Polarimetric Attenuation Correction in Heavy Rain at C Band

Ji-Young Gu Department of Environmental Atmospheric Sciences, Pukyong National University, Busan, Korea

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A. Ryzhkov Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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P. Zhang Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma

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P. Neilley WSI Corporation, Andover, Massachusetts, and Enterprise Electronics Corporation, Enterprise, Alabama

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M. Knight WSI Corporation, Andover, Massachusetts, and Enterprise Electronics Corporation, Enterprise, Alabama

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B. Wolf Valparaiso University, Valparaiso, Indiana

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Dong-In Lee Department of Environmental Atmospheric Sciences, Pukyong National University, Busan, Korea

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Abstract

The ability of C-band polarimetric radar to account for strong attenuation/differential attenuation is demonstrated in two cases of heavy rain that occurred in the Chicago, Illinois, metropolitan area on 5 August 2008 and in central Oklahoma on 10 March 2009. The performance of the polarimetric attenuation correction scheme that separates relative contributions of “hot spots” (i.e., strong convective cells) and the rest of the storm to the path-integrated total and differential attenuation has been explored. It is shown that reliable attenuation correction is possible if the radar signal is attenuated by as much as 40 dB. Examination of the experimentally derived statistics of the ratios of specific attenuation Ah and differential attenuation ADP to specific differential phase KDP in hot spots is included in this study. It is shown that these ratios at C band are highly variable within the hot spots. Validation of the attenuation correction algorithm at C band has been performed through cross-checking with S-band radar measurements that were much less affected by attenuation. In the case of the Oklahoma storm, a comparison was made between the data collected by closely located C-band and S-band polarimetric radars.

Corresponding author address: Dong-In Lee, Dept. of Environmental Atmospheric Sciences, Pukyong National University, 599-1, Daeyeon 3-Dong, Nam-Gu, Busan, Korea. Email: leedi@pknu.ac.kr

Abstract

The ability of C-band polarimetric radar to account for strong attenuation/differential attenuation is demonstrated in two cases of heavy rain that occurred in the Chicago, Illinois, metropolitan area on 5 August 2008 and in central Oklahoma on 10 March 2009. The performance of the polarimetric attenuation correction scheme that separates relative contributions of “hot spots” (i.e., strong convective cells) and the rest of the storm to the path-integrated total and differential attenuation has been explored. It is shown that reliable attenuation correction is possible if the radar signal is attenuated by as much as 40 dB. Examination of the experimentally derived statistics of the ratios of specific attenuation Ah and differential attenuation ADP to specific differential phase KDP in hot spots is included in this study. It is shown that these ratios at C band are highly variable within the hot spots. Validation of the attenuation correction algorithm at C band has been performed through cross-checking with S-band radar measurements that were much less affected by attenuation. In the case of the Oklahoma storm, a comparison was made between the data collected by closely located C-band and S-band polarimetric radars.

Corresponding author address: Dong-In Lee, Dept. of Environmental Atmospheric Sciences, Pukyong National University, 599-1, Daeyeon 3-Dong, Nam-Gu, Busan, Korea. Email: leedi@pknu.ac.kr

1. Introduction

The S-band weather radars in the United States are primarily utilized for the observations of severe storms. The major reason for this is that shorter-wavelength radars may experience significant attenuation in heavy precipitation. A long-standing problem of attenuation correction at shorter radar wavelengths can be efficiently resolved if the radar has dual-polarization capability.

According to the National Weather Service plans, single-polarization Weather Surveillance Radars-1988 Doppler (WSR-88D) will be retrofitted in the next few years by adding polarimetric capability and, in the long run, may be complemented by C-band and X-band polarimetric radars for better areal coverage. Note that all weather radars utilized by the Federal Aviation Administration in the terminal areas of airports operate at C band. Television companies also use C-band Doppler radars, some of which already have polarimetric diversity. Hence, it is important to investigate and demonstrate abilities of such radars to quantitatively assess characteristics of severe storms in the presence of strong attenuation.

Polarimetric methods for attenuation correction of radar reflectivity Z and differential reflectivity ZDR utilize measurements of differential phase ΦDP, which is immune to attenuation (Bringi and Chandrasekar 2001). Simplified versions of the attenuation correction techniques assume that the coefficients of proportionality α and β between the Z and ZDR biases and ΦDP do not vary much (Bringi et al. 1990). The correction factors α and β are equal to the ratios Ah/KDP and ADP/KDP, respectively, where Ah is specific attenuation of microwave radiation at horizontal polarization, ADP is specific differential attenuation, and KDP is specific differential phase [see Bringi and Chandrasekar (2001) for definitions]. However, at C band, these ratios are highly variable in convective cells containing large raindrops and hail because of effects of resonance scattering (Carey et al. 2000; Keenan et al. 2001; Bringi et al. 2001; Ryzhkov et al. 2006, 2007; Gourley et al. 2006; Vulpiani et al. 2008; Tabary et al. 2008, 2009; Borowska et al. 2009, 2011).

In rain, the ratio α = Ah/KDP at C band usually varies between 0.05 and 0.18 dB per degree as reported by Bringi et al. (1990), Carey et al. (2000), Gourley et al. (2006), Ryzhkov et al. (2007), and Keranen and Yllasjarvi (2008). The ratio β = ADP/KDP varies over an interval from 0.008 to 0.1 dB per degree and exhibits a strong correlation with the maximum value of ZDR in an attenuating rain cell (Carey et al. 2000; Keenan et al. 2001; Ryzhkov et al. 2007; Tabary et al. 2009). Borowska et al. (2009, 2011) estimated much higher local values of α and β within “hot spots” containing large raindrops and melting hail.

More-sophisticated polarimetric schemes for attenuation correction attempt to take into account the variability of α and β (Carey et al. 2000; Bringi et al. 2001; Ryzhkov et al. 2007; Vulpiani et al. 2008). Bringi et al. (2001) suggested the self-consistent method with constraints to optimize the coefficients α and β by examining the radial profile of ΦDP and imposing constraints on the corrected value of ZDR at the far side of an attenuating rain cell. This method implies that these coefficients change from ray to ray but remain constant along each particular ray. Vulpiani et al. (2008) allowed for variability of the coefficients α and β along the propagation path by identifying the prevailing rain regime in each range gate, but a single correction factor weighted by KDP for any given path is used for attenuation correction along the path. Carey et al. (2000) took into account that the parameters α and β can also vary along the radial and assigned different fixed values of them in hot spots or “big drop zones” and the rest of the propagation path. The idea of Carey et al. (2000) was further advanced by Ryzhkov et al. (2006, 2007) who proposed a procedure for a more objective estimation of α and β within hot spots. The latter method is described and explored in this paper.

The proposed method for attenuation correction is tested for two heavy-rain events that were observed with two different C-band polarimetric radars in central Oklahoma and in the Chicago, Illinois, metropolitan area. Both radars were built by the Enterprise Electronics Corporation. One of them belongs to Valparaiso University, in Valparaiso, Indiana, and another one belongs to the University of Oklahoma.

Results of attenuation correction are validated using self-consistency between radar polarimetric variables and comparisons with the measurements from a nearby polarimetric prototype of the WSR-88D (KOUN) in Oklahoma and from a single-polarization WSR-88D (KLOT) in the Chicago area that did not experience much attenuation in the storms.

The paper is organized as follows. The description of the hot-spot attenuation correction procedure and its comparison with the self-consistent method of Bringi et al. (2001) are presented in section 2. Section 3 contains a validation of the results of the attenuation correction at C band through direct comparison with the measurements from the nearby KOUN radar in Oklahoma. Section 4 is devoted to the analysis of the Chicago storm and statistics of the parameters α and β derived from C-band polarimetric measurements, and section 5 includes a summary of the results.

2. Algorithm for attenuation correction

a. Brief review of polarimetric techniques for attenuation correction at C band

The first polarimetric technique for attenuation correction of Z and ZDR was suggested by Bringi et al. (1990). According to this method, the biases of Z and ZDRZ and ΔZDR, respectively) are estimated from simple formulas:
i1558-8432-50-1-39-e1
i1558-8432-50-1-39-e2
where the coefficients α and β are supposed to be constant. The coefficient α is the ratio of specific attenuation Ah and specific differential phase KDP, whereas the coefficient β is the ratio of specific differential attenuation ADP and KDP. Testud et al. (2000) proposed another correction algorithm for Z (the “ZPHI” rain-profiling algorithm) that also assumes a fixed coefficient α.
According to the ZPHI method, the Hitschfeld and Bordan (1954) scheme is used with an integral constraint based on the total span of differential phase within the range interval (r0, rm) that contains radar echo so that
i1558-8432-50-1-39-e3
where
i1558-8432-50-1-39-e4
A radial profile of Ah(r) is estimated using attenuated radar reflectivity Za and ΔΦDP through the formula
i1558-8432-50-1-39-e5
where
i1558-8432-50-1-39-e6
i1558-8432-50-1-39-e7
The parameter b is an exponent in the relation Ah = aZb and the radar reflectivity factor in (5)(7) is expressed in linear units.
Later on, Bringi et al. (2001) extended the ZPHI method to optimize the coefficient α for each radial of data (a self-consistent method with constraints). The self-consistent method does not require a fixed a priori value for α, but rather searches for an optimal α value within a predetermined range (αmin, αmax) for each particular radial. For each α value in the predetermined range, a model profile of differential phase is calculated as
i1558-8432-50-1-39-e8
and is compared with the measured (and filtered) ΦDP(r) over the entire range from r0 to rm through an attenuating rain cell. An optimal α(opt) minimizes the difference Δ between the measured and calculated profiles:
i1558-8432-50-1-39-e9
where i denotes the range gate index from r0 to rm.
Differential reflectivity is corrected according to the formula
i1558-8432-50-1-39-e10
in which specific differential attenuation ADP(r) is prescribed to be proportional to the optimized Ah[r, α(opt)]:
i1558-8432-50-1-39-e11
with the coefficient of proportionality γ determined from
i1558-8432-50-1-39-e12
In (12), and ZDR(rm) are measured (biased by differential attenuation) and expected differential reflectivity, respectively, at range rm for corrected radar reflectivity Z(rm). In other words, the corrected value of ZDR at range rm has to be equal to what is expected (in rain) at reflectivity Z(rm). This principle of ZDR correction was first suggested by Smyth and Illingworth (1998) (with ZDR equal to 0 dB in the shadow of an attenuating cell) and later modified by Bringi et al. (2001) and Tabary et al. (2009), who assumed that the value of ZDR is a function of corrected radar reflectivity factor there.

b. Attenuation and differential attenuation in hot spots

High variability of the correction factors α and β in strong convective cells is attributed to strong resonance scattering effects at C band that impact Ah, ADP, and KDP for raindrop sizes exceeding 5 mm (Carey et al. 2000; Zrnić et al. 2000; Keenan et al. 2001; Ryzhkov and Zrnić 2005). The effects of resonance scattering at C band are illustrated in Figs. 1 –3, where results of simulations of different radar variables from the measured drop size distributions (DSD) in central Oklahoma are presented. Computations were made assuming that temperature of raindrops is 20°C, their shape depends on equivolume diameter as prescribed by Brandes et al. (2002), the width of the canting angle distribution is 10°, and maximal raindrop diameter is 8 mm. Similar to analogous simulations by Keenan et al. (2001), Dmax = 8 mm was chosen to accentuate the “large drop” resonance effects.

Differential reflectivity ZDR exhibits extreme variability for Z > 45 dBZ (Fig. 1). Very high ZDR can be associated with relatively moderate values of Z. The scatterplots of Ah and ADP versus KDP are shown in Fig. 2. The degree of scatter is substantially reduced for ZDR < 3 dB and the ratios Ah/KDP and ADP/KDP are much more stable for lower ZDR. In general, both parameters α = Ah/KDP and β = ADP/KDP tend to increase with increasing ZDR (e.g., Carey et al. 2000; Keenan et al. 2001). This tendency is especially well pronounced for the ratio ADP/KDP (Fig. 3). Such a strong dependence of β on the magnitude of ZDR was recently confirmed by observations reported by Tabary et al. (2009). Very similar simulation results based on DSDs measured in tropical rain in Australia and reported by Carey et al. (2000) and Keenan et al. (2001) indicate the universal character of resonance effects attributed to large raindrops in different climate regions.

The major conclusion from the simulations and observations is that both α and β become extremely unstable for Z > 45 dBZ and ZDR > 3 dB. Enhanced variability of α and β within hot spots was first noticed in the study of Carey et al. (2000), who suggested identifying hot spots and treating them separately from the rest of the ray. Carey et al. (2000) recommended using different pairs of α and β values inside and outside hot spots.

c. Hot-spot method for attenuation correction

As mentioned in the introduction, Ryzhkov et al. (2006, 2007) utilized the idea of Carey et al. (2000) and proposed a procedure for automatic determination of the parameters α and β within hot spots. In this study, we adopt such an approach after its slight modification.

The suggested hot-spot (HS) algorithm implies that
i1558-8432-50-1-39-e13
i1558-8432-50-1-39-e14
in the HS (Fig. 4), where the “background” values α0 and β0 are constant outside hot spots for a given radar sweep. These background values can be set equal to their average climatological values or can be estimated from the data, as will be described later.

Identification of hot spots is a crucial component of the algorithm. For a given radar sweep, the rays potentially containing hot spots are identified using a simple reflectivity threshold Z(th) (usually between 45 and 50 dBZ), after Z is preliminarily corrected using (1) with α = 0.06 dB per degree (which is considered to be an average climatological value). If the maximal Z associated with weather echo (where cross-correlation coefficient ρhv is higher than 0.7) does not exceed Z(th) anywhere along the radial, then this radial does not contain hot spots and is qualified as a “non–hot spot” (NHS) radial. Carey et al. (2000) utilized the ρhv threshold of 0.97 to detect big-drop zones, which are similar to what are referred to as hot spots in this study. We refrain from using this threshold in our analysis because many areas with much lower ρhv were found in the observed storms that are obviously not associated with hot spots and might be affected, for example, by nonuniform beam filling (Ryzhkov 2007).

The background values α0 and β0 generally depend on temperature as well as the prevalent type of DSD (e.g., Jameson 1992) and can be roughly estimated using the data from the NHS radials by examining minimal values of measured and maximal values of along each NHS radial where ZDR drops as low as −1 dB because of differential attenuation. Then, β0 is estimated as a median value of ratios taken at each NHS radial where and , where ZDR is the expected value of ZDR (not biased by differential attenuation) in the ZDR minimum estimated from Z after reflectivity is corrected for attenuation using (1) with α = 0.06 dB per degree:
i1558-8432-50-1-39-e15
Equation (15) is similar to the relations utilized by Bringi et al. (2001) and Tabary et al. (2009) but is optimized for rain in Oklahoma using simulations based on the measured DSDs (gray line in Fig. 1). As Fig. 3 shows, the value of β0 strongly depends on the prevalent ZDR.

The background factor α0 depends on temperature (similarly to β0), but it is much less sensitive to ZDR. The scatterplots of β0 versus α0 simulated from disdrometer measurements in Oklahoma for two different temperatures, 10° and 20°C, are displayed in Fig. 5. Simulations are made for ZDR < 3 dB to avoid contamination from hot spots and for ZDR > 0.5 dB. At lower ZDR, the ratio Ah/KDP can increase dramatically as a result of lower KDP associated with near-spherical drops. Nevertheless, our analysis shows that in Oklahoma the contribution of drops with ZDR less than 0.5 dB does not exceed 10% of total Ah integrated over the average DSD. Figure 5 shows that α0 almost linearly depends on β0 at a given temperature except for very low β0 and that the range of α0 variability is significantly smaller than that of β0 in a relative sense. Note that the slopes of the α0β0 dependences simulated from disdrometer data are lower than the factor of 3.33 suggested by Vulpiani et al. (2008) (dashed line in Fig. 5).

Once the background value β0 is determined for a given sweep, the corresponding value of α0 can be determined from the gray curves in Fig. 5 if the average temperature along the propagation path is known. Note that temperature uncertainty of 10°C results in about a 10% uncertainty in α0 for larger β0 and may be tolerated in a first approximation. According to the suggested method, the background values α0 and β0 may vary from sweep to sweep as functions of elevation and time.

Once background values α0 and β0 are determined, a preliminary attenuation correction of Z and ZDR is performed for all radials in the sweep using equations
i1558-8432-50-1-39-e16
i1558-8432-50-1-39-e17

These preliminarily corrected Z and ZDR are used to identify hot spots using the following criteria: 1) Z > Z(th) and ρhv > 0.7 everywhere in the hot spot, 2) the maximal value of ZDR within the hot spot exceeds (usually equal to 3 dB), 3) the hot spot has sufficient length (usually 2 km), and 4) the change of total differential phase ΦDP within the hot spot exceeds (typically 10°). The corresponding thresholds are adaptable parameters that may depend on the quality of polarimetric radar data and can be optimized in further studies. If there are several hot spots detected along the ray, the parameters Δα and Δβ in (13) and (14) are assumed to be the same in all hot spots for a particular radial. However, these parameters are different for different radials.

Given (13), the constraint equation in (3) can be rewritten as
i1558-8432-50-1-39-e18
where integration in the second integral is performed within hot spots and ΔΦDP(HS) stands for the ΦDP increase within hot spots. Equation (18) stipulates that in the basic equation in (5) for the traditional ZPHI method the term αΔΦDP(r0; rm) should be replaced with the term α0ΔΦDP(r0; rm) + ΔαΔΦDP(HS):
i1558-8432-50-1-39-e19
where
i1558-8432-50-1-39-e20
This means that two measured differential phase parameters, ΔΦDP(r0; rm) and ΔΦDP(HS), are used for constraining the procedure instead of one. As a result, the radial profile of Ah estimated from (5) becomes dependent on the value of Δα. The appropriate factor Δα should be defined from the iterative process of incrementing Δα until a certain condition is satisfied. Following Ryzhkov et al. (2006, 2007), it is required that
i1558-8432-50-1-39-e21
where integration is performed over the gates outside hot spots (OHS) and
i1558-8432-50-1-39-e22
The condition (21) implies that the correctly estimated specific attenuation Ah is equal to α0KDP outside hot spots and that the corresponding integrals should also be equal.
Last, the corrected radar reflectivity factor is expressed as
i1558-8432-50-1-39-e23
where Z and Za are in reflectivity decibels (dBZ) and Ah[s, Δα(opt)] is the profile of specific attenuation determined from (19) with the parameter Δα(opt) satisfying condition (21).

The conception of the method is illustrated in Figs. 4 and 6. Figure 4 shows simple model profiles of Z and ΦDP. It is assumed that Z is equal to 45 and 53 dBZ outside and inside the hot spot, respectively, and that the parameter α is equal to 0.10 dB per degree within the hot-spot area and to 0.06 dB per degree outside it. The corresponding profile of Ah is computed using the relation Ah = (2.98 × 10−5)Z0.8 from Le Bouar et al. (2001) and is indicated by a solid line in the three panels of Fig. 6 for three possible locations of the hot spot along the propagation path. In these model examples, r0 = 0 km, rm = 25 km, and the radial extension of the hot spot area is 5 km. Applying relations (19) and (20) with a varying parameter Δα in (13) results in the different retrieved profiles of Ah shown in Fig. 6. Note that Ah changes not only within the hot spot but also outside it. In Fig. 6, L/R means the ratio of the left-hand and right-hand sides of (21).

The retrieved Ah is lower than its true value if Δα = 0.0 dB per degree (dashed lines) and the retrieved radar reflectivity factor is underestimated. This is equivalent to utilizing the unmodified ZPHI equation in (5) with α = α0 = 0.06 dB per degree everywhere along the propagation path. In this case, the ratio L/R is less than 1 regardless of hot-spot location along the ray. If Δα is too high (0.08 dB per degree), then L/R > 1 and retrieved Ah is overestimated (dotted lines). The retrieved and true profiles of Ah match precisely (solid lines) only if Δα = 0.04 dB per degree and L/R = 1, that is, if condition (21) is satisfied.

It is important that the method yields an unbiased estimate of Δα(opt) even in the situation in which there is no radar echo (or valid data) behind the hot spot or in the rear side of the convective cell with respect to the radar (r2 = rm). This happens very often when the radar signal is totally extinct because of attenuation within a hot spot or differential phase becomes very noisy as a result of the drop of ρhv (Tabary et al. 2008). However, the sensitivity of the algorithm is somewhat diminished in such a situation. Indeed, the change of the ratio L/R is within 0.72–1.30 if Δα varies between 0.0 and 0.08 dB per degree and the hot spot is at the near end of the propagation path (r1 is close to r0 as in Fig. 6b). The corresponding span of L/R is smaller (between 0.86 and 1.10) for r2 = rm (Fig. 6c) and the algorithm is less robust.

The procedure for the ZDR attenuation correction is based on the original idea of Smyth and Illingworth (1998), according to which the measured value of ZDR behind the attenuating cell is compared with what is expected in light rain in the shadow of this cell. This idea was later modified by Bringi et al. (2001) and Tabary et al. (2008, 2009), as described in section 2a. In our algorithm, the attenuation-related bias in differential reflectivity is determined as
i1558-8432-50-1-39-e24
where β0 and Δβ are defined by (14) and [r1, r2] is the range interval containing the hot spot (Fig. 4). The parameter Δβ is estimated from
i1558-8432-50-1-39-e25
where the expected value of differential reflectivity in the shadow of an attenuating cell is determined using (15).
If one assumes that ΦDP(r0) = 0, path-integrated attenuation ΔZ(rm) and differential attenuation ΔZDR(rm) can be expressed as
i1558-8432-50-1-39-e26
i1558-8432-50-1-39-e27
Note that it can be shown that the self-consistent method with constraints of Bringi et al. (2001) yields
i1558-8432-50-1-39-e28
i1558-8432-50-1-39-e29

3. Attenuation correction in heavy rain in Oklahoma

The performance of the HS algorithm for attenuation correction has been tested in the case of heavy rain that occurred on 10 March 2009 in Oklahoma. Multiple precipitation bands have been characterized by very high Z (exceeding 60 dBZ). According to the National Oceanic and Atmospheric Administration (NOAA) publication Storm Data, no hail was reported on the ground, but melting hail aloft should not be excluded. It is possible that most of the hail completely melted before reaching the surface because the freezing level was very high (at 3.4 km) on that day.

This event has been observed with nearly collocated C-band and S-band polarimetric radars. The C-band University of Oklahoma Polarimetric Radar for Innovations in Meteorology and Engineering (OU PRIME) has a 1-MW transmitted power and a ½° antenna beam that in combination with 0.125-km gate spacing provides very high spatial resolution of polarimetric data. The data collected by the polarimetric prototype of the S-band WSR-88D (KOUN) have been used for comparison and validation of the procedure for attenuation/differential attenuation correction. The S-band radar is at a distance of 6.86 km and an azimuth of 337.3° with respect to the C-band radar. The KOUN radar has a 1° beam, and the radial resolution of the data collected during the storm was 0.25 km.

Absolute calibration of Z for both radars was checked using comparisons with the nearby operational WSR-88D near Oklahoma City, Oklahoma (KTLX). The consistency between Z and KDP in rain was also utilized to evaluate the absolute calibration of Z. The general principles of the polarimetric consistency checks are described by Gorgucci et al. (1992), Goddard et al. (1994), and Ryzhkov et al. (2005), among others. It is expected that Z and KDP are consistent for moderate to heavy rain within the radar reflectivity interval between 40 and 50 dBZ.

Examination of ZDR in dry aggregated snow or dry graupel above the melting layer and analysis of the ZZDR scatterplots in rain for Z < 40 dBZ (in the areas where attenuation is insignificant) were utilized to remove the bias in the measurements of ZDR at both C and S bands. According to Ryzhkov et al. (2005), intrinsic ZDR in dry aggregated snow should be within the range 0.1–0.2 dB. The observed scatterplot of ZDR versus Z in rain has to be in agreement with that obtained from theoretical simulations (see Fig. 1). We believe that the combination of both methods allows us to reduce the ZDR calibration bias to 0.1–0.2 dB.

The scanning strategies of the two radars were not synchronized, and their antenna elevations were slightly different, which makes it difficult to achieve a good match between the two datasets. However, it was possible to select volume scans of data with a time difference less than 30 s for which the fields of C-band and S-band data exhibit very good resemblance. An example of such data is presented in Fig. 7, where the fields of the measured C-band and S-band Z, ZDR, and ΦDP taken at elevations of 0.41° (C band) and 0.48° (S band) and around 0309 UTC are displayed.

First, it is obvious that the better spatial resolution of the OU PRIME data is a great benefit, as comparison with KOUN data reveals. The impact of differential attenuation on the ZDR measurements at C band is clearly visible in the sector with enhanced differential phase where ZDR drops as low as −8.5 dB and the corresponding values of S-band ZDR are mainly within the range between 0.5 and 1.5 dB. Negative bias in C-band Z is apparent in the area just behind the first precipitation line (marked as B) and within the second line of precipitation (marked as A), which is farther away from the radar.

The comparison of composite RHIs taken at azimuth = 285.5° at C band and azimuth = 280° at S band provides additional evidence of substantial differences between the C-band and S-band data caused by attenuation and effects of resonance scattering at C band (Fig. 8). Indeed, the second precipitation line is disconnected from the first one in the C-band plots and is associated with a reflectivity factor that is about 20 dB lower than that measured at S band. Differential reflectivity at C band is higher than at S band in the updraft area at the leading edge of the squall line (because of resonance scattering on large raindrops), but then it decreases rapidly along the propagation path deeper into the storm. Notable is a significantly lower cross-correlation coefficient ρhv at C band, which is also attributed to resonance scattering.

Estimation of the parameter β0 using the data from the radials void of hot spots on the radar scan shown in Fig. 7 yields a value of 0.03 dB per degree if the method described in section 2c is used. This is a typical background value in continental storms (Tabary et al. 2009) and is 2–3 times as high as in tropical rain dominated by smaller drops (Bringi et al. 2006; Ryzhkov et al. 2007). The corresponding value of α0 obtained from Fig. 5 at temperature T = 10°C is about 0.1 dB per degree.

In qualitative terms, the hot-spot algorithm does a good job in reducing attenuation-related biases, as Fig. 9 shows. The corrected fields of Z and ZDR at C band agree very well with the corresponding S-band fields except for a narrow azimuthal sector marked by a dashed line where the OU PRIME beam is significantly blocked by the nearby building. It is apparent that negative Z bias in the areas A and B in Fig. 7 is almost eliminated after the attenuation correction procedure is applied. Intrinsic values of ZDR at C band are noticeably higher than the ones at S band within the squall line, which is attributed to the resonance scattering. A spot of very high ZDR combined with low Z at about X = −73 km and Y = 18 km in C-band panels is not an artifact but a real signature produced by size sorting in the updraft of a small growing convective cell, as a more detailed analysis of RHI plots indicates (not shown).

A more quantitative validation of the attenuation correction scheme was performed by converting C-band and S-band radar data from a polargrid to a Cartesian grid with 1 km × 1 km resolution and comparing the gridded Z and ZDR data before and after correction for attenuation. Such a comparison was made only in the areas affected by noticeable attenuation where the measured (uncorrected) ZDR at C band is below −1 dB. The scatterplots of the differences Z(S band) − Z(C band) vs ZDR(S band) − ZDR(C band) before and after correction using the hot-spot algorithm are displayed in Fig. 10. The scatter is very significant in both panels of Fig. 10 because of the spatial/temporal mismatch of the C-band and S-band radar fields and because of the differences in the intrinsic values of Z and ZDR at the two radar wavelengths due to effects of resonance scattering. Nevertheless, the positive effect of attenuation correction is obvious: median values of the Z and ZDR differences are very close to zero after the correction is performed.

A notable feature of the examined case of continental rain is significant attenuation/differential attenuation (over 20/7 dB) associated with very modest values of differential phase, which does not exceed 120°. If the background values α0 = 0.1 dB per degree and β0 = 0.03 dB per degree were used for attenuation correction utilizing (16) and (17) everywhere in the PPI, it would result in significant underestimation of path-integrated attenuation and differential attenuation along the radials containing hot spots, and the estimated Z and ZDR biases would not exceed 12 and 3.6 dB, respectively. In fact, these are at least 2 times as high, as the top panel in Fig. 10 shows. The terms ΔαΔΦDP(HS) and ΔβΔΦDP(HS) in (26) and (27) compensate for this underestimation.

4. Attenuation correction for the Chicago storm

The second storm for which polarimetric attenuation correction at C band was tested was observed in the Chicago metropolitan area. This very severe thunderstorm hit the area at about 0000 UTC 5 August 2008, producing damaging winds and torrential rain. Thousands of travelers at Chicago O’Hare International Airport and fans attending a baseball game at Wrigley Field were evacuated. Many homes and businesses were damaged as a result of the storm. Wind gusts sped up to over 90 mi h−1 (≃40 m s−1), and one fatality was reported in northwestern Indiana as a result of a falling tree. No hail was reported on the ground during this storm.

The storm was in the coverage area of the C-band “Sidpol” radar (owned by Valparaiso University) for at least 2 h before the leading edge of the squall line passed over the radar site at approximately 0149 UTC 5 August 2008 and radar data recording was interrupted because of lightning strikes. The storm position between the Sidpol radar and the Chicago WSR-88D (KLOT), which are approximately 90 km apart, provided an opportunity (although not as good a one as in Oklahoma) to compare radar reflectivities at C and S bands and assess the impact of attenuation at C band.

Sidpol radar data were available with a radial resolution of 0.125 km and an azimuthal resolution of about 0.83° within the range of 180 km from the radar. Extremely high values of ΦDP have been measured in this storm, as opposed to the storm observed in Oklahoma. An example of the radial profile of measured ΦDP is shown in Fig. 11a. The recorded differential phase exhibits double aliasing and needs to be dealiased before the estimation of its radial derivative, specific differential phase KDP, can be performed. A three-step procedure was used for the ΦDP dealiasing and processing. This implies downward shifting of differential phase, as shown in Fig. 11b; elimination of the ΦDP jump caused by aliasing; and editing and smoothing of ΦDP using the measurements of ρhv (Fig. 11c).

Attenuation correction of Z and ZDR was performed for all radar scans every 6 min during the 2-h period of observations after data-quality issues were addressed. The estimated background parameter β0 in the attenuation correction scheme was significantly lower than in the Oklahoma storm and varied mostly between 0.008 and 0.012 dB per degree from scan to scan. Hence, the corresponding background value α0 obtained from Fig. 5 was about 0.06 dB per degree at an average temperature of 20°C.

The degree of attenuation at C band was striking in this storm, as can be seen from Fig. 12, where the fields of the measured Z (before correction for attenuation), corrected Z, differential phase ΦDP, and Z obtained from the S-band KLOT radar at 0149 UTC are displayed. The difference between measured and corrected Z at C band approaches 30–40 dB over extended areas of the storm. This is not surprising given the fact that ΦDP exceeds 300° in large azimuthal sectors west and north of Sidpol.

The WSR-88D provides good reference for validating attenuation correction at C band because the S-band signal experiences much lower attenuation and the WSR-88D is located behind the squall line at 0149 UTC; hence, the propagation path of the S-band microwave radiation through heavy rain is relatively short. It is evident that the corrected Z at C band agrees well with that measured by the WSR-88D within the squall line. However, if the attenuated C-band signal drops below the noise level, as in the remote areas in the northern and western azimuthal sectors, then attenuation correction is not possible. The difference between corrected C-band Z and S-band Z in the stratiform part of the storm is caused either by the height mismatch of the radar sampling volumes of the two radars at elevation 0.5° in this area or by possible error in the reading of antenna elevation by the Sidpol radar (i.e., its actual elevation might be higher than 0.5°). In the latter case, the Sidpol radar samples a good part of the melting layer, whereas the corresponding radar resolution volume of theWSR-88D is below the melting layer and, therefore, S-band Z is lower than C-band Z there.

Because the C-band and S-band radars were so far away from each other, it was hard to perform quantitative verification of the attenuation correction scheme by direct comparison of reflectivities measured by both radars as was done for the Oklahoma case. Instead, we checked the consistency of corrected Z and ZDR with KDP in rain by examining the scatterplot of the difference 10 log(KDP) − Zh versus ZDR and comparing it with theoretical dependencies at C band (Fig. 13). The solid line in Fig. 13b corresponds to the simulations based on measured DSD in Oklahoma, whereas the dashed line depicts theoretical results of Gourley et al. (2006). Median values of Z before correction for attenuation (shown by asterisks) are 5–12 dB below what is expected for a given KDP and ZDR (corrected for attenuation). After the attenuation correction is made, median values of Z (shown by diamonds) are within 1 dB with respect to their model values as dictated by consistency, which attests to the good quality of the attenuation correction.

The largest recoverable attenuation bias of about 40 dB is estimated along the radial at an azimuth of 257.2° (line in Fig. 12), where ΦDP as high as 602° has been measured (Fig. 14a). To the best of our knowledge, this is the highest value of differential phase ever reported. It is much higher than anything measured in the previous C-band studies in Europe and Australia. An amazing result is that the polarimetric algorithm for attenuation correction is capable of reliably restoring the radar reflectivity in the situation in which 99.99% of signal power is lost (Fig. 14b). Note that the Hitschfeld–Bordan attenuation correction scheme for a single-polarization radar experiences serious problems if attenuation barely reaches 10 dB or is even lower.

Total differential attenuation along the same ray reaches 7 dB, as Fig. 14c shows. The minimal reliably measured ZDR measured at the end of this ray is about −6 dB, with the corresponding ΦDP exceeding 600°. Thus, the net value of β averaged over the path is 0.01 dB per degree. Note that in the Oklahoma case ZDR drops to lower values at the radials with maximal differential phase of only 120°, which is ⅕ of the maximal ΦDP measured along the propagation path in Fig. 11. We speculate that the Oklahoma storm contained a higher concentration of large raindrops with resonance size than did the Chicago storm. This is consistent with the facts that maximal ZDR measured in the Oklahoma event is 1–2 dB higher than in the Chicago case and that there is a strong correlation between maximal ZDR and parameter β (Carey et al. 2000; Keenan et al. 2001; Tabary et al. 2009; Borowska et al. 2011).

In addition to cross-checking with S-band measurements, the quality of the attenuation correction can be also attested to through comparison of the rain-rate profiles computed from corrected Z and KDP using the relations
i1558-8432-50-1-39-e30
i1558-8432-50-1-39-e31
derived from C-band simulations using measured DSDs in Oklahoma. In (30) and (31), KDP is expressed in degrees per kilogram and Z is in reflectivity decibels. The R(KDP) estimate does not depend on attenuation. Figure 14d confirms that the R(Z) and R(KDP) profiles along the radial at azimuth = 257.2° are in a good agreement if the rain rate is less than 100 mm h−1.

The quality of the ZDR correction for differential attenuation is illustrated in Fig. 15, where the composite PPI plot of Z, ΦDP, ρhv, and three fields of ZDR are presented for the radar scan at 0124 UTC. Uncorrected differential reflectivity exhibits strong differential attenuation in the sectors of high ΦDP where measured ZDR drops below −5 dB. The blank azimuthal sector in the northwestern direction is caused by total attenuation of the radar signal. A simplistic correction procedure for differential attenuation based on the use of (17) with β0 = 0.01 dB per degree significantly improves the ZDR estimate but falls short of eliminating the relatively large areas of negative ZDR where differential attenuation is especially severe (Fig. 15c, marked as linear correction). This means that the parameter β should be increased significantly in certain azimuthal directions to fix the problem. The hot-spot or “adaptive” technique that automatically determines an appropriate coefficient β apparently does a much better job (Fig. 15d, marked as adaptive correction) and ensures positive and more-realistic- looking ZDR. There is no apparent artificial drop of ZDR next to the blank sector with severe attenuation.

Because the reference S-band KLOT radar lacks polarimetric capability, it cannot be used for validation of the differential attenuation correction in the Chicago case. The algorithm robustness can be assessed by taking into account the absence of negatively corrected ZDR, its general consistency with Z, and the spatial/temporal continuity of the fields of corrected ZDR. Detailed analysis of the images of corrected ZDR for 2-h periods of observation indicates that the suggested algorithm for differential attenuation correction is robust and reliable. Occasional “bad radials” of corrected ZDR take place but they are relatively rare and can be eliminated by using considerations of azimuthal continuity.

Every radial of radar data containing hot spots is characterized by particular values of α and β that turn out to be highly variable. Scatterplots of parameters α and β versus the maximal value of ZDR in hot spots are shown in Figs. 16a and 16b. These scatterplots summarize results for all radar scans at elevation 0.5° and indicate large variability of α and β in hot spots at C band. Most values of α are within the range of 0.05 and 0.20 dB per degree, whereas β varies mainly between 0.01 and 0.04 dB per degree. The estimates of α and β in this study are generally consistent with the previous findings of the authors for C-band observations in Alabama and Canada (Ryzhkov et al. 2007), the estimates by Tabary et al. (2008, 2009) in France, and the results of Keranen and Yllasjarvi (2008) in Finland. Ryzhkov et al. (2007) reported median values of α between 0.08 and 0.22 dB per degree in rain and rain/hail mixture, whereas Keranen and Yllasjarvi (2008) found most of these to be between 0.06 and 0.18 dB per degree. Tabary et al. (2008, 2009) and Keranen and Yllasjarvi (2008) claimed median values of β of 0.025 and 0.035 dB per degree, respectively, in their investigations. Much higher local values of α and β have been reported in melting hail in the recent study of Borowska et al. (2011).

Figures 16a and 16b show that both α and β tend to increase with increasing ZDR in hot spots but that such a tendency is clouded by large scatter. The scatterplot of β versus α indicates a certain degree of correlation between the two parameters, as is to be expected in rain (Fig. 16c). Vulpiani et al. (2008) assumed that the ratio β/α is approximately constant and is equal to 0.3 in rain. Although the average slope of the βα scatterplot in Fig. 16c is close to 0.3, the excessive scatter testifies to the fact that the coefficients α and β are only loosely connected. We do not exclude, however, the possibility that at least part of the excessive scatter might be attributed to the uncertainty in estimating the radial extension of hot spots and, therefore, the corresponding change in differential phase ΔΦDP(HS). Possible underestimation of hot-spot extension (due to radar miscalibration or utilization of undercorrected Z and ZDR) may be associated with lower ΔΦDP(HS) and artificially high Δα and Δβ. However, overestimation of Δα and Δβ does not necessarily mean overestimation in path-integrated attenuation/differential attenuation because it is determined by the products ΔαΔΦDP(HS) and ΔβΔΦDP(HS) [see (26) and (27)], which are much more stable, as our analysis shows.

Unaccounted-for attenuation may severely restrict the capability of single-polarization radar to quantify precipitation at C band. The extent of this problem is illustrated in Fig. 17, where the fields of rain rates estimated from the measured and corrected C-band Z and KDP and from Z measured by WSR-88D are displayed for the radar scan at 0149 UTC. Heavy underestimation of the rain rate retrieved from uncorrected Z is obvious practically everywhere within the storm. In the areas west of the Sidpol radar where rain rates estimated from corrected C-band Z, KDP, and S band exceed 100 mm h−1, the corresponding rain rates retrieved from the measured (uncorrected) C-band Z are less than 1 mm h−1.

5. Conclusions

This investigation confirms the conclusions of several previous studies that the ratios α = Ah/KDP and β = ADP/KDP at C band can be anomalously high in hot spots and, therefore, that the hot spots should be treated separately from the rest of the storm for attenuation correction. The hot-spot method for attenuation correction originally suggested by Ryzhkov et al. (2006, 2007) has been modified and applied for two heavy-rain events (in Oklahoma and in the Chicago area) for which radar reflectivity factor exceeded 60 dBZ but no hail was reported on the ground.

The proposed technique demonstrated good overall skill in correcting radar reflectivity Z and differential reflectivity ZDR, as was testified to by direct comparisons with measurements by S-band radars; by the consistency of corrected Z, ZDR, and KDP in rain; by the absence of negative ZDR in the corrected fields of differential reflectivity; and by the spatial/temporal continuity of the corrected fields of Z and ZDR. For the first time, the results of attenuation correction at C band were validated through direct comparison with simultaneously collected data obtained with a nearly collocated S-band polarimetric radar in Oklahoma. In the Chicago case, the measured differential phase ΦDP, which is proportional to path-integrated attenuation, exceeded 600° in some azimuthal directions and the radar reflectivity Z has been successfully recovered after the signal was attenuated by about 40 dB!

The values of estimated correction factors α and β in hot spots exhibit high variability and are consistent with those previously reported in the literature. We hypothesize that the high variability of the parameters α and β in hot spots at C band can be attributed to the effects of resonance scattering by large raindrops that may or may not be associated with hail. In other words, anomalous attenuation and differential attenuation may happen in pure rain as well. This is in agreement with previous findings by Carey et al. (2000) and Keenan et al. (2001), who reported anomalously high attenuation at C band in the absence of hail on the ground. However, the presence of hail aloft usually increases the supply of large drops that originate from melting hail. Recent theoretical studies of melting hail by Ryzhkov et al. (2009) indicate that shedding of water from melting hailstones leads to enhancement in the concentration of very large drops with size of about 8 mm. In other words, dry hailstones with very different sizes melt into giant raindrops with approximately the same size. Such an enhancement in the number of very large drops may not be offset by their breakup if there is plenty of melting hail in the storm.

Although the hot-spot method for attenuation correction demonstrated reasonably good performance for the two cases of heavy rain investigated in this study, further refinement of the algorithm and more validation studies are needed. There are indications that the methods for attenuation correction based on differential phase ΦDP may fail if ΦDP becomes excessively erratic in the shadow of attenuating cells as a result of a loss of correlation between orthogonally polarized signals and the effects of nonuniform beam filling (Ryzhkov 2007). In this situation, which can be very common in the presence of melting hail (Borowska et al. 2011), differential phase may not be usable for attenuation correction at all at shorter wavelengths and approaches using different principles may have to be explored.

Acknowledgments

This research was supported by the National Research Foundation of Korea (NRF) through a grant provided by the Korean Ministry of Education, Science and Technology(MEST) in 2010 (Grant K20607010000). Authors A. Ryzhkov and P. Zhang are supported by the NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA17RJ1227, U.S. Department of Commerce. We are very grateful to Prof. R. Palmer, Dr. B. Cheong, and R. Kelly from the Atmospheric Radar Research Center at the University of Oklahoma for providing C-band polarimetric data from the recently established OU PRIME radar that was manufactured by Enterprise Electronics Corporation. Also, Drs. D. Zrnić and L. Borowska reviewed the manuscript and helped to clarify several aspects of our analysis. The authors also appreciate very constructive comments and suggestions by the anonymous reviewers.

REFERENCES

  • Borowska, L., and Coauthors, 2009: Attenuation of radar signal in melting hail at C band. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., P2.7. [Available online at http://ams.confex.com/ams/pdfpapers/155402.pdf].

    • Search Google Scholar
    • Export Citation
  • Borowska, L., A. Ryzhkov, D. Zrnić, C. Simmer, and R. Palmer, 2011: Attenuation and differential attenuation of 5-cm-wavelength radiation in melting hail. J. Appl. Meteor. Climatol., 50 , 5976.

    • Search Google Scholar
    • Export Citation
  • Brandes, E., G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41 , 674685.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić, 1990: An examination of propagation effects in rainfall on polarimetric variables at microwave frequencies. J. Atmos. Oceanic Technol., 7 , 829840.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., T. D. Keenan, and V. Chandrasekar, 2001: Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints. IEEE Trans. Geosci. Remote Sens., 39 , 19061915.

    • Search Google Scholar
    • Export Citation
  • Bringi, V., M. Thurai, K. Nakagawa, G. Huang, T. Kobayashi, A. Adachi, H. Hanado, and S. Sekizawa, 2006: Rainfall estimation from C-band polarimetric radar in Okinawa, Japan: Comparison with 2D-video disdrometer and 400 MHz wind profiler. J. Meteor. Soc. Japan, 84 , 705724.

    • Search Google Scholar
    • Export Citation
  • Carey, L. D., S. A. Rutledge, D. A. Ahijevych, and T. D. Keenan, 2000: Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase. J. Appl. Meteor., 39 , 14051433.

    • Search Google Scholar
    • Export Citation
  • Goddard, J., J. Tan, and M. Thurai, 1994: Technique for calibration of radars using differential phase. Electron. Lett., 30 , 166167.

  • Gorgucci, E., G. Scarchilli, and V. Chandrasekar, 1992: Calibration of radars using polarimetric techniques. IEEE Trans. Geosci. Remote Sens., 30 , 853858.

    • Search Google Scholar
    • Export Citation
  • Gourley, J., P. Tabary, and J. Parent du Chatelet, 2006: Empirical estimation of attenuation from differential propagation phase measurements at C band. J. Appl. Meteor. Climatol., 46 , 306317.

    • Search Google Scholar
    • Export Citation
  • Hitschfeld, W., and J. Bordan, 1954: Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteor., 11 , 5867.

    • Search Google Scholar
    • Export Citation
  • Jameson, A., 1992: The effect of temperature on attenuation-correction schemes in rain using polarization propagation differential phase. J. Appl. Meteor., 31 , 11061118.

    • Search Google Scholar
    • Export Citation
  • Keenan, T., L. Carey, D. Zrnić, and P. May, 2001: Sensitivity of 5-cm wavelength polarimetric radar variables to raindrop axial ratio and drop size distribution. J. Appl. Meteor., 40 , 526545.

    • Search Google Scholar
    • Export Citation
  • Keranen, R., and J. Yllasjarvi, 2008: Estimates for polarimetric attenuation coefficients in rain using multi season statistics of polarimetric C-band radar data in midlatitudes, with a case comparison to S band. Extended Abstracts, Fifth European Conf. on Radar in Meteorology and Hydrology, Helsinki, Finland, Finnish Meteorological Institute. [Available online at http://erad2008.fmi.fi/proceedings/extended/erad2008-0259-extended.pdf].

    • Search Google Scholar
    • Export Citation
  • Le Bouar, E., J. Testud, and T. Keenan, 2001: Validation of the rain profiling algorithm “ZPHI” from the C-band polarimetric weather radar in Darwin. J. Atmos. Oceanic Technol., 18 , 18191837.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24 , 729744.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., and D. S. Zrnić, 2005: Radar polarimetry at S, C, and X bands. Comparative analysis and operational implications. Preprints, 32nd Int. Conf. on Radar Meteorology, Albuquerque, NM, Amer. Meteor. Soc., 9R.3. [Available online at http://ams.confex.com/ams/pdfpapers/95684.pdf].

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., S. E. Giangrande, V. M. Melnikov, and T. J. Schuur, 2005: Calibration issues of dual-polarization radar measurements. J. Atmos. Oceanic Technol., 22 , 11381155.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., D. Hudak, and J. Scott, 2006: A new polarimetric scheme for attenuation correction at C band. Preprints, Fourth European Conf. on Radar in Meteorology and Hydrology, Barcelona, Spain, GRAHI–UPC, 29–32.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., P. Zhang, D. Hudak, J. Alford, M. Knight, and J. Conway, 2007: Validation of polarimetric methods for attenuation correction at C band. Preprints, 33rd Conf. on Radar Meteorology, Cairns, Australia, Amer. Meteor. Soc., P11B.12. [Available online at http://ams.confex.com/ams/pdfpapers/123122.pdf].

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., S. Ganson, A. Khain, M. Pinsky, and A. Pokrovsky, 2009: Polarimetric characteristics of melting hail at S and C bands. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., 4A.6. [Available online at http://ams.confex.com/ams/34Radar/techprogram/paper_155571.htm].

    • Search Google Scholar
    • Export Citation
  • Smyth, T. J., and A. J. Illingworth, 1998: Correction for attenuation of radar reflectivity using polarization data. Quart. J. Roy. Meteor. Soc., 124 , 23932415.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., G. Vulpiani, J. J. Gourley, A. J. Illingworth, and O. Bousquet, 2008: Unusually large attenuation at C-band in Europe: How often does it happen? What is the origin? Can we correct for it? Extended Abstracts, Fifth European Conf. on Radar in Meteorology and Hydrology, Helsinki, Finland, Finnish Meteorological Institute. [Available online at http://erad2008.fmi.fi/proceedings/extended/erad2008-0170-extended.pdf].

    • Search Google Scholar
    • Export Citation
  • Tabary, P., G. Vulpiani, J. J. Gourley, A. J. Illingworth, R. Thompson, and O. Bousquet, 2009: Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data. J. Appl. Meteor. Climatol., 48 , 20372053.

    • Search Google Scholar
    • Export Citation
  • Testud, J., E. Le Bouar, E. Obligis, and M. Ali-Mehenni, 2000: The rain profiling algorithm applied to polarimetric weather radar. J. Atmos. Oceanic Technol., 17 , 332356.

    • Search Google Scholar
    • Export Citation
  • Vulpiani, G., P. Tabary, J. Parent du Chatelet, and F. Marzano, 2008: Comparison of advanced radar polarimetric techniques for operational attenuation correction at C band. J. Atmos. Oceanic Technol., 25 , 11181135.

    • Search Google Scholar
    • Export Citation
  • Zrnić, D., T. Keenan, L. Carey, and P. May, 2000: Sensitivity analysis of polarimetric variables at a 5-cm wavelength in rain. J. Appl. Meteor., 39 , 15141526.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

Scatterplot of ZDR vs Z in pure rain at C band; Z and ZDR are computed from 25 920 DSDs measured in central Oklahoma. Raindrop temperature is 20°C. The shape–size dependence of raindrops is assumed to be as in Brandes et al. (2002). The gray line indicates the dependence of median ZDR on Z for 25 < Z < 45 dBZ.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 2.
Fig. 2.

Scatterplots of (top) AH and (bottom) ADP vs KDP in pure rain at C band for (a),(c) all ZDR and (b),(d) ZDR < 3dB. Radar variables are computed from 25 920 DSDs measured in Oklahoma.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 3.
Fig. 3.

Scatterplot of the ratio ADP/KDP vs ZDR in pure rain at C band. Radar variables are computed from 25 920 DSD measured in Oklahoma.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 4.
Fig. 4.

Conceptual plot illustrating the hot spot between ranges r1 and r2 in the radial profiles of Z and ΦDP.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 5.
Fig. 5.

Scatterplots of α0 vs β0 simulated from disdrometer data in Oklahoma for T = 10° and 20°C for ZDR varying between 0.5 and 3.0 dB. Dashed line depicts the dependence α0 = 3.33β0 from Vulpiani et al. (2008).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 6.
Fig. 6.

Retrieved radial profiles of specific attenuation Ah for α0 = 0.06 dB per degree, different values of Δα in a hot spot, and different locations of a hot spot along the propagation path. The true value of Δα in a hot spot is equal to 0.04 dB per degree. Here, L/R is the ratio of the left and right sides of Eq. (21). The retrieved profile of Ah for Δα = 0.04 dB per degree coincides with the “true” profile of Ah.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 7.
Fig. 7.

Fields of measured (top) Z, (middle) ZDR, and (bottom) ΦDP at (left) C and (right) S bands for the storm at 0309 UTC 10 Mar 2009. Here, the elevation (C band) = 0.41° and the elevation (S band) = 0.48°. The C-band radar is at X = 0, Y = 0. The areas of visible negative bias of Z caused by attenuation at C band are marked as A and B in the top-left panel. In the left panels, a line indicates the azimuthal direction for which the RHI plot in Fig. 8 is displayed.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 8.
Fig. 8.

Composite RHI plot of (top) Z, (middle top) ZDR, (middle bottom) ΦDP, and (bottom) ρhv at (left) C and (right) S bands for the storm at 0309 UTC 10 Mar 2009. Here, azimuth (C band) = 285.5° and azimuth (S band) = 280°. The azimuthal direction of the vertical cross section is shown in Fig. 7.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 9.
Fig. 9.

Fields of (left) corrected C-band Z and ZDR and (right) measured S-band Z and ZDR for the PPI in Fig. 7. The elevation (C band) = 0.41° and the elevation (S band) = 0.48°. The dashed line in the left panels indicates the azimuthal direction with strong partial blockage of the OU PRIME beam.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 10.
Fig. 10.

Scatterplots of the differences Z(S band) − Z(C band) vs ZDR(S band) − ZDR(C band) (top) before and (bottom) after attenuation correction for the part of the radar scan in Figs. 7 and 9 for which measured (uncorrected) ZDR is lower than −1 dB.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 11.
Fig. 11.

Radial profiles of the differential phase (top) that was measured by the Sidpol radar, (middle) after downward phase shift, and (bottom) after editing, unfolding, and smoothing at 0149 UTC 5 Aug 2008 at azimuth = 257.2° and elevation = 0.5°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 12.
Fig. 12.

Fields of (a) measured and (c) corrected Z at C band, (b) ΦDP at C band, and (d) Z measured by S-band radar (KLOT WSR-88D) at 0149 UTC 5 Aug 2008. The antenna elevation is 0.5°. The Sidpol radar is situated at X = 0, Y = 0 km. The star marks the location of the WSR-88D. The straight line indicates azimuth 257.2° (see Figs. 11 and 14).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 13.
Fig. 13.

Validation of Z and ZDR attenuation correction for the radar scan in Fig. 12 using self-consistency among Z, ZDR, and KDP in rain. (a) Scatterplot of 10 log(KDP) − Zh vs ZDR after Z and ZDR are corrected for attenuation using the hot spot method. (b) Median values of the estimated difference between 10 log(KDP) and Zh as functions of ZDR for uncorrected Zh (asterisks) and corrected Zh (diamonds) as compared with the corresponding theoretical curves based on simulations at C band from disdrometer data in Oklahoma (solid line) and from Gourley et al. (2006) (dashed line).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 14.
Fig. 14.

Radial profiles of (a) ΦDP (thick line) and ρhv (thin line), (b) measured (thin line) and corrected (thick line) Z, (c) measured (thin line) and corrected (thick line) ZDR, and (d) R(Z) (thin line) after Z is corrected and R(KDP) (thick line) at azimuth 257.2° at 0149 UTC 5 Aug 2008. Attenuation correction of Z is performed using the hot-spot algorithm with constraint condition (21).

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 15.
Fig. 15.

Fields of (a) corrected Z, (b) measured and (c),(d) corrected ZDR, (e) ΦDP, and (f) ρhv at 0124 UTC 5 Aug 2008. The antenna elevation is 0.5°.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 16.
Fig. 16.

Scatterplots of the measured parameters (a) α and (b) β vs maximal ZDR in the hot spotat elevation 0.5° and (c) scatterplot of β vs α in the hot spots.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

Fig. 17.
Fig. 17.

Fields of rain rates obtained from (a) measured and (b) corrected Z at C band, (c) KDP, and (d) S-band Z at 0149 UTC 5 Aug 2008. A star indicates the location of the WSR-88D.

Citation: Journal of Applied Meteorology and Climatology 50, 1; 10.1175/2010JAMC2258.1

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  • Borowska, L., and Coauthors, 2009: Attenuation of radar signal in melting hail at C band. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., P2.7. [Available online at http://ams.confex.com/ams/pdfpapers/155402.pdf].

    • Search Google Scholar
    • Export Citation
  • Borowska, L., A. Ryzhkov, D. Zrnić, C. Simmer, and R. Palmer, 2011: Attenuation and differential attenuation of 5-cm-wavelength radiation in melting hail. J. Appl. Meteor. Climatol., 50 , 5976.

    • Search Google Scholar
    • Export Citation
  • Brandes, E., G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41 , 674685.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 636 pp.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., V. Chandrasekar, N. Balakrishnan, and D. S. Zrnić, 1990: An examination of propagation effects in rainfall on polarimetric variables at microwave frequencies. J. Atmos. Oceanic Technol., 7 , 829840.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., T. D. Keenan, and V. Chandrasekar, 2001: Correcting C-band radar reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints. IEEE Trans. Geosci. Remote Sens., 39 , 19061915.

    • Search Google Scholar
    • Export Citation
  • Bringi, V., M. Thurai, K. Nakagawa, G. Huang, T. Kobayashi, A. Adachi, H. Hanado, and S. Sekizawa, 2006: Rainfall estimation from C-band polarimetric radar in Okinawa, Japan: Comparison with 2D-video disdrometer and 400 MHz wind profiler. J. Meteor. Soc. Japan, 84 , 705724.

    • Search Google Scholar
    • Export Citation
  • Carey, L. D., S. A. Rutledge, D. A. Ahijevych, and T. D. Keenan, 2000: Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase. J. Appl. Meteor., 39 , 14051433.

    • Search Google Scholar
    • Export Citation
  • Goddard, J., J. Tan, and M. Thurai, 1994: Technique for calibration of radars using differential phase. Electron. Lett., 30 , 166167.

  • Gorgucci, E., G. Scarchilli, and V. Chandrasekar, 1992: Calibration of radars using polarimetric techniques. IEEE Trans. Geosci. Remote Sens., 30 , 853858.

    • Search Google Scholar
    • Export Citation
  • Gourley, J., P. Tabary, and J. Parent du Chatelet, 2006: Empirical estimation of attenuation from differential propagation phase measurements at C band. J. Appl. Meteor. Climatol., 46 , 306317.

    • Search Google Scholar
    • Export Citation
  • Hitschfeld, W., and J. Bordan, 1954: Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteor., 11 , 5867.

    • Search Google Scholar
    • Export Citation
  • Jameson, A., 1992: The effect of temperature on attenuation-correction schemes in rain using polarization propagation differential phase. J. Appl. Meteor., 31 , 11061118.

    • Search Google Scholar
    • Export Citation
  • Keenan, T., L. Carey, D. Zrnić, and P. May, 2001: Sensitivity of 5-cm wavelength polarimetric radar variables to raindrop axial ratio and drop size distribution. J. Appl. Meteor., 40 , 526545.

    • Search Google Scholar
    • Export Citation
  • Keranen, R., and J. Yllasjarvi, 2008: Estimates for polarimetric attenuation coefficients in rain using multi season statistics of polarimetric C-band radar data in midlatitudes, with a case comparison to S band. Extended Abstracts, Fifth European Conf. on Radar in Meteorology and Hydrology, Helsinki, Finland, Finnish Meteorological Institute. [Available online at http://erad2008.fmi.fi/proceedings/extended/erad2008-0259-extended.pdf].

    • Search Google Scholar
    • Export Citation
  • Le Bouar, E., J. Testud, and T. Keenan, 2001: Validation of the rain profiling algorithm “ZPHI” from the C-band polarimetric weather radar in Darwin. J. Atmos. Oceanic Technol., 18 , 18191837.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24 , 729744.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., and D. S. Zrnić, 2005: Radar polarimetry at S, C, and X bands. Comparative analysis and operational implications. Preprints, 32nd Int. Conf. on Radar Meteorology, Albuquerque, NM, Amer. Meteor. Soc., 9R.3. [Available online at http://ams.confex.com/ams/pdfpapers/95684.pdf].

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., S. E. Giangrande, V. M. Melnikov, and T. J. Schuur, 2005: Calibration issues of dual-polarization radar measurements. J. Atmos. Oceanic Technol., 22 , 11381155.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., D. Hudak, and J. Scott, 2006: A new polarimetric scheme for attenuation correction at C band. Preprints, Fourth European Conf. on Radar in Meteorology and Hydrology, Barcelona, Spain, GRAHI–UPC, 29–32.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., P. Zhang, D. Hudak, J. Alford, M. Knight, and J. Conway, 2007: Validation of polarimetric methods for attenuation correction at C band. Preprints, 33rd Conf. on Radar Meteorology, Cairns, Australia, Amer. Meteor. Soc., P11B.12. [Available online at http://ams.confex.com/ams/pdfpapers/123122.pdf].

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A. V., S. Ganson, A. Khain, M. Pinsky, and A. Pokrovsky, 2009: Polarimetric characteristics of melting hail at S and C bands. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., 4A.6. [Available online at http://ams.confex.com/ams/34Radar/techprogram/paper_155571.htm].

    • Search Google Scholar
    • Export Citation
  • Smyth, T. J., and A. J. Illingworth, 1998: Correction for attenuation of radar reflectivity using polarization data. Quart. J. Roy. Meteor. Soc., 124 , 23932415.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., G. Vulpiani, J. J. Gourley, A. J. Illingworth, and O. Bousquet, 2008: Unusually large attenuation at C-band in Europe: How often does it happen? What is the origin? Can we correct for it? Extended Abstracts, Fifth European Conf. on Radar in Meteorology and Hydrology, Helsinki, Finland, Finnish Meteorological Institute. [Available online at http://erad2008.fmi.fi/proceedings/extended/erad2008-0170-extended.pdf].

    • Search Google Scholar
    • Export Citation
  • Tabary, P., G. Vulpiani, J. J. Gourley, A. J. Illingworth, R. Thompson, and O. Bousquet, 2009: Unusually high differential attenuation at C band: Results from a two-year analysis of the French Trappes polarimetric radar data. J. Appl. Meteor. Climatol., 48 , 20372053.

    • Search Google Scholar
    • Export Citation
  • Testud, J., E. Le Bouar, E. Obligis, and M. Ali-Mehenni, 2000: The rain profiling algorithm applied to polarimetric weather radar. J. Atmos. Oceanic Technol., 17 , 332356.

    • Search Google Scholar
    • Export Citation
  • Vulpiani, G., P. Tabary, J. Parent du Chatelet, and F. Marzano, 2008: Comparison of advanced radar polarimetric techniques for operational attenuation correction at C band. J. Atmos. Oceanic Technol., 25 , 11181135.

    • Search Google Scholar
    • Export Citation
  • Zrnić, D., T. Keenan, L. Carey, and P. May, 2000: Sensitivity analysis of polarimetric variables at a 5-cm wavelength in rain. J. Appl. Meteor., 39 , 15141526.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Scatterplot of ZDR vs Z in pure rain at C band; Z and ZDR are computed from 25 920 DSDs measured in central Oklahoma. Raindrop temperature is 20°C. The shape–size dependence of raindrops is assumed to be as in Brandes et al. (2002). The gray line indicates the dependence of median ZDR on Z for 25 < Z < 45 dBZ.

  • Fig. 2.

    Scatterplots of (top) AH and (bottom) ADP vs KDP in pure rain at C band for (a),(c) all ZDR and (b),(d) ZDR < 3dB. Radar variables are computed from 25 920 DSDs measured in Oklahoma.

  • Fig. 3.

    Scatterplot of the ratio ADP/KDP vs ZDR in pure rain at C band. Radar variables are computed from 25 920 DSD measured in Oklahoma.

  • Fig. 4.

    Conceptual plot illustrating the hot spot between ranges r1 and r2 in the radial profiles of Z and ΦDP.

  • Fig. 5.

    Scatterplots of α0 vs β0 simulated from disdrometer data in Oklahoma for T = 10° and 20°C for ZDR varying between 0.5 and 3.0 dB. Dashed line depicts the dependence α0 = 3.33β0 from Vulpiani et al. (2008).

  • Fig. 6.

    Retrieved radial profiles of specific attenuation Ah for α0 = 0.06 dB per degree, different values of Δα in a hot spot, and different locations of a hot spot along the propagation path. The true value of Δα in a hot spot is equal to 0.04 dB per degree. Here, L/R is the ratio of the left and right sides of Eq. (21). The retrieved profile of Ah for Δα = 0.04 dB per degree coincides with the “true” profile of Ah.

  • Fig. 7.

    Fields of measured (top) Z, (middle) ZDR, and (bottom) ΦDP at (left) C and (right) S bands for the storm at 0309 UTC 10 Mar 2009. Here, the elevation (C band) = 0.41° and the elevation (S band) = 0.48°. The C-band radar is at X = 0, Y = 0. The areas of visible negative bias of Z caused by attenuation at C band are marked as A and B in the top-left panel. In the left panels, a line indicates the azimuthal direction for which the RHI plot in Fig. 8 is displayed.

  • Fig. 8.

    Composite RHI plot of (top) Z, (middle top) ZDR, (middle bottom) ΦDP, and (bottom) ρhv at (left) C and (right) S bands for the storm at 0309 UTC 10 Mar 2009. Here, azimuth (C band) = 285.5° and azimuth (S band) = 280°. The azimuthal direction of the vertical cross section is shown in Fig. 7.

  • Fig. 9.

    Fields of (left) corrected C-band Z and ZDR and (right) measured S-band Z and ZDR for the PPI in Fig. 7. The elevation (C band) = 0.41° and the elevation (S band) = 0.48°. The dashed line in the left panels indicates the azimuthal direction with strong partial blockage of the OU PRIME beam.

  • Fig. 10.

    Scatterplots of the differences Z(S band) − Z(C band) vs ZDR(S band) − ZDR(C band) (top) before and (bottom) after attenuation correction for the part of the radar scan in Figs. 7 and 9 for which measured (uncorrected) ZDR is lower than −1 dB.

  • Fig. 11.

    Radial profiles of the differential phase (top) that was measured by the Sidpol radar, (middle) after downward phase shift, and (bottom) after editing, unfolding, and smoothing at 0149 UTC 5 Aug 2008 at azimuth = 257.2° and elevation = 0.5°.

  • Fig. 12.

    Fields of (a) measured and (c) corrected Z at C band, (b) ΦDP at C band, and (d) Z measured by S-band radar (KLOT WSR-88D) at 0149 UTC 5 Aug 2008. The antenna elevation is 0.5°. The Sidpol radar is situated at X = 0, Y = 0 km. The star marks the location of the WSR-88D. The straight line indicates azimuth 257.2° (see Figs. 11 and 14).

  • Fig. 13.

    Validation of Z and ZDR attenuation correction for the radar scan in Fig. 12 using self-consistency among Z, ZDR, and KDP in rain. (a) Scatterplot of 10 log(KDP) − Zh vs ZDR after Z and ZDR are corrected for attenuation using the hot spot method. (b) Median values of the estimated difference between 10 log(KDP) and Zh as functions of ZDR for uncorrected Zh (asterisks) and corrected Zh (diamonds) as compared with the corresponding theoretical curves based on simulations at C band from disdrometer data in Oklahoma (solid line) and from Gourley et al. (2006) (dashed line).

  • Fig. 14.

    Radial profiles of (a) ΦDP (thick line) and ρhv (thin line), (b) measured (thin line) and corrected (thick line) Z, (c) measured (thin line) and corrected (thick line) ZDR, and (d) R(Z) (thin line) after Z is corrected and R(KDP) (thick line) at azimuth 257.2° at 0149 UTC 5 Aug 2008. Attenuation correction of Z is performed using the hot-spot algorithm with constraint condition (21).

  • Fig. 15.

    Fields of (a) corrected Z, (b) measured and (c),(d) corrected ZDR, (e) ΦDP, and (f) ρhv at 0124 UTC 5 Aug 2008. The antenna elevation is 0.5°.

  • Fig. 16.

    Scatterplots of the measured parameters (a) α and (b) β vs maximal ZDR in the hot spotat elevation 0.5° and (c) scatterplot of β vs α in the hot spots.

  • Fig. 17.

    Fields of rain rates obtained from (a) measured and (b) corrected Z at C band, (c) KDP, and (d) S-band Z at 0149 UTC 5 Aug 2008. A star indicates the location of the WSR-88D.

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