Microphysical data from thunderstorms are sparse, yet they are essential to validate microphysical schemes in numerical models. Mobile, dual-polarization, X-band radars are capable of providing a wealth of data that include radar reflectivity, drop shape, and hydrometeor type. However, X-band radars suffer from beam attenuationin heavy rainfall and hail, which can be partially corrected with attenuation correction schemes. In this research, the authors compare surface disdrometer observations to results from a differential phase-based attenuation correction scheme. This scheme is applied to data recorded by the National Oceanic and Atmospheric Administration (NOAA) X-band dual-polarized (NOXP) mobile radar, which was deployed during the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). Results are presented from five supercell thunderstorms and one squallline (183 min of data). The median disagreement (radar-disdrometer) in attenuation-corrected reflectivity Z and differential reflectivity ZDR is just 1.0 and 0.19dB, respectively. However, two data subsets reveal much larger discrepancies in Z (ZDR): 5.8(1.6)dB in a hailstorm and -13 (-0.61) dB when the radar signal quality index (SQI) is less than 0.8. The discrepancies are much smaller when disdrometer and S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) Z are compared, with differences of -1.5 dB (hailstorm) and -0.66 dB (NOXP SQI < 0.8). A comparison of the hydrometeor type retrieved from disdrometer and NOXP radar data is also presented, in which the same class is assigned 63% of the time.
(ProQuest: ... denotes formulae omitted.)
The lack of surface microphysical and in situ data is a critical obstacle in our attempts to understand and model severe thunderstorms accurately. Microphysical processes (e.g., accretion, collision, coalescence, drop breakup, melting, and evaporation) affect storm be- havior and evolution by serving as a crucial link between the storm dynamics and thermodynamics. For example, the melting of hail influences the strength and size of the low-level cold pool, which changes the near-surface buoyancy tendency and, as suggested by several recent studies, the tornadogenesis potential (Markowski et al. 2002; Shabbott and Markowski 2006; Grzych et al. 2007). To collect the surface microphysical data re- quired to understand and quantify these interactions, Particle Size and Velocity (PARSIVEL) optical dis- drometers were deployed during the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2) to obtain particle diameter and fall speed distributions in severe thunderstorms. For the first time, these deployments were coordinated with X-band, mo- bile, polarimetric Doppler radars in severe thunder- storms, which provided a three-dimensional dataset of radar reflectivity Z, differential reflectivity ZDR, and differential phase CDP that is needed to characterize microphysical processes throughout thunderstorms.
The VORTEX2 measurements of supercell thunder- storm microphysics with disdrometers and mobile X-band radars are unprecedented, since both sets of instruments were deployed close to the storm and yiel- ded high-resolution information near and at the sur- face. This dataset provides researchers with a unique opportunity to compare disdrometer data to output from hydrometeor classification schemes that are based on dual-polarization radar observations. However, the measurement accuracy of both instruments is strongly affected by the severe nature of the storms, which contain hail and strong winds. To combine in situ microphysical data at the surface with three-dimensional radar imagery, microphysical data need to be quality controlled and rain and hail particles must be discriminated. In addition, at- tenuation of the X-band radar signal must be corrected using algorithms that may be error prone, particularly when the radar samples mixed-phase precipitation. A proven algorithm to correct attenuation in hail does not yet exist (Borowska et al. 2011; Ryzhkov et al. 2013a), although recent efforts to develop a scheme valid in melting hail are presented in Ryzhkov et al. (2013a,b). Because supercell thunderstorms often contain large amounts of hail, attenuation correction schemes designed for rain will not always yield accurate results.
In this paper, we compare attenuation-corrected radar data and hydrometeor classifications to surface dis- drometer measurements in supercell thunderstorms. Can disdrometer data be used to provide guidance on the performance of radar attenuation correction schemes, and therefore to provide a measure of radar data quality? To investigate, we first apply a quality- control algorithm and a hydrometeor classification scheme for in situ disdrometer data that uses the particle size and fall speed distributions from the disdrometer to classify particles as rain, small hail (2 , d , 5 mm), and large hail (d . 5 mm; note that in this study, ''large'' is simply relative to the small hail class and is not meant to be an argument against the typical definition of large hail of d . 20 mm). We then assess the performance of the attenuation correction scheme by comparing disdrometer- derived Z and ZDR to X-band radar Z and ZDR and to S-band radar Z. Comparisons between the disdrometer hydrometeor classification scheme and an existing scheme for X-band radar data are also provided.
A brief review of the different techniques that can be used to correct attenuation is now given. Several at- tenuation correction schemes use the propagation dif- ferential phase FDP and specific differential phase KDP to estimate the total and specific attenuation, re- spectively (e.g., Carey et al. 2000; Testud et al. 2000; Bringi et al. 2001; Anagnostou et al. 2006; Steiner et al. 2009). The quantity KDP is the range derivative of FDP, which must be calculated from the radar-measured total differential phase CDP. The CDP is the sum of FDP and the backscatter differential phase d. The terms CDP, FDP, d, and KDP are related via Eq. (1):
where r is the radar range. The quantity d is only sig- nificant in the Mie scattering regime, which applies to rain drops with d . 2.3 mm at a temperature of 208CatX band (Ryzhkov et al. 2011). Therefore, d must be esti- mated before FDP and KDP can be used to correct the attenuation. Each attenuation correction scheme differs in the method used to calculate d. Anagnostou et al. (2006) uses the differential reflectivity ZDR in an itera- tive approach to estimate d, while Steiner et al. (2009) applies the iterative, finite impulse response filter from Hubbert and Bringi (1995) to the measured CDP field. Once corrected Z, ZDR, and KDP are obtained, a fuzzy logic hydrometeor classification scheme [section 3b(2)] can be applied to the radar data to determine the dominant hydrometeor type observed in each range gate (Vivekanandan et al. 1999; Liu and Chandrasekar 2000; Iwanami et al. 2007; Park et al. 2009; Dolan and Rutledge 2009; Snyder et al. 2010).
To our knowledge, this study is one of the first to use disdrometer observations to analyze the performance of attenuation correction and hydrometeor classification schemes for X-band radar measurements in severe thunderstorms. Most previous studies that compared radar and disdrometer data developed empirical re- lationships between reflectivity and rainfall rate (e.g., Schuur et al. 2001; Ulbrich and Miller 2001; Bringi et al. 2003; Kanofsky and Chilson 2008; Huang et al. 2010). In addition, such studies have primarily been conducted in stratiform precipitation (e.g., Geotis 1978; Goddard et al. 1982; Thomson and List 1996; Zhang et al. 2011), while only a few comparisons have been performed in severe thunderstorms (Schuur et al. 2001; Thurai et al. 2010, 2011). X-band radar attenuation correction schemes have mostly been evaluated through compari- son with S-band radar data, which are less attenuated (e.g., Anagnostou et al. 2006; Steiner et al. 2009; Snyder et al. 2010). Here, we propose an alternative method to evaluate attenuation correction schemes with surface disdrometer data. While we do not argue that this ap- proach outperforms comparisons with S-band radar, the question remains whether disdrometers could be used if no nearby S-band radars are present. In addition, be- cause the S-band Weather Surveillance Radar-1988 Doppler (WSR-88D) dual-polarization upgrade was not complete in 2010, mobile radar ZDR measurements corrected for differential attenuation and results from mobile radar hydrometeor classification algorithms cannot be validated with traditional S-band radar com- parisons. Therefore, the goal of this study is to determine the relative quality of the VORTEX2 disdrometer and X-band radar data with the intention of improving the results from future observational analyses and numerical modeling studies that use these datasets for microphysical retrievals.
2. Cases, instruments, and data collection
a. Case selection
Coordinated radar and disdrometer data were obtained from ;36 severe thunderstorms during the second year of VORTEX2, a 12-week field campaign conducted in the Great Plains of the United States during May and June of 2009 and 2010 (Wurman et al. 2012). For this study, three criteria were used for case selection: 1) radar data above the disdrometer sites were available for at least 5 min, 2) the disdrometers observed Z . 20 dBZ (approximate threshold between drizzle and light rain; Rinehart 2004) for at least 5 min, and 3) the distance between the radar and the disdrometers was less than 45 km. Based on these criteria, we consider data from five supercell thunder- storms and one squall line (total of ;183 min of data). Table 1 provides details on the cases, and Fig. 1 shows examples of radar reflectivity from each case at an eleva- tion angle of 18.
b. Disdrometer measurements
The OTT PARSIVEL optical disdrometer (Loeuroffler- Mang and Joss 2000) is an integrated laser transmitter- receiver that uses a 180-mm-long, 30-mm-wide, and 1-mm-thick light sheet to detect the diameter and fall speed of precipitation particles. More information about the measurement principle can be found in Loeuro ffler- Mang and Joss (2000), Loeuroffler-Mang and Blahak (2001), Yuter et al. (2006), and references within. During VORTEX2, two types of disdrometers (Fig. 2) were deployed: articulating disdrometers (denoted as UF01 and UF03), with a measurement volume that was ori- ented continuously perpendicular to the 10-s running average of the particle trajectory of a 1.2-mm raindrop (Friedrich et al. 2013b), and stationary disdrometers (denotedas CU01, UF04, UF05, UF06, andUF07),with a measurement volume that remained fixed and parallel to the ground. For supercell thunderstorms, the dis- drometers were deployed in advance of the southern side of the forward-flank downdraft (Fig. 3), with the mobile weather radars deployed to the southeast of the thunderstorm. The distance between the disdrometers and the radar ranged from 10 to 45 km, with a median distance of 20 km. Further details on the deployment strategy are provided in Friedrich et al. (2013b).
c. Radar measurements
Radar data were obtained from the National Oceanic and Atmospheric Administration (NOAA) X-band dual- polarized (NOXP) mobile radar (Palmer et al. 2009; Burgess et al. 2010). Table 2 provides a summary of the radar configuration during VORTEX2. For the cases considered in this research, the size of the radar reso- lution volume above the disdrometer sites ranged from 74m 3 87 m3 175m at10-kmrangeto 74 m3 393m 3 785 m at 45-km range in range, azimuth, and height, respectively. The radar was electronically leveled, and a digital compass was used to record its heading. With respect to the location of the disdrometers, the height of the lowest radar beam ranged from 0.2 to 1 km AGL, but was mainly below 0.6 km AGL (Table 1).
3. Data processing
1) QUALITY CONTROL AND HYDROMETEOR CLASSIFICATION SCHEME
A quality-control procedure (Fig. 4) was applied to the stationary and articulating disdrometer data to address three documented error sources: strong winds, particles that only partially transect the sample volume (i.e., margin fallers), and splashing (e.g., Sevruk 1982; Illingworth and Stevens 1987; Ne^spor et al. 2000; Schuur et al. 2001; Kruger and Krajewski 2002; Barthazy et al. 2004; Thurai and Bringi 2005; Yuter et al. 2006; Friedrich et al. 2013a). Friedrich et al. (2013a) analyzed wind-induced errors in PARSIVEL disdrometer data collected in a tropical cyclone and two supercell thunderstorms with wind speeds up to 30 m s21, using six stationary and two ar- ticulating disdrometers. Misclassified particles, with d . 5 mm and unphysically slow fall speeds (y , 1ms21), were identified in the stationary (but not the articulat- ing) disdrometer data at wind speeds as slow as 10 m s21 and were observed consistently at wind speeds larger than 20 m s21. To avoid misclassified particles in this analysis, we remove entire time steps in which the sta- tionary disdrometers observed particles with d . 5mm and slow fall speeds (y , 1ms21). Second, margin fallers and splashing raindrops are removed from both types of disdrometer data by eliminating raindrops with a fall speed more than 60% faster or slower than the fall speed-diameter relationship for rain (Gunn and Kinzer 1949; Atlas et al. 1973), based on a study of PARSIVEL disdrometer accuracy by Jaffrain and Berne (2011).
The decision to classify a particle as rain, small hail, or large hail is based on its diameter and fall speed (Fig. 4). While the reader is referred to Friedrich et al. (2013b) for a detailed description of the classification scheme, two notes are merited here. First, we distinguish be- tween small and large hail because small ice particles in thunderstorms are partially melted hailstones that consist of a torus of liquid water that surrounds an ice core (Rasmussen and Heymsfield 1987; Bringi and Chandrasekar 2001). Therefore, small and large hail need to be assigned different fractional water contents when the transition (T-) matrix method is used to compute the scattering properties of the particle size distribution [PSD; see section 3a(2) and Table 3]. Ap- pendix A demonstrates that for the PSDs in this study, the sensitivity of disdrometer Z and ZDR to the small hail fractional water content is less than 0.1 dB, because the small sample area of the PARSIVEL disdrometer captures relatively few hailstones. Second, while rain- drop fall speed is a well-defined function of diameter (Gunn and Kinzer 1949; Atlas et al. 1973), the various shapes, densities, and water loadings of hail make it possible for an ice particle to have a range of fall speeds for a given diameter, raising the possibility that a hail particle could be erroneously classified as rain. In addi- tion, the disdrometer hydrometeor classification scheme (Fig. 4) uses the fall speed curves for dry graupel to define the small hail region, following Friedrich et al. (2013b). However, because the bulk density of small hail in thunderstorms exceeds that of graupel, the graupel fall speed relations are likely less than the fall speeds observed here. Therefore, some of the small hail may be detected in the unclassified region between the small hail and rain classes in Fig. 4. Because there is un- certainty over whether particles in this region are rain or small hail, these particles are left unclassified. Appendix B explores the sensitivity of the results to whether par- ticles in the unclassified region are included in the analysis, revealing a mean sensitivity of ;0.2 dB in Z and 0.01 dB in ZDR (relative to Z and ZDR obtained by excluding the particles).
2) COMPUTATION OF METEOROLOGICAL VARIABLES FROM DISDROMETER DATA
Before calculating Z and ZDR from the disdrometer data, number distributions were accumulated over pe- riods of 60 s to obtain sufficiently large particle samples. The 60-s accumulation time causes higher-frequency variations in the PSD to be lost. These variations would likely be retained in the radar data due to the excellent range resolution (74 m), possibly causing the radar and disdrometer measurements to represent different PSDs (this issue is partially addressed by averaging the radar data; see section 3c). Next, the T-matrix method (Vivekanandan et al. 1991; Bringi and Chandrasekar 2001) was used to compute Z and ZDR for each 60-s time step. Because the scattering properties of rain and ice particles differ, separate rain, small hail, and large hail distributions were input to the T-matrix program for each time step. For rain particles, the drop shape model from Beard and Chuang (1987) was chosen, which re- mains accurate at the large drop diameters present in convective weather (i.e., within 64% of the measured axis ratios at d . 5 mm; Thurai et al. 2009). The rain- drops were assumed to have a temperature of 158C, a mean canting angle of 0 8 , and a canting angle standard deviation of 7.58 (Huang et al. 2008). Of these settings, Z and ZDR display the greatest sensitivity to the canting angle standard deviation; however, the change in ZDR is generally less than 0.1 dB across the range of physically reasonable values (18-108; Kwiatkowski et al. 1995). Hail particles were assumed to have a canting angle mean and standard deviation of 08 and 508, respectively (Snyder et al. 2010; Ryzhkov et al. 2011), and were as- signed a temperature of 08C. The hailstones were mod- eled as a uniform mixture of ice and liquid water using the Maxwell-Garnett mixing formula, with ice (liquid water) as the matrix and liquid water (ice) as the inclusions in large (small) hailstones (Bringi and Chandrasekar 2001; Ryzhkov et al. 2011). Table 3 summarizes the parameters used in the T-matrix program for rain, small hail, and large hail.
b. Radar data processing
1) RADAR ATTENUATION CORRECTION SCHEME
The attenuation correction scheme from Steiner et al. (2009) is applied to the radar data. Steiner et al. (2009) evaluated the performance of this scheme with data that were collected in convective storms during the 2002 International H2O Project (IHOP) by the National Observatory of Athens (NOA) X-band radar. For X-band radars with simultaneous horizontal and vertical polarization (SHV) transmit, attenuation correction in heavy rain was found to be most accurate when ZDR was not used to estimate the attenuation or differential at- tenuation (Steiner et al. 2009). Potential biases in ZDR caused by antenna and depolarization errors as CDP increases (Ryzhkov and Zrni^c 2007; Hubbert et al. 2010a,b; Zrni^c et al. 2010) are thereby avoided.
The Steiner et al. (2009) attenuation correction scheme is modified from the differential phase-based algorithm presented in Anagnostou et al. (2006). The first modifi- cation is that d was removed from CDP with five iterations of the finite impulse response filter from Hubbert and Bringi (1995), rather than using ZDR to estimate d.The smoothed FDP range profile was then used to estimate the path-integrated attenuation at horizontal polarization [Eq. (2)] and to correct ZH[Eq. (3)]:
where PIAH is the path-integrated attenuation at hori- zontal polarization (dB), r is the radar range (km), AH is the specific attenuation at horizontal polarization (dB km21), g is an empirical constant equal to 0.3006 in rain [average of g values in Table 3 of Anagnostou et al. (2006)], and ZH0 is the corrected reflectivity at horizontal polarization. Another modification to the Anagnostou et al. (2006) technique was to relate the differential at- tenuation directly to PIAH following Park et al. (2005) and Gorgucci et al. (2006). Once an initial estimate of PIAH was made, the path-integrated differential atten- uation PIADP was calculated as a function of PIAH [Eq. (4)], and ZDR was corrected with Eq. (5):
where ZD0 R is the corrected ZDR and « 5 0:173 in rain.
2) RADAR HYDROMETEOR CLASSIFICATION SCHEME
Once radar data were corrected for attenuation, the hydrometeor classification scheme from Snyder et al. (2010) was applied. This fuzzy logic scheme was originally devised at S band by Park et al. (2009) and adapted to X band by Snyder et al. (2010). The algorithm uses the following dual-polarization radar variables as inputs: ZH, ZDR, 10(logKDP), copolar cross-correlation coefficient at lag zero (rHV), reflectivity texture, and total differential phase texture. The membership functions used by the scheme are trapezoidal in shape and are derived from T-matrix simulations of observed and idealized PSDs of rain and hail. The membership functions are defined for six hydrometeor classes: ground clutter/anomalous pro- pagation (GC/AP), biological scatterers (BS), big drops (BD), rain (RA), heavy rain (HR), and rain-hail mixture (RH). Only the latter four classes are retained for comparison with the PARSIVEL disdrometer, since the disdrometer does not detect GC/AP or BS. The output values of the membership functions are weighted according to Park et al. (2009) and then summed for each hydrometeor class. The class with the largest sum is then assigned to the radar range gate.
c. Radar-disdrometer comparison method
To select data for comparison, radar Z and ZDR were averaged over a 3 3 3 array of range gates, centered on the gate that contained the disdrometer. Time steps with sharp horizontal reflectivity gradients (.35 dB km21) and deployments with ground clutter (Z . 0dBZ and near-zero Doppler velocity) near the disdrometer sites were excluded from the analysis. Radar and disdrometer data were then paired so that the time difference be- tween the observations did not exceed 30 s.
Despite the exclusion of reflectivity gradients larger than 35 dB km21 and the averaging of radar range gates, precipitation particle advection and the height differ- ence between the radar beam and the surface are po- tentially large error sources in this analysis. As an example, consider a raindrop of d 5 1 mm, which has a terminal fall speed of y 5 4ms2 1. If this drop is at a height of 1 km when the radar observes it, the drop will not reach the ground until 250 s later. Assuming a mean horizontal wind speed of 10 m s21, the drop will be ad- vected 2.5 km downstream from the point in space where it was observed by the radar, a distance of nearly 34 radar range gates (in the worst case scenario). Thus, the PSDs observed by the radar and disdrometer may be different due to the strong low-level winds that often accompany supercell thunderstorms. A sensitivity test was performed in which the radar data were averaged over various windows, ranging from 3 3 3to113 11 range gates (not shown). Aside from a ;0.25-dB im- provement in the ZDR agreement when a 3 3 3 aver- aging window was used versus no averaging, the results are not affected by the size of the window. In addition, no correlation was found between the disagreement in the radar and disdrometer data and the radar beam height (not shown). Growth and evaporation of rain- drops between the radar beam and the surface, however, are nevertheless error sources.
4. Results and discussion
a. Radar and disdrometer comparison of Z and ZDR
1) X-BAND RADAR Z AND ZDR
Figure 5 presents scatterplots of disdrometer and ra- dar Z for all cases in the analysis (Table 1; Fig. 1) before (Fig. 5a) and after (Fig. 5b) the attenuation correction scheme was applied. Two data subsets are identified, which will be discussed in sections 4b and 4c: the 17 May 2010 hailstorm (red plus signs) and data with radar signal quality index (SQI) , 0.8 (blue plus signs). SQI (SIGMET 2009) is related to signal-to-noise ratio (SNR) and spectrum width (W):
Of the 183 uncorrected radar Z values (97%), 177 are weaker than the corresponding disdrometer observa- tions, with a median difference (radar Z 2 disdrometer Z)of217 dB (all data in Fig. 5a). When the attenuation correction scheme is applied, the distribution shifts to- ward larger radar Z (all data in Fig. 5b). The median difference (radar Z 2 disdrometer Z) after attenuation correction is 1.0 dB, and 48% of the radar Z values are weaker than the disdrometer values. These statistics indicate that the attenuation correction scheme has re- moved the overall negative bias in the radar observa- tions. Twenty-five percent of the radar Z values are larger than the PARSIVEL disdrometer sampling un- certainty, 30% are smaller, and 45% are within the sampling uncertainty (gray shading in Fig. 5), quantified by Jaffrain and Berne (2011). In the Jaffrain and Berne study, two PARSIVEL disdrometers were collocated and sampled ;990 h of light-to-moderate rainfall. The standard deviation of the difference in the moments (i.e., the sampling uncertainty) that were derived from each drop size distribution was then calculated (Tables B4 and B5 in Jaffrain and Berne 2011). Since the mea- surements in this study were taken in severe thunder- storms that often contained heavier rainfall rates, hail, and strong winds, the sampling uncertainty from Jaffrain and Berne (2011) should be considered a lower bound on the uncertainty in this research.
Scatterplots of ZDR before and after attenuation correction are presented in Figs. 5c and 5d, respectively. Differential attenuation is clearly evident in the un- corrected radar ZDR, with 50% of the radar observations having ZDR , 0dB(Fig. 5c). After attenuation correc- tion was applied (Fig. 5d), the median difference (radar ZDR 2 disdrometer Z DR) improves from 2 2.7 to 0.19 dB. Of the corrected observations, 38% are within the sampling uncertainty of the PARSIVEL dis- drometer (gray shaded region in Fig. 5d), compared to 20% prior to correction. Similar to the reflectivity, a large number of points lie outside the sampling un- certainty (gray shaded region in Fig. 5d), with 37% (25%) of the radar ZDR values larger (smaller) than the disdrometer sampling uncertainty.
2) S-BAND RADAR Z
To provide a benchmark for comparison, disdrometer Z is also compared to Z from the nearest WSR-88D at the 0.58 elevation angle (Fig. 6) for all cases in the analysis. In comparing Fig. 5b to Fig. 6, we note that the median disagreement in radar and disdrometer Z is changed from 1.0 to 21.9 dB (all plus signs) when the S-band WSR-88D data are compared to the disdrometer- derived data. However, the median disagreement in Z for two of the data subsets (i.e., the 17 May 2010 hailstorm, red plus signs, and SQI , 0.8, blue plus signs) decreases when WSR-88D data are used, from 5.8 to 21.5 dB (hailstorm; red plus signs) and 213 to 20.66 dB (SQI , 0.8; blue plus signs). These results imply that the X-band radar attenuation correction scheme partially contrib- utes to the disagreement in these subsets, since S-band radar data compare more favorably with the dis- drometer data (this inference, however, is complicated by differences in the X- and S-band radar beam heights; see Table 1). These details will be explored further in sections 4b-d, in which three case studies are examined: a supercell with large hail on 17 May 2010, a supercell on 9 June 2010, and a squall line on 12 June 2010.
b. 17 May 2010: Supercell with radar Z and ZDR larger than disdrometer values
On 17 May 2010, a high precipitation supercell thunderstorm was observed near Artesia, New Mexico. The disdrometers sampled the forward-flank downdraft of the storm (Fig. 1a). The authors observed large hail (d ; 50 mm) between 2220 and 2232 UTC, which se- verely damaged the windshields of the deployment ve- hicles. Figure 7 shows a time series plot comparing Z (Fig. 7a) and ZDR (Fig. 7b) values recorded by the radar and disdrometer CU01 during this event. The total ice volume (assuming spherical particles) and the largest hail size observed by the disdrometer are also plotted with time (Figs. 7c,d). One might expect that the radar observations would not be heavily attenuated in the portion of the storm nearest the radar and that the at- tenuation could be accurately corrected. However, the time series data (Figs. 7a,b) reveal that, on average, corrected Z and ZDR measured by the X-band radar were 8.3 and 1.5 dB larger, respectively, than the cor- responding measurements from CU01. In fact, during the 27-min period shown, Z recorded by CU01 never exceeded that of the radar, and the CU01 ZDR was greater than the radar ZDR for only 2 of the 10 time steps. The trend of generally larger attenuation-corrected radar variables relative to all of the disdrometer measurements made on 17 May is also shown in Figs. 5b and 5d (red plus signs), a discrepancy that is not reflected in the remainder of the dataset (blue and black plus signs).
We hypothesize that the disagreement evident in the disdrometer and radar observations on 17 May is partly due to large, wet hail causing resonant (Mie) scattering of the radar beam. Because of Mie scattering, strong attenuation at horizontal polarization and differential attenuation have been observed at C- and X-bands in the presence of hail (e.g., Steiner et al. 2009; Tabary et al. 2009; Snyder et al. 2010; Borowska et al. 2011). Attenuation correction in the presence of hail is un- certain (Vulpiani et al. 2008; Borowska et al. 2011; Gu et al. 2011) because the relationship between differential phase and attenuation in a rain/hail mixture has only recently been examined. Ryzhkov et al. (2013a,b) found that the coefficients g and « in Eqs. (2) and (4) differ for rain and melting hail. Therefore, correcting attenuation in mixed-phase precipitation with coefficients meant for rain may lead to large errors (Steiner et al. 2009).
Because it is known that attenuation correction schemes designed for rain may perform poorly in the presence of hail, disdrometers can be used to detect hail on the ground and to flag radar observations beyond the location of the disdrometers as poor quality. Figure 8 shows the disdrometer data accumulated over this event as a function of particle fall velocity and diameter, with large hail up to d 5 20 mm present (note that the mea- surement limit of the PARSIVEL disdrometer is d 5 26 mm, and undercatchment is likely at these large sizes, as discussed later). Figure 7c shows that between 2218 and 2233 UTC, up to 15 cm3 of ice were observed per 1-min time step by CU01. Although the ice volume de- creases to ,5cm3 min21 after 2233 UTC, a 5-15-dBZ discrepancy remains in Z, likely because the hail core is located between the radar and disdrometer sites. Range gates located behind the hail core may exhibit erroneous Z values due to the cumulative nature of attenuation correction errors.
An important limitation of this analysis is that large hail is sparse (number concentration of 1022 m23; Straka 2009) relative to the sample area (54 cm2)of the PARSIVEL disdrometer. Therefore, disdrometer data might not indicate that radar data are suspect if only a few hailstones fall at the disdrometer site. In addition, even in thunderstorms with large amounts of ice, the PARSIVEL disdrometer will underes- timate the hailstone concentration due to the small sample area. Undercatchment is especially likely for the largest hailstones, as Fig. 7d demonstrates that the largest hailstones detected by disdrometer CU01 during matched observations with the radar are d 5 13 mm, despite hailstones of d 5 50 mm being ob- served. In an attempt to determine whether under- catchment is the primary cause of the disagreement (rather than deficiencies in the attenuation correc- tion scheme), we compare disdrometer Z to that of KFDX, the nearest S-band WSR-88D, at 0.58 eleva- tion angle (Fig. 6). For the hailstorm case (red plus signs in Fig. 6), the median disagreement is 21.5 dB when S-band radar is used, but jumps to 5.8 dB for attenuation-corrected X-band radar (Fig. 5b). Note, however,thatthetworadarsaresamplingatdifferent heights (NOXP at 0.6km AGL and KFDX at 4.2km AGL; Table 1), which prevents us from making a de- finitive conclusion about the cause of the improved agreement.
c. 9 June 2010: Supercell thunderstorm with radar Z and ZDR less than disdrometer values
A supercell thunderstorm developed in the late af- ternoon of 9 June 2010 and moved into the western Nebraska panhandle near Scottsbluff. The core of the thunderstorm passed ;5 km south of the disdrometer deployments, which placed the disdrometers behind the precipitation core relative to the NOXP radar, which was deployed south of the storm core (Fig. 9a). Because the heaviest precipitation passed between the radar and disdrometers, the radar data collected near the dis- drometer locations were heavily attenuated. Time series of corrected radar and disdrometer (UF01) data are shown in Figs. 10a and 10b. The radar SQI [Eq. (6)]is also plotted (Figs. 9b, 10c).
Between 0130 and 0140 UTC, the disdrometer recorded Z and ZDR values that are 10-15 dB and 1- 3 dB larger, respectively, than the values obtained by the radar after attenuation correction. During this time, SQI ranges from 0.4 to 0.5, which is poor relative to the other observations considered in this analysis (76% have SQI . 0.8). Data with SQI , 0.8 are plotted in blue in Fig. 5 and exhibit smaller radar Z relative to the disdrometer, a trend that is not present in the other data subsets (black and red plus signs). We find that the median disagree- ment in Z (radar Z 2 disdrometer Z)forSQI, 0.8 is 212 dB, while the median disagreement in Z for SQI . 0.8 is 2.1 dB. These results indicate that it is much more likely for radar Z to be smaller than disdrometer Z when SQI is small and most of the radar signal has been lost due to attenuation. To verify that the disagreement is not solely due to errors in the disdrometer data, we note from Fig. 6 (blue plus signs) that the comparison improves markedly for S-band radar data (median disagreement of 20.66 versus 213 dB for X-band radar data corrected for attenuation). The radar beam heights are also more similar than in the 17 May hailstorm (0.5 km AGL for NOXP and 1.5 km AGL for KCYS; Table 1). This evidence supports our claim that a negative bias exists in the attenuation-corrected NOXP radar data when SQI , 0.8.
d. 12 June 2010: Squall line with radar Z and ZDR similar to disdrometer values
At approximately 2100 UTC on 12 June 2010, a squall line developed near Gruver, Texas. Radar and dis- drometer (UF05) time series data are shown in Fig. 11. The median attenuation-corrected radar and disdrometer Z and ZDR values are in closer agreement than in pre- vious case studies (5.0 and 1.2 dB, respectively). The best agreement (to within 5 and 0.5 dB) is found from 2139 to 2155 UTC, with greater disagreement (.15 and .1.5 dB) during the first two time steps (i.e., 2130 and 2136 UTC). From 2130 to 2136 UTC, the radar data (Fig. 12) show that a small convective cell (;2km in north-to-south extent) near the leading edge of the squall line moves over disdrometer UF05. The ice vol- ume recorded by the disdrometer (Fig. 11c) is largest during this time period, peaking at 5.6 cm3 min21 at 2130 UTC, before dropping below 4 cm3 min21 after 2139 UTC. The time series of maximum hail size (Fig. 11d) and accumulated PSD (Fig. 13) also depict the hail from the convective cell and show hailstones up to d 5 13 mm. From 2130 to 2136 UTC, hail resulted in larger radar Z and ZDR values relative to the dis- drometer data (Fig. 11), which is the same result found in section 4b. A radial stripe of suspiciously large radar Z (.55 dBZ) and ZDR (.6 dB) values is also present in the radar imagery at 2136 UTC (red circles in Fig. 12) in the southwestern portion of the squall line, possibly caused by the presence of hail there.
Following the passage of the convective cell and the hail at ;2137 UTC at the disdrometer site, agreement in Z and Z DR improves and the discrepancies are generally within 5 and 0.5 dB, respectively. During the period of agreement (2137-2155 UTC), the radar imagery depicts precipitation that is nearly uniform in time and space near the disdrometer site. Additionally, the observed ice volume remains small (median 0.7 cm3 min21), suggest- ing that hail is not biasing the attenuation correction. The large radar SQI (.0.95, not shown) and the relative absence of hail are the likely reasons for the improved agreement.
e. Radar and disdrometer hydrometeor classification comparisons
We now compare output from the radar and dis- drometer hydrometeor classification schemes. All of the disdrometer and radar data from Fig. 5 are included. The disdrometer hydrometeor classes consist of rain (RA), small hail (S. Hail), and large hail (L. Hail), while the radar classes of interest are BD, RA, HR, and RH. Because the radar scheme does not have firm rain rate or reflectivity thresholds that can be applied to the dis- drometer data to discriminate between BD, RA, and HR, these radar classes are combined into a general rain class. Therefore, the purpose of the comparison is to analyze the agreement between the liquid and ice classes of the two schemes. Because of error sources that in- clude overlapping rain and hail signatures in the radar data, errors in attenuation and differential attenuation correction, and particle advection, we do not expect perfect agreement; however, we can nevertheless use the data to explain under what conditions we expect disagreement and why.
The comparison results are shown in Fig. 14. Sectors that represent disagreement [i.e., the disdrometer (ra- dar) observes hail, but the radar (disdrometer) does not] are separated from the remainder of the chart. Of the 179 observations, 113 (63%) are in agreement. The most common scenarios are that both schemes detect hail (36% of the time) or that both detect rain (27% of the time). Of the 60 observations that disagree, 13 (7%) of them disagree because the radar scheme identifies hail when the disdrometer does not observe any. One likely explanation for this disagreement is that due to the sparseness of the hail, no hailstones passed through the sample volume of the disdrometer during the same time step as observed by the radar. In addition, it is also possible that the hail melted as it fell from the height of the radar volume to the disdrometer. Since the center of the radar beam was always 0.2-1 km AGL for the ob- servations considered here, this possibility is most likely when small hail was present at the height of the radar beam, which would be more susceptible to complete melting.
Disagreement in the remaining 53 observations (29%) results from the disdrometer detecting hail when the radar does not. It is important to note that the dis- drometer ice scheme does not account for the number of hailstones present; if just one hailstone is recorded during a 60-s time step, a classification of hail is still assigned by the disdrometer scheme, even though hail may not be the dominant contributor to the corre- sponding radar measurements. The median number of hailstones and median hailstone size observed in a 60-s time step by the disdrometer is greater when both the radar and the disdrometer schemes agree that hail is present (median of two hailstones and 8.5 mm when the schemes agree versus one hailstone and 6.0 mm). The radar classification scheme uses the dual-polarization radar variables to identify the dominant hydrometeor class within the radar volume, but other hydrometeor types may nevertheless be present. Thus, it may be that the radar scheme does not assign the hail class when the radar volume is dominated by rain and there are rela- tively few small hailstones present. This is possible be- cause the membership functions for rain and hail in the radar fuzzy logic scheme overlap, but it is only the class with the maximum rule strength (i.e., the maximum weighted sum of the membership function values) that is assigned to the radar range gate. When the disdrometer classifies hail but the radar does not, the median rule strength of the radar hail (rain) class is 0.6 (1.5), com- pared to 0.5 (1.5) when both instruments classify rain. However, the radar algorithm will not classify hail in either case because rain is the dominant scatterer in the radar volume.
An additional factor that is likely to cause the PARSIVEL disdrometer to report hail when the radar does not is the possibility that multiple particles may be present within the disdrometer sample volume at the same time. If two 5-mm raindrops were present inthesamplevolume,forinstance, the disdrometer would record a single 10-mm particle, which would be classified as a hailstone (Fig. 4). For a simulated heavy convective rain with intercept parameter N0 5 1400m23 mm21 and rainfall rate R 5 300mmh21, Loeuroffler-Mang and Joss (2000) found that the proba- bility of coincidences in the PARSIVEL disdrometer sample volume is ;5%. Therefore, disagreement between the hail detections of the radar and dis- drometer schemes is possible due to a combination of particle coincidences in the disdrometer sample vol- ume and the use of the fuzzy logic scheme for classi- fying the radar data.
5. Summary and conclusions
In this paper, we applied an attenuation correction scheme designed for rain (Steiner et al. 2009) to X-band dual-polarization radar data collected by NOXP in five supercell thunderstorms and one squall line during the VORTEX2 field campaign in 2010. The attenuation- corrected radar Z and ZDR were then compared to those derived from PSDs recorded by PARSIVEL dis- drometers using the T-matrix program, which required assumptions to be made about the axis ratio, fractional water content, and canting angle of the observed hail- stones (see Table 3 and appendix A). The Snyder et al. (2010) hydrometeor classification scheme was then ap- plied to the corrected radar data, and the results were compared to the output from a hydrometeor classifica- tion scheme that was developed for disdrometers in convective weather.
When the disdrometer and attenuation-corrected ra- dar data were compared, it was shown that 45% (38%) of the Z (ZDR) observations agree to within the sam- pling uncertainty of the PARSIVEL disdrometer (Figs. 5b,d). A case study analysis of a supercell thunderstorm with large hail demonstrated that the attenuation- corrected X-band radar Z (ZDR) tends to be larger than the values recorded by the disdrometer by 8.3 dB (1.5 dB), respectively (Fig. 7a). However, when S-band WSR-88D and disdrometer Z are compared, the mea- surements differ by only 21.5 dB (red plus signs in Fig. 6). The discrepancy between the X-band radar data and the disdrometer measurements is possibly due to the attenuation correction scheme overcorrecting the radar data within and behind the hail core of the supercell thunderstorm, although undercatchment of large hail- stones by the disdrometer may have also contributed to the disagreement. A second case study of a super- cell thunderstorm (Fig. 10) demonstrated that the dis- drometer tends to record larger Z and ZDR (by 13 and 0.61 dB, respectively) than the X-band radar when the radar signal quality is poor (SQI , 0.8). For the same data subset, only a 0.66-dB discrepancy in Z exists when the disdrometer and WSR-88D are compared (blue plus signs in Fig. 6). Disagreement between the disdrometer and attenuation-corrected X-band radar data due to poor SQI is most likely to occur within trailing pre- cipitation that is located behind heavy rainfall (relative to the radar location). A third case study analysis showed that when 1) large hail is not detected, 2) the radar signal quality is good (SQI . 0.8), and 3) the precipitation structure is horizontally homogeneous, Z and Z DR observations from both instruments agree to within 5 and 0.5 dB (2137-2155 UTC in Fig. 11).
When the hydrometeor classification schemes for the radar and the disdrometer are compared (Fig. 14), they agree 63% of the time. Disagreement results when the radar scheme diagnoses hail and the disdrometer scheme does not (7% of the observations) and when the disdrometer observes hail and it is not detected by the radar scheme (29%). Hail may be detected solely by the radar because small hail is present in the radar vol- ume that melts prior to reaching the surface or because the hail was especially sparse and not detected by the disdrometer. When the opposite situation occurred (i.e., the disdrometer observed hail but the radar scheme did not), it was shown that fewer, smaller hailstones were observed by the disdrometer than when the two instruments both observed hail. In these cases, the nonzero rule strength (i.e., the weighted sum of the membership function values) of the hail class suggests that hail may have been present in the radar volume, but because the radar hydrometeor classification scheme identifies the most dominant hydrometeor in the sam- pling volume, the hail was not classified.
The data quality analysis presented here may be particularly valuable to those who undertake future VORTEX2 microphysical process and data assimila- tion studies. We have shown that attenuation of radar data in severe thunderstorms can be substantial even in the portion of the thunderstorm that is initially penetrated by the radar beam. Further, since the as- sumptionsintheattenuationcorrectionschemeused in this study are not valid in ice, large errors may result in and beyond hail cores. This research may also be helpful to those who use the VORTEX2 disdrometer observations to validate model-predicted surface precipitation types. With the hydrometeor classifica- tion scheme in Fig. 4, median diameter and number concentration can be derived from the disdrometer data for each hydrometeor class and compared to those from numerical models.
Acknowledgments. This research was sponsored by NSF ATM-0910424 and NSF DGE-1144083. Funding for Donald Burgess came from NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement NA11OAR430072. Funding for NOXP data came from NSF ATM-0802717. We thank Gwo-Jong Huang and Prof. Bringi (Colorado State University) for the T-matrix program, in addition to George Fernandez, Carlos Lopez, and Forrest Masters (University of Florida), who designed the articulating disdrometers and supplied four of the stationary dis- drometers. We also thank Stephanie Higgins (University of Colorado) for writing many of the routines that process the disdrometer data. We are grateful to George Fernandez, Stephanie Higgins, Rachel Humphrey, Scott Landolt, Carlos Lopez, Daniel Nuding, and Cameron Redwine for deploying instruments during VORTEX2. The helpful feedback from two anonymous reviewers substantially improved an earlier version of this manu- script. Any opinions, findings, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.
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EVAN A. KALINA AND KATJA FRIEDRICH
Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, Colorado
SCOTT M. ELLIS
National Center for Atmospheric Research, Boulder, Colorado
DONALD W. BURGESS
Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and National Severe Storms
Laboratory, Norman, Oklahoma
(Manuscript received 28 January 2014, in final form 11 March 2014)
Corresponding author address: Evan A. Kalina, Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, UCB 311, Boulder, CO 80309.
Sensitivity to Hailstone Characteristics in the T-Matrix Program
To calculate Z and ZDR from disdrometer data that contain hail, characteristics of the hail must be specified, including axis ratio, fractional water content, and fall behavior. Table 3 provides the default values used in this analysis. However, since no measurements of axis ratio, fractional water content, or canting angle were made, the chosen values represent a source of uncertainty. Here, we examine the sensitivity of the results to some of the hailstone characteristics in the T-matrix scattering calculations.
To quantify the sensitivity, we select the PSD ob- served by disdrometer CU01 on 17 May 2010 (Fig. 8), since these data are from a hailstorm and should exhibit the greatest sensitivity to the hailstone characteristics. The quantities Z and ZDR are calculated for two values of the fractional water content of small hail (0.35 and 0.65), axis ratio of large hail (0.5 and 0.65), and canting angle standard deviation of all hail (358 and 658). These values, together with those provided in Table 3, provide a reasonable range over which these characteristics can be expected to vary (Knight 1986; Lesins and List 1986; Ryzhkov et al. 2011). The resulting sensitivities in Z and ZDR for the entire time series recorded by CU01 are shown in Fig. A1, relative to Z and ZDR obtained using the default values of the parameters in Table 3.No sensitivity is evident with respect to the small hail frac- tional water content (Fig. A1a). In contrast, up to 2-dB sensitivity in Z and 0.9 dB in ZDR is present when the large hail axis ratio is varied (Fig. A1b), although these sensitivities are only present in ;5 time steps of the disdrometer data. The Z and ZDR display more consis- tent sensitivity to hail canting angle standard deviation, although this sensitivity remains within 0.2 and 0.6 dB, respectively (Fig. A1c). Considering only the data in- cluded in Fig. 5 from CU01 on 17 May (Table A1), the mean sensitivity in Z (ZDR) to large hail axis ratio and hail canting angle standard deviation, respectively, is just 20.01 dB (0.03 dB) and 0.05 dB (0.1 dB). Simi- lar results (Table A1) were obtained from the PSD observed by disdrometer UF05 on 12 June 2010 (Fig.13).
In summary, because the PSDs in this study contain little hail relative to rain, Z and ZDR exhibit limited sensitivity to the hailstone axis ratio, fractional water content, and canting angle. This result does not mean that Z and Z DR are generally insensitive to hailstone characteristics. Rather, the small sample volume of the PARSIVEL disdrometer caused relatively few hailstones to be observed, which reduced the sensi- tivity of the results to the hailstone characteristics and meant that rain was the dominant contributor to Z and Z DR.
Sensitivity to Disdrometer Hydrometeor Classification Scheme
A partially melted hailstone of a given diameter can exhibit a range of fall speeds depending on its fractional water content and bulk density (Rasmussen and Heymsfield 1987). In the disdrometer hydrometeor classification scheme of Friedrich et al. (2013b), fall speed curves for dry graupel (Locatelli and Hobbs 1974)areused to determine the fall speed thresholds for the small hail region with 2 , d , 5mm(Fig. 4). Because small hailstones in supercell thunderstorms have a bulk density greater than that of graupel and are likely embedded in a torus of liquid water, it is reasonable to expect that these particle fall speeds are greater than the graupel curves offered by Locatelli and Hobbs (1974), but somewhat less than the fall speeds for pure rain given by Atlas et al. (1973).IntheFriedrich et al. (2013b) classification scheme, such particles are left unclassified (see Fig. 4) and are excluded from T-matrix computations of Z and ZDR,sincethereis uncertainty about whether they should be modeled as rain or small hail.
To examine the sensitivity of Z and ZDR to these excluded particles, we again use the data recorded by disdrometer CU01 during the 17 May 2010 hailstorm (Fig. 8) and compute Z and ZDR for two different tests: one that assumes the previously unclassified particles are rain, and a second that assumes the particles are hail. Figure B1a illustrates the sensitivity in Z (red lines) and ZDR (blue lines) for both the rain (solid lines) and hail (broken lines) tests. Up to 13-dB (1.5 dB) sensitivity in Z (ZDR) is evident for the time step at 2212 UTC. However, in all but one of the other 86 1-min time steps, negligible sensitivity is present. The reason for the large sensitivity at 2212 UTCis due to small disdrometer reflectivity (23 dBZ, not shown), coupled with a relatively large particle of d 5 4.25mm within the unclassified region. Because of the small total number of particles observed at 2212 UTC, the particle within the unclassified region has marked influence on Z and ZDR. In heavy rainfall typical of the thunderstorms observed in this study, however, Z and ZDR are relatively insensitive to whether particles in the unclassified region are discounted or assumed to be rain or hail. Table A1 indicates that for the data included in Fig. 5 from CU01 on 17 May, the mean sensitivity to the unclassified region is less than 0.2 and 0.02 dB for Z and ZDR, respectively. In fact, when all small hail particles are removed from the 17May PSD, Fig. B1b shows that Z and ZDR change by less than 0.2 dB for the entire time series recorded by CU01. For the data included in Fig. 5, the mean change in Z (ZDR) is 20.004 dB (0.002 dB; see Table A1). These tests demonstrate that despite the uncertainty in small hailstone characteristics, the impact on the results is small, likely because the PSDs examined here contain little small hail compared to rain.