflectivity-based thresholds. This is consistent with the differences between the scaled and unscaled results of Cecil and Blankenship (2012), where regional differences in typical radar reflectivity profiles were used to scale the 36-GHz-based hail distributions. The scaled distribution in their Fig. 6a is more like the reflectivity-based distribution here, except that Cecil and Blankenship showed lower values in west-central Africa than in the subtropical Americas, Bangladesh, or Pakistan. Both the PCT-based thresholds and the radar-based thresholds in Fig. 8 instead place the overall maximum in west-central Africa. There are some key differences in methodology that could account for that discrepancy. In this paper, any PF with 37-GHz PCT below 230 K is treated as a potential hailstorm. Cecil and Blankenship eliminated any PF with 36-GHz PCT above 200 K, because of the high false-alarm rate and an expectation that the procedure for assigning hail reports to PFs artificially inflates the probability of hail occurrence for higher values of PCT. Cecil and Blankenship also assigned greater weight to PFs on the basis of how low their PCT values were; for example, a PF with 150-K PCT is more than 2 times as likely to have hail as one with 200-K PCT. Since storms producing the lowest PCT values are disproportionately found in certain subtropical hotspots (Zipser et al. 2006), this favors those subtropical hotspots over west-central Africa.
To further investigate the reasons for the regional differences between results from PCT-based thresholds and reflectivity-based thresholds, we selected three regions with positive percentage differences (deep tropical South America, the Maritime Continent, and west-central Africa), and three regions with negative values (Argentina, South Africa, and the southeastern and south-central United States). Only samples over land in the boxed regions in Fig. 8c are analyzed below.
The number of PFs satisfying the PCT-based threshold (MIN37PCT colder than 230 K) is listed for each region in Table 2, along with the percentage of those PFs that also satisfy the reflectivity-based threshold (44-dBZ echo-top temperature colder than −22°C). In the three subtropical regions, more than two-thirds of the PFs satisfying the PCT-based threshold also satisfy the radar-based threshold. Fewer than 10% of those in the Maritime Continent satisfy both criteria; only 22% in deep tropical South America and 39% in west-central Africa satisfy both criteria. The median PCT values are generally higher at 37 GHz and lower at 85 GHz for the tropical regions relative to the subtropical regions. This is consistent with the tropical regions having a weaker but deeper convective structure than the subtropical regions, analogous to differences between tropical oceanic and tropical continental convection noted by Toracinta et al. (2002). A deeper column of relatively smaller particles could be consistent with the higher 37-GHz–lower 85-GHz PCT combination.
Statistical properties of PFs that satisfy the threshold of minimum 37-GHz PCT of less than 230 K in different regions.
This is further demonstrated in Fig. 9, in which two-dimensional histograms of PFs according to 37- and 85-GHz PCT values are shown by the color fill. The mean values of 44-dBZ echo-top temperatures for different PCT combinations are shown by solid contours. Consistent with Table 2, tropical regions have relatively colder MIN85PCT, with the percentage maximum center around 120 K, as compared with the subtropics at 130–140 K. Subtropical regions have lower MIN37PCT values than do the tropics. Tropical regions tend to have much warmer 44-dBZ echo-top temperatures than the subtropical regions do, for any given combination of PCT values.
Two-dimensional histograms of TRMM PFs categorized by minimum 85- and 37-GHz PCT over (a) three tropical regions (the Maritime Continent, west-central Africa, and tropical South America) and (b) three subtropical regions (the southeastern and south-central United States as well as South Africa and Argentina). The population distribution (color fill) is calculated by dividing the number of PFs in each 5-K bin by the total number of PFs with MIN37PCT lower than 230 K from 1998 to 2013. The mean value of the temperature (°C) at maximum 44-dBZ echo top (T_MAXHT44) for each 2-K bin is overlapped with contours (after smoothing).
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
As an alternative, we examine in Fig. 10 the radar reflectivity profiles in the PFs satisfying the PCT criterion. The maximum radar reflectivity profiles are shown in contoured-frequency-by-altitude diagrams (CFAD), with the mean and lines of 10th, 25th, 50th, 75th, and 90th percentile overplotted. In the deep tropical regions (Figs. 10a–c), more than one-half of the PFs have 20-dBZ echo tops reaching levels with temperatures as low as −70°C. In the three subtropical regions, a similar fraction reach levels colder than −60°C. Relative to tropical regions, the maximum radar reflectivity profiles have larger variations over the subtropics. As seen before in Table 2, most of these subtropical PFs easily satisfy the radar-based threshold of 44 dBZ reaching −22°C (the red plus sign in each panel) but most of the tropical PFs do not. Also in Table 2, the subtropical regions produce PFs that more easily satisfy the 230-K threshold for MIN37PCT. The median values of MIN37PCT are up to 10 K lower for the subtropical regions than for the tropical regions, and the 10th-percentile values are up to 30 K lower. Accordingly, the median profiles and the high-reflectivity edges of the CFADs bulge toward much higher values for the subtropics than for the tropics in Fig. 10.
CFAD of reflectivity vs temperature for TRMM PFs satisfying the threshold of minimum 37-GHz PCT of less than 230 K from 1998 to 2013 in (a) the Maritime Continent, (b) tropical South America, (c) west-central Africa, (d) southeastern and south-central United States (SEUS), (e) South Africa, and (f) Argentina. The plussign is the point with 44 dBZ at −22°C. The dashed lines are the reflectivity at the 10th, 25th, 50th, 75th, and 90th percentiles. Solid lines are the mean reflectivity at each level in the temperature coordinate.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
As shown in Fig. 11, the median profiles of reflectivity from subtropical PFs with low microwave TB have a lower echo top and stronger reflectivity in the middle level when compared with those from the tropics. The strong radar reflectivity found in the hail-growth zone in the layer between −10° and −30°C (Miller et al. 1988) in the southeastern and south-central United States is consistent with the observed frequent hail occurrence at the surface. For those land PFs in the three tropical regions, abundant smaller ice particles distributed through deeper layers (as indicated by radar echoes above −40°C) would be the main reason for the strong depression in the microwave TB at 85 GHz. Relatively weaker reflectivity in the middle level between −10° and −30°C makes it less probable to find large hail at the surface. The high-reflectivity echo top and weaker reflectivity at middle levels in the tropics (Figs. 10 and 11) explain why it has colder 85-GHz PCT than the subtropical regions, as shown in Fig. 9. Meanwhile, the strong reflectivity in the middle levels in subtropical systems implies a high possibility of larger ice particles, which could lead to stronger scattering at 37 GHz.
Median reflectivity profiles of TRMM PFs that have minimum 37-GHz PCT of less than 230 K over land from 1998 to 2013, as shown in Fig. 10.
Citation: Journal of Applied Meteorology and Climatology 56, 10; 10.1175/JAMC-D-17-0065.1
4. Summary and discussion
On the basis of previous studies about global distributions of hailstorms using passive microwave observations, we examine the performance of spaceborne precipitation radar reflectivity and passive microwave brightness temperature for the detection of hailstorms with large-size hail (>19 mm). Precipitation features derived from 16 years of TRMM observations are collocated with the hail reports in the southeastern and south-central United States. Criteria that are based on temperature at maximum echo top for different radar reflectivity values and minimum 37-GHz PCT are developed to distinguish hail PFs from nonhail PFs. For the reflectivity criterion, the threshold of 44 dBZ at −22°C has the maximum CSI score (0.24) and HSS (0.37). The CSI score and HSS for the optimum PCT criterion (230 K for MIN37PCT) are smaller (less skillful) than those that are based on the reflectivity criterion because of the large miss rate in the low-PCT range. The reflectivity threshold obtained here corroborates previous detection methods using single-polarization radar. With upcoming spaceborne radar observation of high-latitude regions, the hailstorm climate up to ±65° could be constructed more directly from the active remote sensing observations.
The application of the reflectivity threshold and PCT threshold to the GPM precipitation features extends the derived global hail map to higher latitudes and shows a considerable number of potential hail events in Europe and Canada, along with scattered hail events in Eurasia. The PCT-based threshold estimates more hailstorms over deep tropical South America and the Maritime Continent than does the reflectivity-based threshold. In three tropical regions, reflectivity profiles of PFs meeting the PCT-based threshold have deep layers exceeding 20 dBZ, but the reflectivity decreases more quickly above the freezing level than in the profiles from three subtropical regions. The deeper layers of precipitation ice in the deep tropical South America, west-central Africa, and Maritime Continent profiles may contribute to strong PCT depressions and overestimation of large hail occurrence in these regions, especially at 85 or 89 GHz. To the contrary, the PFs satisfying the PCT-based threshold in the three subtropical regions are more likely to also meet the reflectivity criterion of 44 dBZ at −22°C and have stronger reflectivity in hail-growth regions between −10° and −30°C. Consequently, the subtropical regions have lower MIN37PCT (but higher MIN85PCT) than do the tropics.
In the tropics, convection with very deep layers of graupel and small hail may allow storms to more easily produce the low microwave brightness temperatures that are more typically associated with large hail in the subtropics. Without accounting for this, uniform application of relationships between hail occurrence and low TB could have significant regional biases (i.e., overestimation of large hail in the tropics, relative to the subtropics). Many factors are responsible for the regional differences in storm characteristics. In comparisons of reflectivity profiles of intense convection in tropical and subtropical regions, the storm heights are significantly different [Figs. 10 and 11, and related analyses by Cecil (2011)]. The intense convection that is studied in this paper is very different from the weaker convection that is predominant, although some analogies do appear to be relevant. Differences in the shape of the reflectivity profiles between the tropical and subtropical regions in Figs. 10 and 11 are qualitatively similar to the differences between the shapes of reflectivity profiles for typical oceanic convection versus typical continental convection (e.g., Zipser and Lutz 1994; Cecil and Zipser 2002) but even the weakest radar reflectivity profiles in Fig. 10, with 40 dBZ reaching the −10°C level and 35 dBZ reaching −20°C, would easily rank among the top 10th percentile of all PFs and near the median values for PFs that produce at least one lightning flash per minute (Cecil et al. 2005). Any storm satisfying the criteria used in this paper likely has strong (>10 m s−1) updrafts and large graupel and/or hail, but the ones satisfying the radar reflectivity–based criteria are more likely to have hail that is large enough to fall to the surface without melting.
Relative to using the PCT threshold, using the reflectivity method leads to lower estimates of hail occurrence in the tropics. Because there are very few hail studies in these regions, however, it is difficult to validate these results with surface hail reports. Different formats and regulations in hail reports of different regions make it more difficult to conduct regional comparisons among them. The ability to apply uniform standards is a strength of satellite-based approaches. Nevertheless, further validation using regional surface hail reports, especially over the tropics, is still essential for verifying the methods developed in this study. This study grounds future research about hailstorm climatology using long-term TRMM and GPM observations. As more GPM observations become available, the method developed here would be further validated. In addition, the possibility of using the dual-frequency precipitation radar in the detection of hailstorms (Mroz et al. 2017) is also worth investigating.
Acknowledgments
Thanks are given to three anonymous reviewers for valuable suggestions. Authors Ni and Zhang were supported by the Chinese National Science Foundation under Grants 41330421 and 41461164006; Ni also gratefully acknowledges financial support from the China Scholarship Council. Authors Liu and Cecil were supported by the NASA PMM Science Team (NNH15ZDA001N-PMM). All precipitation-feature data are processed by NASA’s Precipitation Processing System.
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