## 1. Introduction

Anomalously high attenuation and differential attenuation at C band have been documented in recent studies (Ryzhkov et al. 2007; Vulpiani et al. 2008; Tabary et al. 2009). A motivating factor for the interest in attenuation is the potential to restore partially lost signals by applying a relation between the bias caused by attenuation (or differential attenuation) and differential phase (Bringi et al. 1990). It turns out that a relatively stable correction can be made if precipitation is pure rain. In the cases of hail or rain mixed with hail there appears to be no known robust correction. This is likely due to two factors. The relation between differential phase and attenuation (or differential attenuation) in hail or rain–hail mixture is not known. Apart from the fact that attenuation in hail is larger at shorter weather radar wavelengths (*λ* ≤ 5 cm) (Battan 1971), little else is known about its value because it is hard to estimate directly. Tabary et al. (2009) present compelling evidence of juxtaposition of high differential reflectivity *Z*_{DR} > 5 dB, reflectivity factor *Z _{c}* > 60 dB

*Z*, cross-correlation coefficient between horizontally and vertically polarized returns

*ρ*

_{hυ}below 0.93, and specific differential phase

*K*

_{DP}> 4° km

^{−1}in regions of anomalously high attenuation. These authors emphasize the importance of specific differential attenuation and its relation to

*K*

_{DP}. In conclusion they state that “it will be very difficult to correct the ray profiles behind the hot spot for attenuation.”

Our goal is to quantify the specific attenuation–differential attenuation in the storms’ hot spots at 5-cm wavelength and allude to microphysical causes. Estimation is done by comparing *Z* and *Z*_{DR} obtained with two almost-collocated polarimetric weather radars. One is the University of Oklahoma 5-cm weather radar (OU-PRIME), and the other is the National Oceanic and Atmospheric Administration (NOAA)/National Severe Storms Laboratory (NSSL) 10-cm dual-polarization radar (KOUN).

Our work attempts to identify possible causes of anomalous specific attenuations; knowing those causes would help researchers to devise robust correction procedures. It is not clear which hydrometeor population—heavy rain, melting hail, or both—is the main contributor. High specific differential attenuation *A*_{DP} has often been manifested by large negative *Z*_{DR} in the rear side (with respect to radar location) of strong convective cells. It is obviously caused by nonspherical-oriented hydrometeors. Thus, the key question here concerns the relation or correlation between large negative *Z*_{DR} and the specific attenuation at horizontal polarization *A _{h}*. Everything else being the same, large differential attenuation favors the use of the reflectivity factor at vertical polarization (

*Z*) to estimate rainfall rather than the one at horizontal polarization (

_{υ}*Z*) in regions where

_{h}*A*

_{DP}is substantial.

In this paper, specific attenuation and specific differential attenuation at C band are estimated in storm cells suspected of having hail or a rain–hail mixture. Specific attenuation in rain and melting hail is interpreted using simulations of these parameters based on disdrometer measurements and a simplified melting-hail model. Observations and methodology for estimating specific attenuation and specific differential attenuation are discussed in section 3, and quantitative interpretations are presented in section 4.

## 2. Specific attenuations in rain and melting hail

### a. Specific attenuation in rain

*A*and specific differential attenuation

_{h}*A*

_{DP}, are well examined in numerous theoretical and experimental studies (e.g., Bringi et al. 1990, 2001; Carey et al. 2000; Testud et al. 2000; Zrnić et al. 2000; Le Bouar et al. 2001; Keenan et al. 2001; Gourley et al. 2007; Vulpiani et al. 2008; Tabary et al. 2009). The range of variability of

*A*and

_{h}*A*

_{DP}at C band is illustrated in Fig. 1, in which the scatterplots between

*A*and

_{h}*Z*,

_{h}*A*

_{DP}and

*Z*, and

_{h}*A*

_{DP}and

*A*are displayed. These scatterplots are obtained via simulations using disdrometer measurements in central Oklahoma. The simulations are performed for a radar wavelength of 5.45 cm and a raindrop temperature of 0°C, assuming that the raindrop shape depends on its equivolume diameter as described by Brandes et al. (2002). The mean canting angle is assumed to be zero, and the width of the canting angle distribution is set to 10°. The disdrometer measurements are truncated at a maximum diameter of 8 mm and therefore might contain some contribution from small hail. For the overwhelming majority of the measured drop size distributions (DSDs) we get

_{h}*A*< 0.8 dB km

_{h}^{−1}and

*A*

_{DP}< 0.3 dB km

^{−1}. Overlaid in Fig. 1a are three mean curves describing the dependencies of

*A*on

_{h}*Z*according to Le Bouar et al. (2001) and Zhang and Moayeri (1999):

_{h}*A*= 0.22 × 10

_{h}^{−2}

*R*

^{1.2}valid for 5 GHz and

*T*= 0°C according to Zhang and Moayeri (1999) into the Marshall–Palmer relation (

*Z*= 200

*R*

^{1.6}).

The *A _{h}*–

*Z*and

*A*

_{DP}–

*Z*dependencies are affected by the DSD type, and the median volume drop diameter

*D*

_{0}is known to be well correlated with differential reflectivity

*Z*

_{DR}. According to Figs. 1a and 1b, most DSDs (with

*Z*> 55 dB

*Z*) are characterized by high values of

*Z*

_{DR}exceeding 4 dB (crosses in the figures), and the majority of the corresponding values of

*A*are below all three curves (Fig. 1a). The spread of

_{h}*A*and

_{h}*A*

_{DP}increases with

*Z*, especially at values larger than 50 dB

*Z*, and

*A*and

_{h}*A*

_{DP}are almost linearly correlated (Fig. 1c) so that the average ratio

*A*/

_{h}*A*

_{DP}is close to 3. This is in good agreement with the results of other studies (e.g., Bringi et al. 2001; Gourley et al. 2007; Vulpiani et al. 2008; Tabary et al. 2009).

The quantities *A _{h}* and A

_{DP}also depend on temperature (Jameson 1992); both increase with decreasing temperature for raindrops smaller than 5 mm in diameter, but the relation can be opposite for larger raindrops due to resonance scattering effects.

Polarimetric measurements provide an efficient and straightforward way to correct for attenuation by rain via differential phase Φ_{DP}. This variable is not affected by attenuation or by differential attenuation; hence, the attenuation-caused bias in *Z* and *Z*_{DR} can be estimated by multiplying Φ_{DP} with the factors *α* and *β* equal to the ratios *A _{h}*/

*K*

_{DP}and

*A*

_{DP}/

*K*

_{DP}, respectively. These factors are relatively stable in rain void of excessive numbers of large drops (i.e., diameters exceeding 5 mm at C band). The changes in

*α*and

*β*due to temperature variation between 0° and 20°C are within 40%.

In rain, the ratio *α* = *A _{h}*/

*K*

_{DP}at C band usually varies between 0.05 and 0.13 decibels per degree as reported by Bringi et al. (1990), Carey et al. (2000), Gourley et al. (2007), and Ryzhkov et al. (2007). Because

*K*

_{DP}rarely exceeds 6° km

^{−1}at C band, the maximum

*A*in rain is expected to be below 0.8 dB km

_{h}^{−1}, which is consistent with Fig. 1c. In contrast, the ratio

*β*=

*A*

_{DP}/

*K*

_{DP}varies over a much wider interval (from 0.008 to 0.1 decibels per degree) and is highly correlated with the maximum value of

*Z*

_{DR}in an attenuating rain cell (Ryzhkov et al. 2007; Tabary et al. 2009). Such a strong dependence of the parameter

*β*on

*Z*

_{DR}is illustrated in Fig. 2, in which the simulation results from the Oklahoma’s DSD measurements (crosses) and experimental observations in France by Tabary et al. (2009) (diamonds) are presented. Both Ryzhkov et al. (2007) and Tabary et al. (2009) speculate that very high values of

*β*(>0.06 decibels per degree) are possibly attributed to hail aloft or near the surface. Tabary et al. (2009) report that extremely high values of

*β*are associated with attenuating cells having unusually high (larger than 4 dB) intrinsic

*Z*

_{DR},

*Z*> 55 dB

*Z*,

*K*

_{DP}> 4° km

^{−1}, and a cross-correlation coefficient

*ρ*

_{hυ}below 0.93. If

*β*= 0.06 dB km

^{−1}is used as a possible cutoff value for pure rain, then the maximum

*A*

_{DP}in pure rain is expected to be below 0.4 dB km

^{−1}(for a maximum

*K*

_{DP}of 6° km

^{−1}).

### b. Specific attenuation in melting hail

Computations of polarimetric radar variables corresponding for melting hail at S and C bands using the model of Rasmussen and Heymsfield (1987) have been performed in the studies of Aydin and Zhao (1990), Vivekanandan et al. (1990), Aydin and Giridhar (1991), and Ryzhkov et al. (2009). Here we briefly summarize relevant results from the most recent work by Ryzhkov et al. (2009).

There is little doubt that water-coated melting large hail can significantly increase specific attenuation *A _{h}*. It is not clear if similar trends apply to specific differential attenuation

*A*

_{DP}and differential reflectivity

*Z*

_{DR}. Falling hailstones have more random orientations than large raindrops, which should considerably reduce

*A*

_{DP}and

*Z*

_{DR}. On the other hand, the torus of water surrounding a melting hailstone tends to stabilize its orientation, and therefore it is quite possible that water-coated hailstones may behave like giant raindrops, producing high

*Z*

_{DR}and

*A*

_{DP}.

*f*from 40° to 50° for dry hail to 10° for totally melted particles. It is assumed that dry hailstones with diameters above 1 cm have aspect ratios equal to 0.8 and that this ratio linearly increases from 0.8 to 1.0 as the dry graupel/hail diameter decreases from 1 to 0 cm. Similar to orientation, the aspect ratio of a melting particle is prescribed to change linearly with the mass water fraction so that the particle eventually acquires the shape of the raindrop to which it completely melts. A melting hailstone with a diameter larger than 1 cm cannot retain all melted water on its surface and starts shedding it so that the maximal mass of retained water

_{m}*M*and the mass of the ice core

_{w}*M*are related as (Rasmussen and Heymsfield 1987)

_{i}*M*and

_{w}*M*are expressed in grams. The computations have been performed assuming that the temperature lapse rate is 6.5° km

_{i}^{−1}, the relative humidity is 100%, and the original density of ice particles is equal to that of solid ice (0.92 g cm

^{−3}).

Smaller hailstones melt faster than larger hailstones when they have the same density; thus their *f _{m}* is higher than that of larger hailstones, which also lose their water mass due to shedding. Therefore, smaller melting hailstones (say, with diameters between 10 and 20 mm) have thicker water coatings [up to 4 mm; see also Aydin and Zhao (1990)] and a less random orientation compared to larger hailstones. Nonetheless, according to the results of Ryzhkov et al. (2009), the amount of water that can be retained by smaller hailstones before shedding occurs is not high enough to produce

*Z*

_{DR}in excess of the

*Z*

_{DR}for large raindrops with diameters between 5 and 8 mm. This is illustrated in Fig. 3, in which the dependencies of

*Z*

_{DR}on equivolume diameter across the particle spectrum ranging from pure raindrops (

*D*< 8 mm) to partially melted hailstones (

*D*> 8 mm) are displayed for S and C bands. Ryzhkov et al. (2009) showed that starting from the height level where raindrops (originating from melting hail) can reach diameters up to 8 mm, the

*f*–

_{m}*D*dependence does not change, and size dependencies of

*Z*

_{DR}in Fig. 3 remain the same for lower altitudes.

Differential reflectivity of melting hailstones (*D* > 8 mm) at S and C bands is lower than the *Z*_{DR} of large raindrops [which can reach up to 8 dB, for the resonance size of about 6 mm at C band according to Zrnić et al. (2000)]. On the other hand, the values of *A _{h}* and

*A*

_{DP}of melting hailstones are generally much higher than the ones associated with raindrops. The relative contributions by rain originating from complete melting of graupel/hail, from water shedding of partially melted hailstones, and from water-coated hail depend on the size distributions of the mother species. Ryzhkov et al. (2009) considered a biexponential distribution of dry ice at the freezing level and followed its evolution to lower levels as imposed by the Rasmussen–Heymsfield melting model for individual hailstones.

As an example, in Fig. 4 we present the Ryzhkov et al. (2009) results regarding the relative contributions of rain and melting hail to the C band *Z _{h}*,

*Z*,

_{υ}*A*,

_{h}*A*

_{DP}, and

*K*

_{DP}at the heights of 0 and 2 km aboveground in the case of large hail (maximum hail size is 35 mm and the freezing level is at 4 km). At 2 km, hydrometeors still contain ice cores if their diameters are larger than 5.7 mm. Figure 4 (left) shows that these partially melted hailstones with sizes between 5.7 and 25 mm make dominant contributions to all radar variables except

*K*

_{DP}. At the surface, only particles with

*D*> 8 mm still contain ice cores, and the contribution of melting hailstones to

*A*

_{DP}almost vanishes. Nonetheless, melting hailstones still contribute significantly to

*Z*,

_{h}*Z*, and

_{υ}*A*, along with pure raindrops having

_{h}*D*< 8 mm.

Ryzhkov et al. (2009) indicate that because of shedding of water, melting hailstones that had initial diameters between 8 and 15 mm end up as raindrops with similar sizes close to 8 mm. Thus melting hail enhances the concentration of the largest raindrops in the mixture with hail and pushes *Z*_{DR} and *A*_{DP} beyond the limits typical for “regular rain,” which originates from melting of smaller size graupel.

In summary, we can conclude that specific differential phase *K*_{DP} is mainly determined by raindrops with diameters below 5 mm and is not much affected by the presence of hail in a mixture with rain [see also Balakrishnan and Zrnić (1990) and Ryzhkov et al. (2008)]. Larger raindrops make, however, dominant contributions to *Z*_{DR} and *A*_{DP}, although small melting hail with diameters between 6 and 20 mm can contribute substantially to *A*_{DP} at earlier stages of the hail melting process, that is, at higher altitudes. Melting hail of all sizes adds significantly to *Z* and *A _{h}*, particularly at the beginning of melting. Therefore, according to the simulations, the presence of hail in a mixture with rain might cause a significant enhancement of

*A*and

_{h}*A*

_{DP}(the latter one is primarily due to vigorous production of large raindrops with sizes exceeding 5 mm).

The model simulations presented in Fig. 4 are valid for certain environmental conditions and assumptions about the initial distributions of ice particles aloft. A more detailed analysis of the output of the Rasmussen–Heymsfield model and the spectral (bin) cloud model of the Hebrew University of Jerusalem described by Ryzhkov et al. (2009) point to the same general conclusions, which can be used in the interpretation of polarimetric radar observations at S and C bands.

## 3. Observations and methodology

In this section we describe the characteristics of the observing radars, explain the type of measurements made, and discuss the analysis methods.

### a. Experimental setup

The C-band radar (OU PRIME) is located in Norman, Oklahoma, and belongs to the University of Oklahoma. Its main characteristics are listed in Table 1. The nearly collocated S-band radar (designated KOUN) is NOAA’s research version of Weather Surveillance Radar-1988 Doppler (WSR-88D) and has dual polarization (Melnikov et al. 2003). Both radars operate in the so-called SHV mode; that is, the horizontally and vertically polarized waves are transmitted and received simultaneously. Besides the difference in wavelengths, the two radars differ in beamwidth (0.5° for OU PRIME versus ∼1° for KOUN), range resolution (125 m versus 250 m), and peak power (1 MW versus ∼750 kW).

The radars are separated by 6.9 km, and the line connecting the locations is inclined 22.7° to the west. This separation adds to the uncertainty of comparisons. Nonetheless, there are no closer collocated stationary dual-polarization weather radars anywhere available for comparative studies.

For calibration purposes, the S-band reflectivities were compared with a nearby WSR-88D (KTLX, Oklahoma City) and adjusted accordingly, whereas for the OU PRIME there were no independent comparisons. A bias in either one or both would appear as a difference in reflectivity factors (see Table 2 in section 4). Nonetheless, this possible bias would not propagate into estimates of specific attenuation because these are obtained from *the slope* (with respect to range) of the difference between the two reflectivity factors. Differential reflectivities were calibrated on the data by determining the value in regions of snow aggregates that typically produce *Z*_{DR} less than 0.2 dB (Ryzhkov et al. 2005).

### b. Observations

On few occasions, polarimetric variables have been recorded almost simultaneously (within 30 s) by both radars. The radars operated in surveillance scan mode; the start of the volume scans were not synchronized, but the differences in time did not exceed 3 min. Reflectivity cells for comparisons were chosen based on the S-band reflectivity factor *Z _{s}* of KOUN and the similarity between the reflectivity patterns obtained from both radars. In this paper, data from the cells with

*Z*> 50 dB

_{c}*Z*are analyzed. We have chosen two cases for the comparison of S- and C-band data: a squall line on 10 March 2009 and a storm on 27 March 2009 containing a few hail-bearing cells. In the first case, hail was likely aloft but not on the ground (according to the National Climatic Data Center

*Storm Data*Web site, available online at http://www4.ncdc.noaa.gov/cgi-win/wwcgi.dll?wwevent~storms). In the second case, hail stones with diameters between 1.9 and 2.2 cm on the ground were reported by the

*Storm Data*Web site. Both cases reveal high attenuation and differential attenuation at C band. For the second case, the drop in

*Z*

_{DRc}in the rear of the cells down to −10 dB was substantially larger and connected also to a larger negative bias in

*Z*in comparison with

_{c}*Z*.

_{s}Figure 5 depicts the fields of *Z* and *Z*_{DR} measured at C band from a conical plan position indicator (PPI) scan at antenna elevation 0.42° at 0412 UTC 10 March 2009. The precipitation band is characterized by very high *Z* (exceeding 60 dB*Z*) and *Z*_{DR} over 5–6 dB. The *Z*_{DR} field exhibits differential attenuation in the northwest part of the precipitation band behind the squall line, where *Z*_{DR} values drop as low as −4 dB in some azimuthal directions.

The composite RHIs (Fig. 6) along the 320° azimuth (shown as a line in Fig. 5) display the fields of *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} measured by OU PRIME (left) and KOUN (right). It is evident that vertically elongated areas of high reflectivity appear “skinnier” at C band, which is a manifestation of stronger attenuation at the shorter wavelength. A quantitative comparison of *Z* fields indicates that signal attenuation at C band is between 10 and 15 dB.

Differential reflectivity *Z*_{DR} at C band is 1–2 dB higher than at S band below the freezing level, which was at about 3.4 km on that day. This difference is attributed to resonance scattering, which is well illustrated in Fig. 3. Resonance scattering is also the primary reason why the cross-correlation coefficient *ρ*_{hυ} is significantly lower at C band. Total differential phase is higher at the height interval between 2 and 4 km relative to the layers closer to the surface because the large amount of precipitating water formed aloft above the inflow region likely did not yet reach the ground at that time. Correspondingly, differential attenuation is higher at 3 km than in the layers below.

The fields of *Z* and *Z*_{DR} on a conical scan (PPI) and vertical cross sections (RHI) of the polarimetric variables from strong isolated hailstorms on 27 March 2009 are depicted in Figs. 7 and 8. The measurements were made with KOUN at 1211 UTC and OU PRIME at 1208 UTC. Several isolated convective cells producing hail up to 22 mm in diameter cause significant attenuation and differential attenuation at C band. According to the *Storm Data* Web site, the cell centered at *x* = 80 km and *y* = −10 km produced hail with diameters up to 1.9 and 2.2 cm at 1313 and 1330 UTC, respectively. The storm cell moved in the northeast direction and was too far from both radars to allow for a good quality comparison at the times when hail was actually reported. Hence, we decided to compare vertical cross sections of the S-band and C-band data at an earlier time (1208–1211 UTC), when the storm was still relatively close to the radar but had already developed a tall column of high reflectivity, which qualified it as a hail-bearing storm according to the probability of hail (POH) criterion (Delobbe and Holleman 2006; Tabary et al. 2009). Figure 8 shows two strong very close convective cells centered at ranges 75 and 85 km from the KOUN radar. The heights of the 45-dB*Z* contour and the freezing level are at 8.0 and 2.4 km, respectively. Hence, POH = 0.319 + 0.133(*H*_{45} − *H*_{0}) > 1. The cell at 85 km almost entirely disappears at lower levels in the C-band data because of anomalously high attenuation. Differential attenuation is much stronger in this case compared to the previous one. Melting hail causes depressions of *Z*_{DR} at S band down until well below the freezing level at 2.4 km. Extremely high values of *Z* at S band approaching 65 dB*Z* are associated with quite low values of *Z*_{DR} (less than 1 dB) close to the surface in the center of the precipitation core at range 75 km from the KOUN radar. This is a classical polarimetric hail signature (Bringi and Chandrasekar 2001). Note that although the hint of decreasing *Z*_{DR} associated with hail is also evident at C band at the distance of 71 km from the OU PRIME radar at a height of about 2 km, the *Z*_{DR} values in the melting hail area are much higher at C band in contrast to S band. It is obvious that anomalously high *Z*_{DR} produced by resonance-size raindrops originating from melting hail completely overwhelms the lower *Z*_{DR} associated with partially melted hail. The value of *Z*_{DR} is also significantly higher in the updraft region centered at about 70 km in the images obtained from the C-band radar. Moreover, *ρ*_{hυ} is much lower at C band compared to S band in the area containing melting hail.

Figure 8 clearly demonstrates that dry hail aloft does not produce noticeable attenuation and differential attenuation at C band because both the *Z* and *Z*_{DR} fields at S and C bands match very well above the height of 5 km. This is also confirmed by comparing composite RHIs at the two wavelengths for another hailstorm that occurred later on the same day (27 March 2009) and had an even longer vertical extension of high reflectivity values (Fig. 9). The scatterers in the region encompassed within the overlaid contours of 50 and 60 dB*Z* apparently do not produce noticeable attenuation and differential attenuation at C band above 2–3-km altitudes. Very high values of *Z* and well-pronounced three-body scattering signatures in *Z*_{DR} at both wavelengths undoubtedly point to the presence of large dry hail aloft (Hubbert and Bringi 2000). The three-body scattering *Z*_{DR} signature at the rear side of the storm is manifested by a tall tilted column of extremely high *Z*_{DR} (as high as 15 dB in this storm!). This *Z*_{DR} column associated with three-body scattering can be easily distinguished from the classical *Z*_{DR} column attributed to convective updraft. The updraft *Z*_{DR} column is usually shorter, is much closer to the main precipitation core, and is characterized by lower values of *Z*_{DR}.

### c. Methodology

The comparison necessitated a labor-intensive search for radials of data from both radars wherein reflectivity profiles matched well. The most difficult part was finding a good match within the storm cores of interest, which critically depends on the time lag between the two observations. This elaborated search was necessary because some data were collected up to 3 min apart. Furthermore, while the relative ranges and azimuths in the radar’s coordinate system are very accurate, the absolute locations can be offset by half a beamwidth. Because the radars are separated by 6.9 km, it was necessary to shift the data in range from one radar (in this case S band) with respect to the other (C band), and the shift obviously depends on the direction of the radar beam, the location of the cell, and the difference in time. Our manual procedure automatically accounts for advection because we searched through several radials (5–10) per storm cell that caused abnormal attenuation. We did so by taking one (e.g., S band) radial and comparing it to several C-band radials (usually up to three on either side of it in azimuth); we also shifted the C-band radials in range until a best subjective match was found.

The procedure produced matches such that the beam centers intersected at the cells of interest where the narrower OU PRIME (0.5°) beam was fully contained within the 1° KOUN beam. Ahead and beyond the intersection, the beams partially overlap over a distance of at least 5 km from the intersection.

The matched radial profiles were then analyzed at the location of beam intersections and its immediate vicinity. The variables that we plot and quantify for comparison are reflectivity factor at horizontal polarization (*Z _{h}*), differential reflectivity (

*Z*

_{DR}), differential phase (Φ

_{DP}), and cross-correlation coefficient (

*ρ*

_{hυ}) at both wavelengths. The plots of these variables were examined and analyzed in detail. To obtain the specific attenuation, the slope in range direction of the difference in reflectivity factors at horizontal polarization

*Z*−

_{s}*Z*was fitted with a straight line. The starting point of the fit for

_{c}*Z*−

_{s}*Z*was easily determined by detecting the location where a monotonic increase with range began. Generally this location coincided with the peak in

_{c}*Z*, and occasional offsets were small (less than couple of kilometers). The fit was made over short range intervals (a few kilometers) where attenuation at S band can be assumed negligible compared to the C-band attenuation. Similarly, the specific differential attenuation was obtained as the slope of

_{c}*Z*

_{DRs}−

*Z*

_{DRc}with respect to range. The starting point of the fit for

*Z*

_{DRs}−

*Z*

_{DRc}was typically at the point where

*Z*

_{DRc}=

*Z*

_{DRs}, about a couple of kilometers away from the peak in

*Z*

_{DRc}. The peak of

*Z*

_{DRc}was always larger than the peak of

*Z*

_{DRs}and was either ahead or behind (in range) of the peak in

*Z*. The end points of the fits were at the plateau of the fitted curves or at a location where the curves began to oscillate. The specific differential phase

_{c}*K*

_{DP}was a least squares fit to the filtered Φ

_{DP}; the filter was a uniform moving average over 2-km range. In cases of obvious contamination by backscatter differential phase,

*K*

_{DP}was estimated from the difference between the plateau of Φ

_{DP}behind the storm core and the value at the storm peak (divided by twice the distance). To avoid influences of the melting layer, all of the 27 March 2009 data at the elevation angle of 1.36° (C band) and 1.45° (S band) had an additional constraint. We interrupted the fits ahead of the melting level to exclude attenuation by wet snow. Subjective censoring of data for our quantitative analysis consisted of the following steps: The difference Δ

*Z*

_{s−c}needed to increase over a distance larger than 3 km, and downrange it had to be followed by a well-defined constant average value. The difference had to be small (<3 dB) at the peak of

*Z*.

_{c}One example of radial profiles from the event of 10 March 2009 is shown in Fig. 10. The differential phase at S band was shifted about 40° for better visual perception. Closer to the radar, the reflectivities from both radars are comparable. Clearly visible, beyond 90 km, is the attenuation of the shorter-wavelength radiation. The comparison of the polarimetric variables between 88 and 91 km suggests the following microphysical interpretation: Upon entering the storm, the beam encounters rain up to about 88 km, as both cross correlations are close to 1. Beyond 88 km the S-band correlation *ρ*_{hυs} maintains its high value, whereas the *ρ*_{hυc} drops. The drop in *ρ*_{hυc} is likely caused by changes in backscatter differential phase *δ _{c}*, which appears as a 20° hump in the differential phase (Fig. 10) at 89.5 km. Computed values of

*δ*for rain drops at a temperature 0°–10°C and sizes 6–8 mm are between 19° and 22° (Zrnić et al. 2000; their Fig. 1f). This is in accord with the observed 20° change.

_{c}The specific attenuation at C band in the region of *Z _{s}* > 45 dB

*Z*is about 2.5 dB km

^{−1}. The specific differential phase (

*K*

_{DP}) derived from the linearly fitted Φ

_{DP}between 90 and 96 km is about 4.3° km

^{−1}. (In cases of large fluctuation in Φ

_{DP}such as this one, the linear fit was done manually.) Thus the coefficient of proportionality

*α*between

*A*and

_{h}*K*

_{DP}is 0.58 decibels per degree, a value at least 4 times the maximum quoted for rain (0.13 decibels per degree; see section 2a). The differential phase at C band is about 2 times larger than at S band, and there is clear evidence of backscatter differential phase at both wavelengths (a hump at range 89.5 km). Beyond about 91 km, it is hard to discern between the backscatter differential phase and the propagation differential phase.

Between 90 and 95 km, the difference in differential reflectivities increases first because the scatterers’ size decreases; hence, the resonance effects subside, and at the same time differential attenuation finally takes over. The estimated value of *A*_{DP} = 0.73 dB km^{−1} is almost 2 times larger than the maximum value reported for rain (section 2a). The corresponding coefficient of proportionality *β* between *A*_{DP} and *K*_{DP} is about 0.17 decibels per degree in this case.

## 4. Data analysis

In this section, we analyze the relation between specific attenuation and specific differential attenuation and the polarimetric variables. We focus in particular on *Z _{c}*,

*Z*, Z

_{s}_{DRc}, and

*Z*

_{DRs}at the locations of peak values in

*Z*. Specific attenuation and specific differential attenuation are estimated over extended ranges beyond the peaks, as explained in section 3c (see Table 2 for a case summary of the observed minimum, median, mean, standard deviation, and maximum).

_{c}During the analysis it became apparent that the radial data from the two storm days differ. Our aim is to quantify attenuation as well as measurements at C band; thus, we first examined the locations of the peaks in *Z*_{DRc} and *Z _{c}* in the chosen radials. These peaks were nearly collocated. There are two reasons for the separation of peaks (typically less than 1 km). First, the maximum of

*Z*

_{DRc}is primarily associated with updrafts, whereas the

*Z*peak is usually centered on the downdraft. Another factor could be that differential attenuation decreases

_{c}*Z*

_{DRc}proportionately more than the decrease of

*Z*by attenuation. Hence, in a truly collocated case the measured peak in

_{c}*Z*

_{DRc}would appear closer to the radar.

According to the *Z*_{DRc}–*Z _{c}* scattergrams (Fig. 11) from the two days, the differential reflectivity for the 27 March case, with few exceptions, is noticeably lower than for the 10 March case at given

*Z*values. But the reflectivity factors at both wavelengths are generally higher for the 27 March case because that storm produced larger hail with lower intrinsic

_{c}*Z*

_{DRc}, and the data were sampled much closer to the freezing level, where the contribution by completely melted hail was smaller.

For the 10 March case, 29 pairs of matched radials were found to be suitable for our analysis. One of the pairs (Fig. 10) is described in section 3. About one-third of the pairs exhibit pronounced attenuation, whereas the rest have weaker attenuation. For half of the pairs, the *Z _{s}* is above 60 dB

*Z*(but not by much). In the 27 March case we found 21 matched pairs. The mean (and median) reflectivity factors at both frequencies are a few decibels larger in the 27 March case (see Table 2); more importantly, the mean values are above 60 dB

*Z*. For both days, the median, mean, and maximum differential reflectivities at C band are larger (mostly by over 1 dB) than the corresponding values at S band, as expected in cases of oriented scatterers such as large raindrops and/or melting small hail [for rain see Fig. 1b in Zrnić et al. (2000)].

At C band the median and mean of *Z*_{DRc} are slightly larger on 10 March than on 27 March, in agreement with the notion that rain constitutes a more significant portion of precipitation (within the resolution volumes) on 10 March. As mentioned in section 3, on 10 March the melting layer was 1 km higher than on 27 March; hence, at the lowest elevations whatever hail was present on 10 March would have undergone considerable melting. On 27 March the storm had larger reflectivities to begin with. Presumably the correspondingly larger hail would have had less time to melt, thus reducing the *Z*_{DRc}. Similar effects are also observed at S band (Table 2), for which *Z*_{DRs} is more than 2 dB lower on 27 March.

Several features can be deduced from examining specific attenuation *A _{h}* as a function of the maximum

*Z*(Fig. 12): All but one value is larger than 1 dB km

_{c}^{−1}, and at any fixed reflectivity the attenuation range is between 1 and 4 dB km

^{−1}. This is much larger than the values obtained from simulations using measured DSDs in rain (Fig. 1), where most

*A*values are less than 0.8 dB km

_{h}^{−1}. Significant variability is expected; although both variables are proportional to hydrometeor concentration, the species type affects each differently. Additional variability might be attributed to the imperfectly matched radials within pairs. In some of the 27 March data, moderate values of

*A*associated with very high

_{h}*Z*imply that large hailstones are not the dominant contributor to attenuation. That is, some very high

_{c}*Z*values (most likely associated with large hail) are not associated with proportionately high

_{c}*A*. This suggests that smaller melting hailstones and large raindrops contributed to the bulk of attenuation in both cases (10 and 27 March). Assuming that the model results in Fig. 4 are applicable, these sizes would be in the 5–15-mm range.

_{h}The solid and dashed curves in Fig. 12 are the same ones as in Fig. 1 (from Le Bouar et al. 2001) but extended to 65 dB*Z*. The curve for convective rain (extrapolated to higher *Z _{c}*) splits the scattergram into two almost equal parts. Thus, the curve can serve as a very crude estimate of expected attenuation associated with the peak

*Z*at values larger than 55 dB

_{c}*Z*.

The estimates of specific attenuation versus estimates of specific differential phase for both days are plotted in Fig. 13. The lower bound of the slope *α* (not shown) in the linear relation *A _{h}* =

*αK*

_{DPc}is about 0.33 decibels per degree; this is more than twice the maximum value reported for ordinary rain (section 2). The median slope in the 10 March case (Fig. 12) is 0.67 decibels per degree and towers at 1.48 decibels per degree for 27 March. Figure 4 can explain the plausible cause of such large difference in the “median” relation between

*A*and

_{h}*K*

_{DPc}.

The height of the freezing level was 1 km lower on 27 March 2009, and the radars sample less rain mixed with melting hail compared to the case on 10 March 2009 because a smaller portion of hail melted completely. Hence, *K*_{DP}, which is almost exclusively determined by the rain component, is lower on 27 March 2009, whereas *A _{h}* is substantial, as the

*A*panels in Fig. 4 indicate. Partially melted hailstones with sizes in the 8–15-mm range contribute most to the values of

_{h}*A*1–2 km below the freezing level. As melting progresses to lower altitudes, the total contribution of raindrops increases, which causes an increase in

_{h}*K*

_{DP}. At the same time, the concentration of melting hailstones with sizes above 10 mm decreases because of shedding, which results in the diminishing contribution to

*A*from the melting hail. Concurrently, the rain-related part of

_{h}*A*tends to increase, but this may not offset the overall decrease of

_{h}*A*. In other words, the ratio

_{h}*A*/

_{h}*K*

_{DP}decreases as melting progresses. Because of this complexity, there does not seem to be a tight dependence

*A*(

_{h}*K*

_{DPc}) that can be reliably used to restore attenuated signals in circumstances similar to those prevailing on either day, as Fig. 13 shows.

Differential attenuation (Fig. 14) is below 0.5 dB km^{−1} up to values of *Z _{c}* ∼ 57 dB

*Z*(excluding few outliers) followed by a significant increase in spread. Some

*A*

_{DP}values from 27 March are associated with higher

*Z*caused by the presence of larger hail. Otherwise the principal contributions to differential attenuation are from hydrometeors between 5 and 9 mm in size (Fig. 4). Thus, larger hail has more likely an isotropic shape and/or its concentration is not sufficient to affect differential attenuation, implying that preferential hydrometeor sizes contributed to differential attenuation and were similarly abundant on both days. The value of

_{c}*A*

_{DP}begins to rise with

*Z*starting at

_{c}*Z*≈ 55 dB

_{c}*Z*; this behavior is also present in simulations based on the disdrometer data (Fig. 1). The spread up to about 57 dB

*Z*generally is within the range (excluding a couple of outliers) of the simulated values (Fig. 1).

Figure 15 contains the scattergram *A*_{DP} versus *K*_{DPc}. The results are reminiscent of Fig. 13 for analogous reasons (the difference in *K*_{DP} being the major one). There is no well-defined tight trend, and the ratio of the “median line” slopes (*β* = 0.36 decibels per degree on 27 March and 0.175 decibels per degree on 10 March) is about 2.

The scattergrams *A _{h}* versus

*A*

_{DP}(Fig. 16) for the two days are intertwined for a larger fraction of points but a significant portion of points does not exhibit a tight correlation between

*A*and

_{h}*A*

_{DP}; very large

*A*

_{DP}correspond to relatively moderate

*A*. Note that the slope

_{h}*γ*=

*A*/

_{h}*A*

_{DP}of the median line, 3.8, is about 25% higher than the value 2.76 applicable to rain in Oklahoma (Fig. 1) and valid up to

*A*

_{DP}≈ 0.3 dB km

^{−1}. It might be fortuitous that the medians of the ratio

*γ*=

*A*/

_{h}*A*

_{DP}(3.8 on 10 March and 2.6 on 27 March; Table 2) bracket the value 2.76 valid in rain (Fig. 1). The value 2.94 provided by Vulpiani et al. (2008) is even better centered between these two medians, hinting that on the average the result from rain extends to melting hail, albeit with large variance.

Scattergrams of specific differential phase (Fig. 17) indicate an even spread about the theoretical curve *K*_{DPc} on that day. The *K*_{DPc} values are smaller on 27 March, implying smaller concentration of rain drops, as mentioned earlier.

## 5. Summary and conclusions

We have presented quantitative estimates of specific attenuation and specific differential attenuation of 5.44-cm radar signals in melting hail by comparing reflectivities and differential reflectivities with measurements of these variables at 10.9-cm wavelength. The comparison was tedious because the two radars are separated by 6.9 km, the data were often collected at slightly different times, and the beamwidths as well as elevation angles were not identical. In spite of these obstacles the comparison yielded plausible and physically realistic results, albeit with significant scatter. Despite the absence of an ideal match in time, it was possible to achieve a meaningful interpretation of the signatures and quantify the attenuation parameters.

We focused on specific attenuation and specific differential attenuation of radar signals (at C band) by storm cores with reflectivities exceeding 50 dB*Z*. Comparisons are made along radials considered to be well matched. The slopes with respect to range of the differences *Z _{s}* −

*Z*and

_{c}*Z*

_{DRs}−

*Z*

_{DRc}were assumed to represent well these specific attenuations; this eliminates the impact of calibration differences between the two radars and mitigates the effects of resonance scattering. Data from two days, 10 and 27 March 2009, were compared. There were several storm cells in a squall line on 10 March with high reflectivity values, but no hail was reported on the ground, and the height of the melting level was at 3.4 km aboveground. The storm on 27 March was an isolated convection on a strong cold front; the melting level was only at 2.4 km, and storm reports indicated hail up to 19–22-mm diameter on the ground. The differences in the height of the melting level and in hail size had an impact on the results.

Observational estimates were checked for consistency with a one-dimensional polarimetric model of melting hail in Ryzhkov et al. (2009).

Findings from this study are as follows:

The same preferential sizes and hydrometeor types (causing the bulk of anomalous specific attenuation) were present in both cases (10 and 27 March). The melting-hail model suggests that the likely size range contributing most to specific attenuation is 5–15 mm.

Specific attenuation has a wide range of values (1–4 dB km

^{−1}) and is highly variable. The median curve representing the relation*A*(_{h}*Z*) turns out to be the one for convective rain (Le Bouar et al. 2001) extrapolated to high values of_{c}*Z*._{c}Most estimates of specific differential attenuation

*A*_{DP}are within 0.2–2 dB km^{−1}, which is also way above the common range in pure rain. The increase in the median*A*_{DP}(*Z*) line and the spread of points look like an extrapolation of the scattergram for rain._{c}Neither

*A*nor_{h}*A*_{DP}exhibits a tight dependence on*K*_{DPc}that could be used to reliably restore attenuated signals in circumstances similar to those prevailing on either day. The median ratios of*A*/_{h}*K*_{DPc}and*A*_{DP}/*K*_{DPc}on 10 March 2009 (i.e.,*α*= 0.66 decibels per degree and*β*= 0.175 decibels per degree) are more than a factor of 2 lower than the corresponding ratios on 27 March 2009 (*α*=1.45 decibels per degree and*β*= 0.36 decibels per degree). This is consistent with model predictions that the ratios*A*/_{h}*K*_{DP}and*A*_{DP}/*K*_{DP}tend to decrease as the proportion of completely melted hail increases.On both days the specific differential phases estimated at C band and S band are consistent, and the scattergram is split evenly about the theoretical value dictated by the difference in these wavelengths. This implies that the dominant contribution to specific differential phases comes from similar hydrometeor species and that these are mainly within the size range of Rayleigh scatterers (at C band). These, according to the melting-hail model, are drops between 2 and 4 mm in diameter.

Somewhat unexpected is a relatively tighter relation between

*A*and_{h}*A*_{DP}wherein the “median line” is the same for both days. Perhaps such a relation could serve as a basis for correcting attenuation along radials where the differential attenuation is easier to estimate.The melting-hail model and observations imply that the primary contribution to

*K*_{DPc}comes from drops between 2 and 4 mm in diameter. The model indicates that hydrometeors (raindrops or small melting hailstones) with diameters between 5 and 9 mm are dominant contributors to*A*_{DP}, although, consistent with radar observation, this assertion has not been verified independently. According to the model, hail diameters between 8 and 15 mm dominate the contributions to*A*. This is also consistent with the observations._{h}Localized values of

*A*,_{h}*A*_{DP},*A*/_{h}*K*_{DPc}, and*A*_{DP}/*K*_{DPc}in storms containing large drops and melting hail can be much higher than the values averaged over the propagation path through the storm. Substantial backscatter differential phase in these regions complicates the estimation of the propagation differential phase. This suggests special treatment of such areas (hot spots) in attenuation correction schemes.

Overall, our findings indicate that an accurate correction of attenuation–differential attenuation in the “hot spot” regions is difficult. First, such regions have to be identified by combining polarimetric variables and the height of the melting layer in a classification scheme. If the cross-correlation coefficient does not drop too low within the hot spot and beyond so that differential phase does not oscillate wildly, then the “hot spot” technique for attenuation correction suggested by Ryzhkov et al. (2007) is a possible choice. However, if differential phase is useless, then average empirical (or model-based) *A _{h}*–

*Z*relations extrapolated to reflectivities higher than 55 dB

*Z*(as in Fig. 12) might be considered for

*Z*correction. Similarly, empirically derived

*Z*

_{DR}in the hot spot] might be the only plausible option for

*Z*

_{DR}correction.

Concerning hail detection and determination of its size, we have the following comment: Criteria valid at S band need significant revision for application to C band. For example, differential reflectivity in melting hail at C band is much larger than at S band, but it drops to small values in dry hail. A significant drop in *Z*_{DR} collocated with high *Z* might indicate gigantic hail. In melting hail the drop in *ρ*_{hυ} at C band is much more pronounced than at S band.

A very important fact emanating from this study is the possibility to deduce bulk properties of hydrometeors by comparing the volumetric fields of the polarimetric variables obtained at S and C bands. Illustrative examples of comparisons indicate that much can be learned about size, orientation, and phase of hydrometeors over volumes that play a role in precipitation production. Therefore, it follows that precipitation evolution and interaction with storm dynamics could be observed. Comparisons of this kind aim to pinpoint the type and size of hydrometeors in the storm volume. We do not advocate operational use of collocated (S and C band) radars. Rather, studies of polarimetric radar data at two wavelengths would improve understanding of precipitation evolution and, in due time, could be applied to polarimetric observations at a single radar wavelength. This is not an advocacy for an operational two-wavelength system; rather it is a call for scientific inquiry with multiple-wavelength radars.

## Acknowledgments

We thank the engineering team lead by Allen Zahrai for making modifications on the research NOAA/NSSL WSR-88D to allow versatile control and data collection. Mike Schmidt and Richard Wahkinney maintained the radar in impeccable condition, and Valery Melnikov was responsible for calibration of dual-polarization variables and data collection efforts. We also thank Alessandro Battaglia, under whose project a part of this work was done, Jan Keller for software consulting, and Richard Doviak for constructive comments about the manuscript. The OU PRIME is a recently established facility operated by the Atmospheric Radar Research Center (ARRC) at the University of Oklahoma (OU) and was manufactured by Enterprise Electronic Corporation (EEC). The authors appreciate the efforts of Redmond Kelley and Boon Leng Cheong in the development, maintenance, and operation of OU PRIME. Funding for the CIMMS author was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–OU Cooperative Agreement NA17RJ1227, U.S. Department of Commerce. The work of Lesya Borowska was funded by a grant of the Deutsche Forschungsgemeinschaft (DFG) in the framework of the Transregional Research Center TRR32. Finally, each of the three anonymous reviewers provided very valuable advice to significantly improve the manuscript; we thank them.

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Scatterplots of the ratio *A*_{DP}/*K*_{DP} vs *Z*_{DR} estimated from simulations based on the measured DSDs (crosses) for *T* = 0°C and from the observations (diamonds) by Tabary et al. (2009).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scatterplots of the ratio *A*_{DP}/*K*_{DP} vs *Z*_{DR} estimated from simulations based on the measured DSDs (crosses) for *T* = 0°C and from the observations (diamonds) by Tabary et al. (2009).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scatterplots of the ratio *A*_{DP}/*K*_{DP} vs *Z*_{DR} estimated from simulations based on the measured DSDs (crosses) for *T* = 0°C and from the observations (diamonds) by Tabary et al. (2009).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Size dependencies of *Z*_{DR} at S (thin line) and C (thick line) band across the particle spectrum of raindrops (*D* < 8 mm) and partially melted hailstones (*D* > 8 mm).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Size dependencies of *Z*_{DR} at S (thin line) and C (thick line) band across the particle spectrum of raindrops (*D* < 8 mm) and partially melted hailstones (*D* > 8 mm).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Size dependencies of *Z*_{DR} at S (thin line) and C (thick line) band across the particle spectrum of raindrops (*D* < 8 mm) and partially melted hailstones (*D* > 8 mm).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Relative contributions of different parts of particle size spectrum to C-band (top to bottom) *Z _{h}* (solid line) and

*Z*(dashed line),

_{υ}*A*,

_{h}*A*

_{DP}, and

*K*

_{DP}at (left) 2-km and (right) 0-km height for a freezing level at 4 km and a maximum dry hail diameter at the freezing level of 35 mm (from Ryzhkov et al. 2009). Dashed lines in top row correspond to

*Z*at vertical polarization.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Relative contributions of different parts of particle size spectrum to C-band (top to bottom) *Z _{h}* (solid line) and

*Z*(dashed line),

_{υ}*A*,

_{h}*A*

_{DP}, and

*K*

_{DP}at (left) 2-km and (right) 0-km height for a freezing level at 4 km and a maximum dry hail diameter at the freezing level of 35 mm (from Ryzhkov et al. 2009). Dashed lines in top row correspond to

*Z*at vertical polarization.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Relative contributions of different parts of particle size spectrum to C-band (top to bottom) *Z _{h}* (solid line) and

*Z*(dashed line),

_{υ}*A*,

_{h}*A*

_{DP}, and

*K*

_{DP}at (left) 2-km and (right) 0-km height for a freezing level at 4 km and a maximum dry hail diameter at the freezing level of 35 mm (from Ryzhkov et al. 2009). Dashed lines in top row correspond to

*Z*at vertical polarization.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 0412 UTC 10 Mar 2009 at elevation 0.42°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 0412 UTC 10 Mar 2009 at elevation 0.42°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 0412 UTC 10 Mar 2009 at elevation 0.42°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Vertical cross sections of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the precipitation band on 10 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 320° at 0412 UTC, whereas the KOUN (S band) data correspond to the azimuth of 319° and 0412 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*. The height is with respect to ground.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Vertical cross sections of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the precipitation band on 10 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 320° at 0412 UTC, whereas the KOUN (S band) data correspond to the azimuth of 319° and 0412 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*. The height is with respect to ground.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Vertical cross sections of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the precipitation band on 10 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 320° at 0412 UTC, whereas the KOUN (S band) data correspond to the azimuth of 319° and 0412 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*. The height is with respect to ground.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The PPI fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 1208 UTC 27 Mar 2009 at elevation 1.37°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The PPI fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 1208 UTC 27 Mar 2009 at elevation 1.37°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The PPI fields of (top) *Z* and (bottom) *Z*_{DR} measured at C band at 1208 UTC 27 Mar 2009 at elevation 1.37°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the storm on 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 98° at 1208 UTC, whereas the KOUN (S band) data correspond to the azimuth of 101° and 1211 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the storm on 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 98° at 1208 UTC, whereas the KOUN (S band) data correspond to the azimuth of 101° and 1211 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top to bottom) *Z*, *Z*_{DR}, Φ_{DP}, and *ρ*_{hυ} at (left) C and (right) S band across the storm on 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 98° at 1208 UTC, whereas the KOUN (S band) data correspond to the azimuth of 101° and 1211 UTC. Overlaid contours correspond to radar reflectivities of 40 and 50 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top) *Z* and (bottom) *Z*_{DR} at (left) C and (right) S band in the hailstorm observed at 1645–1647 UTC 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 151° at 1647 UTC, whereas the KOUN (S band) data correspond to the azimuth of 152° and 1645 UTC. Overlaid contours correspond to radar reflectivities of 50 and 60 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top) *Z* and (bottom) *Z*_{DR} at (left) C and (right) S band in the hailstorm observed at 1645–1647 UTC 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 151° at 1647 UTC, whereas the KOUN (S band) data correspond to the azimuth of 152° and 1645 UTC. Overlaid contours correspond to radar reflectivities of 50 and 60 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The RHI fields of (top) *Z* and (bottom) *Z*_{DR} at (left) C and (right) S band in the hailstorm observed at 1645–1647 UTC 27 Mar 2009. The OU PRIME (C band) data are taken at the azimuth of 151° at 1647 UTC, whereas the KOUN (S band) data correspond to the azimuth of 152° and 1645 UTC. Overlaid contours correspond to radar reflectivities of 50 and 60 dB*Z*.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Radial dependencies of *Z _{s}* and

*Z*

_{DR}at S (black curves) and C (gray curves) bands; and the differences

*Z*−

_{s}*Z*and

_{c}*Z*

_{DRs}−

*Z*

_{DRc}with the black dashed straight lines in the middle panels indicating average slopes from which the estimates of

*A*and

_{h}*A*

_{DP}at C band are obtained. Date is 10 Mar, time is 0332 UTC, and the beam positions are the azimuth of 269.5° and the elevation of 0.42° for C band and the azimuth of 263° and the elevation of 0.48° for S band. The differential phase for S band was shifted about 40° for better visual perception.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Radial dependencies of *Z _{s}* and

*Z*

_{DR}at S (black curves) and C (gray curves) bands; and the differences

*Z*−

_{s}*Z*and

_{c}*Z*

_{DRs}−

*Z*

_{DRc}with the black dashed straight lines in the middle panels indicating average slopes from which the estimates of

*A*and

_{h}*A*

_{DP}at C band are obtained. Date is 10 Mar, time is 0332 UTC, and the beam positions are the azimuth of 269.5° and the elevation of 0.42° for C band and the azimuth of 263° and the elevation of 0.48° for S band. The differential phase for S band was shifted about 40° for better visual perception.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Radial dependencies of *Z _{s}* and

*Z*

_{DR}at S (black curves) and C (gray curves) bands; and the differences

*Z*−

_{s}*Z*and

_{c}*Z*

_{DRs}−

*Z*

_{DRc}with the black dashed straight lines in the middle panels indicating average slopes from which the estimates of

*A*and

_{h}*A*

_{DP}at C band are obtained. Date is 10 Mar, time is 0332 UTC, and the beam positions are the azimuth of 269.5° and the elevation of 0.42° for C band and the azimuth of 263° and the elevation of 0.48° for S band. The differential phase for S band was shifted about 40° for better visual perception.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of *Z*_{DRc}–*Z _{c}* from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of *Z*_{DRc}–*Z _{c}* from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of *Z*_{DRc}–*Z _{c}* from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scatterplot of *A _{h}* vs peak reflectivity at C band for the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scatterplot of *A _{h}* vs peak reflectivity at C band for the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scatterplot of *A _{h}* vs peak reflectivity at C band for the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A _{h}*–

*K*

_{DPc}scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A _{h}*–

*K*

_{DPc}scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A _{h}*–

*K*

_{DPc}scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*Z _{c}* scattergram from data on 10 Mar (diamonds) and 27 Mar (dots).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*Z _{c}* scattergram from data on 10 Mar (diamonds) and 27 Mar (dots).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*Z _{c}* scattergram from data on 10 Mar (diamonds) and 27 Mar (dots).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*K*_{DPc} scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*K*_{DPc} scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

The *A*_{DP}–*K*_{DPc} scattergram from data on 10 Mar (diamonds) and 27 Mar (dots). The dashed and solid median lines are for 10 and 27 Mar, respectively.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific attenuation *A _{h}* and specific differential attenuation

*A*

_{DP}data from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific attenuation *A _{h}* and specific differential attenuation

*A*

_{DP}data from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific attenuation *A _{h}* and specific differential attenuation

*A*

_{DP}data from the 10 and 27 Mar storms.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific differential phases *K*_{DPs} and *K*_{DPc} at S and C bands.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific differential phases *K*_{DPs} and *K*_{DPc} at S and C bands.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Scattergrams of specific differential phases *K*_{DPs} and *K*_{DPc} at S and C bands.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2465.1

Characteristics of the KOUN and OU PRIME radars.

Statistics of the polarimetric measurements at the two wavelengths (10.9 and 5.44 cm), estimates of attenuation and differential attenuation at C band, ratios of attenuation to specific differential attenuation, and ratio of specific differential phase at the two bands.