Use of Specific Attenuation for Rainfall Measurement at X-Band Radar Wavelengths. Part II: Rainfall Estimates and Comparison with Rain Gauges

Malte Diederich Atmospheric Dynamics and Predictability Branch, Hans Ertel Centre for Weather Research, University of Bonn, Bonn, Germany

Search for other papers by Malte Diederich in
Current site
Google Scholar
PubMed
Close
,
Alexander Ryzhkov Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

Search for other papers by Alexander Ryzhkov in
Current site
Google Scholar
PubMed
Close
,
Clemens Simmer Meteorological Institute, University of Bonn, Bonn, Germany

Search for other papers by Clemens Simmer in
Current site
Google Scholar
PubMed
Close
,
Pengfei Zhang Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

Search for other papers by Pengfei Zhang in
Current site
Google Scholar
PubMed
Close
, and
Silke Trömel Atmospheric Dynamics and Predictability Branch, Hans Ertel Centre for Weather Research, University of Bonn, Bonn, Germany

Search for other papers by Silke Trömel in
Current site
Google Scholar
PubMed
Close
Full access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

In a series of two papers, rain-rate retrievals based on specific attenuation A at radar X-band wavelength using the R(A) method presented by Ryzhkov et al. are thoroughly investigated. Continuous time series of overlapping measurements from two polarimetric X-band weather radars in Germany during the summers of 2011–13 are used to analyze various aspects of the method, like miscalibration correction, ground clutter contamination, partial beam blockage (PBB), sensitivity to precipitation characteristics, and sensitivity to temperature assumptions in the retrievals. In Part I of the series, the relations inherent to the R(A) method were used to calculate radar reflectivity Z from specific attenuation and it was compared with measured reflectivity to estimate PBB and calibration errors for both radars. In this paper, R(A) rain estimates are compared to R(Z) and R(KDP) retrievals using specific phase shift KDP. PBB and calibration corrections derived in Part I made the R(Z) rainfall estimates almost perfectly consistent. Accumulated over five summer months, rainfall maps showed strong effects of clutter contamination if R(KDP) is used and weaker impact on R(A). These effects could be reduced by processing the phase shift measurements with more resilience toward ground clutter contamination and by substituting problematic R(KDP) or R(A) estimates with R(Z). Hourly and daily accumulations from rain estimators are compared with rain gauge measurements; the results show that R(A) complemented by R(Z) in segments with low total differential phase shift correlates best with gauges and has the lowest bias and RMSE, followed by R(KDP) substituted with R(Z) at rain rates below 8 mm h−1.

Corresponding author address: Malte Diederich, Hans Ertel Centre for Weather Research, University of Bonn, Auf dem Hügel 20, 53121 Bonn, Germany. E-mail: malte.diederich@uni-bonn.de

Abstract

In a series of two papers, rain-rate retrievals based on specific attenuation A at radar X-band wavelength using the R(A) method presented by Ryzhkov et al. are thoroughly investigated. Continuous time series of overlapping measurements from two polarimetric X-band weather radars in Germany during the summers of 2011–13 are used to analyze various aspects of the method, like miscalibration correction, ground clutter contamination, partial beam blockage (PBB), sensitivity to precipitation characteristics, and sensitivity to temperature assumptions in the retrievals. In Part I of the series, the relations inherent to the R(A) method were used to calculate radar reflectivity Z from specific attenuation and it was compared with measured reflectivity to estimate PBB and calibration errors for both radars. In this paper, R(A) rain estimates are compared to R(Z) and R(KDP) retrievals using specific phase shift KDP. PBB and calibration corrections derived in Part I made the R(Z) rainfall estimates almost perfectly consistent. Accumulated over five summer months, rainfall maps showed strong effects of clutter contamination if R(KDP) is used and weaker impact on R(A). These effects could be reduced by processing the phase shift measurements with more resilience toward ground clutter contamination and by substituting problematic R(KDP) or R(A) estimates with R(Z). Hourly and daily accumulations from rain estimators are compared with rain gauge measurements; the results show that R(A) complemented by R(Z) in segments with low total differential phase shift correlates best with gauges and has the lowest bias and RMSE, followed by R(KDP) substituted with R(Z) at rain rates below 8 mm h−1.

Corresponding author address: Malte Diederich, Hans Ertel Centre for Weather Research, University of Bonn, Auf dem Hügel 20, 53121 Bonn, Germany. E-mail: malte.diederich@uni-bonn.de

1. Introduction

Potential utilization of specific attenuation A for rainfall estimation, mitigation of partial beam blockage (PBB), and radar networking was discussed in the paper by Ryzhkov et al. (2014, hereafter RAL14). They showed that the relation between precipitation intensity R and A depends less on drop size distribution (DSD) than traditional rainfall algorithms based on radar reflectivity Z, differential reflectivity ZDR, and specific differential phase KDP in a wide range of rain intensity. RAL14 estimate A with the so-called ZPHI method from the radial profile of measured Z and the total span of differential phase ΔΦDP following Bringi et al. (1990) and Testud et al. (2000). Since the A estimate based on differential phase is unaffected by reflectivity biases caused by radar miscalibration, attenuation, partial beam blockage (PBB), and wet radomes, the same should hold for rain retrievals based on R(A) relations.

This paper is the second of a series of two papers. In the first paper (Diederich et al. 2015, hereafter DAL1), we introduced the analyzed radar systems and examined the efficiency of using specific attenuation A for correcting Z for radar miscalibration and PBB by comparing reflectivity at horizontal polarization derived from specific attenuation ZH(AH) with measured reflectivity corrected for path-integrated attenuation ZH + IAH. We showed that the PBB-induced biases of ZH estimated using ZH(AH), the ZHZDRKDP consistency in rain, and a digital elevation model (DEM) are almost identical and that the calibration correction estimated in unblocked sectors is consistent between the neighboring radars. We also showed that differences between ZH(AH) and measured ZH corrected for attenuation displayed little sensitivity to assumptions concerning the temperature dependence of A. Thus, the high temporal variability of the differences is most likely a consequence of DSD variability, which is responsible for errors in Z-based rain estimators to a larger degree than in A-based estimators. Accordingly, we may reasonably assume that the same effect may result in improved R(A) estimates compared to R(Z).

In this second paper, we present a thorough validation of the R(A) estimator and its performance compared to other rainfall algorithms via comparison with rain gauge measurements. Section 2 briefly describes the observations used in the study followed by a summary of the algorithms used for rain-rate retrieval in section 3. In section 4, the spatial consistency of accumulated rain fields resulting from different precipitation estimators is investigated with respect to PBB and ground clutter. Radar rainfall estimates are compared to rain gauge observations in section 5, and the results are summarized and discussed in section 6.

2. Observations

The two polarimetric X-band radars BoXPol and JuXPol and the C-band Doppler radar Offenthal used in these investigations were already described in DAL1, as were the methods employed to derive the DEM-based PBB correction (Fig. 1a) and the PBB and calibration corrections derived from ZH(AH) (Fig. 1b).

Fig. 1.
Fig. 1.

(a) Radar reflectivity bias of BoXPol caused by PBB, as simulated with the use of a DEM. (b) Radar reflectivity bias caused by the combined effects of radar miscalibration and PBB, as estimated by calculating BA along uninterrupted ZPHI segments. Locations of the rain gauges are marked by dots.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

Rainfall measurements by 133 weighing-type rain gauges, operating at 1-min temporal resolution and with 0.033-mm sensitivity, were provided by the Landesumweltamt Nordrhein-Westfalen (the state agency for environmental issues), the Erftverband (a regional water management authority), and the city of Bonn (positions shown in Fig. 1 of DAL1). Wind and shading by trees and buildings may affect data quality as no wind correction was applied, which may lead to a slight underestimation of total rainfall by the gauges (Nespor and Sevruk 1999). Some gauges required manual filtering because of data gaps and erroneous measurements, but the overall quality proved to be satisfactory and consistent when comparing with neighboring gauge measurements or radar observations. Only a few rain gauge locations are affected by strong beam blockage, but those affected are fairly close to the radar. This allowed the validation of PBB correction schemes with rain gauges while excluding effects of the vertical profile of reflectivity (VPR; e.g., Hazenberg et al. 2013), total signal loss, and cloud overshooting, which would additionally affect observations at larger distances.

3. Radar rainfall estimators and data processing

We evaluated 12 rainfall estimation algorithms by checking the spatial consistency of their outputs (section 4) and via comparison with rain gauge observations (section 5). The algorithms differ by correcting/neglecting attenuation and PBB, by the techniques used for correcting attenuation and PBB, and by using different radar moments. If reflectivity is corrected for the average constant calibration errors derived in DAL1 (2 dB for BoXPol and 8 dB for JuXPol), then +C is added to the name of a reflectivity-based estimator [such as R(Z + C)]. If the calibration error is estimated dynamically for each scan using Eq. (6) in DAL1, we add +S to the name of the respective estimator instead.

Noise cutoff and Doppler filtering for removing ground clutter were applied to ZH by the signal processor. A radial median filter of 2.5-km length is applied to remove the remaining effects of clutter. No Doppler filter was applied in the signal processor’s cross correlation ρH,V or ΦDP calculation. Although extensive work has been done in attempts to improve ΦDP estimates (Wang and Chandrasekar 2009; Otto and Russchenberg 2011; Maesaka et al. 2012; Giangrande et al. 2013), no universally accepted processing method exists to date. We used two different ways of processing ΦDP to remove ground clutter and noise contamination: one involves “liberal” discrimination criteria such as ρH,V > 0.87, −5.5 < ZDR < 5.5 dB, and |ΦDP(ri) − ΦDP(ri+1)| < t (ri and ri+1 are subsequent radar range bins and t is a threshold that depends on radial resolution and range) constraints to filter out jumps in ΦDP, followed by a running average radial smoothing. In a “stricter” version of the ΦDP processing, we also discard ΦDP measurements within 200-m radial distance of a rejected range bin and use a radial median filter of 2.5-km length instead of smoothing by a running average. The stricter filter provides more immunity to ground clutter contamination but reduces sensitivity in areas of weak echoes and near range gates contaminated by ground clutter. The stricter filter had a relatively large effect when accumulating sums from pure rainfall estimators of R(A) and R(KDP) because of the lowered sensitivity for low rain rates, but little effect when calculating mean reflectivity biases as in DAL1, as only measurements with present KDP or ΦDP values entered the calculation of mean biases.

Despite existing advanced corrections for advection and VPR, which are known to improve the performance and comparability of radar rainfall estimates with gauge measurements considerably in certain situations (e.g., Hazenberg et al. 2011a), such corrections were not applied here. Correction for advection makes the attribution of measurements in areas affected by PBB to gauge locations problematic, and the extrapolation of VPRs are most effective in melting layer cases, which are not applicable to the liquid precipitation R(A) retrievals analyzed here. Both corrections improve radar rainfall estimation performance but would add uncertainty when evaluating the rain-rate retrieval itself.

In the following list, we start with the description of a pure reflectivity-based rain-rate estimator and progressively add complexity.

  1. R(ZH): The widely used Marshall–Palmer relation
    e1
    is inverted and applied to the measured radar reflectivity at ZH before correction for PBB and attenuation is made. The largest errors are expected for this algorithm, especially when applied to the attenuation-prone X-band observations.
  2. R(ZH + IAH): As in (a), but ZH is corrected by adding the two-way path-integrated attenuation by hydrometeors IAH along the radar beam determined as
    e2
    where α = AH/KDP in rain and T is the temperature along the propagation path. A fixed or temperature-dependent α can be applied using values in Table 3 of DAL1. The KDP is still affected by enhancement of ΦDP by backscattering phase shift (so-called δ peaks; see, e.g., Matrosov et al. 1999, 2002; Otto and Russchenberg 2011; Schneebeli and Berne 2012; Trömel et al. 2013), which may lead to overcompensation of attenuation in heavy rain.
  3. R(ZH + IAH + BB) and R(ZH + IAH + BA): As in (b), but including the PBB corrections of ZH described in sections 1 and 3 of DAL1, using either the DEM-derived PBB map (PBB-related reflectivity bias BB; Fig. 1a) or the PBB correction derived from long-term accumulations of ZH(AH) and ZH + IAH (bias of Z attributed to miscalibration and PBB BA; Fig. 1b). We will also use R(ZC) and ZC = ZH + IAH + BB for abbreviation. Note that adding BB does not correct for calibration errors unless +C or +S are added as in R(ZC + C) or R(ZC + S).

  4. R(KDP): Rainfall intensity is estimated from KDP following RAL14:
    e3
    This estimator is by definition independent of radar miscalibration and PBB, but it may produce negative rain rates because of the impact of backscattering differential phase, nonuniform beamfilling (Ryzhkov 2007), and the noisiness of the ΦDP estimate. The KDP used for rain-rate estimation is calculated as the slope of ΦDP with least squares linear fits over 4-km-long radial segments.
  5. R(KDP, ZC): This estimator combines (c) and (d) and utilizes R(KDP) if R(KDP) > 8 mm h−1 and R(ZC) otherwise to avoid the impact of KDP noisiness in light rain.

  6. RBONN(ZC): Similar to R(ZC), but the relation
    e4
    is used instead of Eq. (1). This ZH(R) relation is the one that gave the lowest root-mean-square deviation (RMSD) and bias for BoXPol-derived R estimates compared to observations of the city of Bonn’s gauge network (see cluster of dots around the BoXPol location in Fig. 1) between May and September 2010. This estimator allows testing the importance of regional/empirical rain estimators against global estimators like Eq. (1).
  7. R(AH): Specific attenuation AH is calculated via the simplified ZPHI method and then used in the R(AH) = a(AH)b estimator, as described in DAL1. Similar to R(KDP), R(AH) automatically corrects for PBB and radar miscalibration but replicates the higher spatial discriminative power of reflectivity-based estimators, as demonstrated in RAL14. It is also more resilient to δ peaks associated with backscatter differential phase, as they will only be manifested in ΔΦDP if there is a peak at the edge of a ZPHI segment (Trömel et al. 2013).

  8. R(AH, ZC): As in (g), but for segments with ΔΦDP < 4°, the R(ZC) estimator from (c) is used instead of R(AH). We tested the azimuthal smoothness of the R(AH) results as an alternative filtering criteria, but both methods yielded very similar results.

  9. RFIT(AH, ZC): The ZR relation is altered for each scan fitting the factor a in using R(AH) estimates in all segments where ΔΦDP > 4°. Thus, the R(Z) relation is dynamically adjusted via its bias compared to R(A), and the resulting RFIT(ZC) substitutes R(AH) in segments where ΔΦDP < 4°. With this estimator, we test whether the supposedly nearly DSD-invariant R(A) estimate can be applied for improving R(Z) estimators in a dynamic way, while also correcting for miscalibration of ZH. Rain rates resulting from RFIT(ZC) are very close to those obtained when first calculating and applying the radar calibration bias for a single scan to ZH before using the standard ZR relation [i.e., R(ZC + S)].

  10. R(AV): As in (g), but applied to the vertical polarization (see Tables 3–5 in DAL1 for appropriate parameters). Since ZV is slightly less attenuated and the exponents in the R(AV) and AV(ZV) relations are slightly closer to 1 than at horizontal polarization, one might expect improved rain-rate estimates compared to R(AH).

  11. R(AV, ZC): As in (h), but R(AV) is substituted for R(AH). Again, we expect slightly improved rain rates compared to R(AH, ZC).

  12. RFIT(ZC): As in (i), except that the adaptive R(ZC) is now used as rainfall estimator for the entire scan, without using the R(AH) directly.

4. Consistency of accumulated radar-derived precipitation fields

RAL14 has already shown that the R(A) method is superior to R(KDP) when it comes to rendering the fine structure or rain in single scans. To illustrate the consequences that a “liberal” processing of ΦDP—such as described in section 3—can have on long-term accumulations, the first examples will not use the “strict” filter described.

We first examine 3-h rain totals during an event on 22 June 2011, which was observed by the two X-band radars and the polarimetrically upgraded C-band radar of Offenthal. Accumulations obtained from the attenuation-corrected but not PBB- or calibration-corrected ZR-based estimator (algorithm b in the previous section) and the pure R(AH) estimator (algorithm g), for three radars are shown in Fig. 2. The R(AH) algorithm completely compensates PBB for the Offenthal radar, which is visible in the R(ZH + IAH) accumulations (Figs. 2c,f). The calibration error of JuXPol is also successfully mitigated with the R(AH) algorithm (Figs. 2a,d). The sector of BoXPol subject to almost complete beam blockage is successfully compensated near the radar, but not at greater distances/altitudes because of noise cutoff and loss of signal (Figs. 2b,e). Other obstacles that cause PBB for BoXPol are evidently well corrected for. In the composite of scans based on the R(ZH + IAH) algorithm (Fig. 2g), calibration differences and PBB by industrial chimneys and mountains create artifacts in the structure of the accumulated fields, with significant biases in certain regions. The greater part of these artifacts are removed in the R(AH) composite (Fig. 2h), with the exception of the almost totally blocked sector of BoXPol and a visible edge in the southwest, which is caused by total extinction due to heavy attenuation at X band during parts of the event. The composite shows that calibration errors and PBB are well compensated by R(A), and almost no artifacts from PBB, miscalibration, or ground clutter become evident in the structure of the rainfall field for this 3-h accumulation.

Fig. 2.
Fig. 2.

Maps of 4-h rainfall totals at 1000–1300 UTC 22 Jun 2011. Shown are estimates of R(ZH + IAH) from the (a) 0.5° elevation scan of JuXPol, (b) 1.5° elevation of BoXPol, and (c) 0.5° elevation of Offenthal radars; (d)–(f) the corresponding scans using R(AH); and (g),(h) a composite of these scans composed of values measured at the lowest altitude at each pixel.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

We now analyze the effects of ground clutter contamination and beam blockage on precipitation derived from BoXPol accumulated over the entire period of May–September 2011 in Fig. 3. Melting layer detection and discrimination is generally needed in QPE applications (Gourley and Calvert 2003; Brandes and Ikeda 2004), but for examining structural consistency of the derived fields with respect to ground clutter and PBB, rain accumulations without melting layer discrimination can be interpreted more easily. The cumulative maps show the higher precipitation rates over the higher orography of the Bergisches Land area northeast of BoXPol (see also topography in Fig. 1 in DAL1) caused by increased convective activity and topographic lifting acting on the typically westerly flow. Weak indications of the typical ring structure characteristic of melting layer contamination are visible at approximately 70 km from BoXPol.

Fig. 3.
Fig. 3.

Accumulated BoXPol rainfall estimates from May to September 2011 computed by six of the algorithms described in section 3, applied to 1.5° elevation PPI scans.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

Despite attenuation correction, precipitation estimates still decrease with range because of beam overshooting (VPR effect; Pellarin et al. 2002) and total attenuation (blinding) in heavy rain, which is frequent at X band. These effects are most visible in sectors subject to strong PBB (151°–165° azimuth), where the echoes become undetectable at shorter ranges and result in strongly reduced accumulations. The PBB correction based on a DEM (Fig. 3a) obviously results in less consistent rainfall accumulation than the one based on Z(A) (Fig. 3d) in the southern half of the scan, and also for the structures near 65° and 212° azimuth, with the exception of the chimney at 50° azimuth. The absolute quantitative accuracy of PBB corrections for ZH cannot, however, be deduced from accumulated rainfall maps alone, because of the more frequent reflectivity signal loss in blocked sectors. An overestimation of PBB might also lead to more consistent accumulated rainfall fields.

The accumulated R(KDP) shows strong positive and negative anomalies at places where the radar return is contaminated by ground clutter (Fig. 3b). Such anomalies are not visible in single scans or hourly or even daily sums, as they are masked by the random appearance of the noise in R(KDP) estimates and by higher natural spatial variability typical for rainfall fields accumulated over short periods (cf. Figs. 2, 3). Near-clutter range bins between clutter and radar show positive anomalies, while the opposite sides have negative anomalies. This results from either a systematic positive backscattering phase shift associated with ground clutter or enhanced noisiness of differential phase in clutter-contaminated areas; averaging noisy differential phase over typical dwell times produces a distribution of averaged ΦDP with a broad maximum near the center of the phase interval, that is, at 0°. Since the radar system phase shift attains values around −90° for BoXPol, its compensation leads to, on average, positive phase shift anomalies in the clutter-contaminated regions. Neighboring range bins will be very slightly contaminated and evade any filtering because of the natural noisiness of ΦDP measurements on a scan-to-scan basis, but they will build up strong biases for large integration times.

The R(AH) estimates are also affected by the clutter effect described, when the segment for which ΔΦDP is sampled borders a clutter pixel, which becomes visible in Fig. 3c at close range between radar and Siebengebirge at 112° azimuth. The shorter the segment, the smaller the respective differential phase shift, which in return leads to larger relative error. For the same reason, clutter-induced anomalies disappear when segments with total differential phase shifts below 4° are substituted with R(ZH) in R(AH, ZC) (Fig. 3f). Since the segments of R(AH) can be up to 100 km long with phase shifts over 90°, while the phase shift used to calculate a R(KDP) value can only stretch between 1 and 4 km, R(AH) is less susceptible to this type of error than R(KDP), which still shows clutter-contaminated regions even when merging with R(Z) in R(KDP, ZC) (Fig. 3e).

The clutter artifacts seen in the long-term BoXPol R(KDP) and R(AH) accumulations displayed in Figs. 3b and 3c resulted from liberal ΦDP filtering followed by running mean smoothing, which yields higher sensitivity in weak signals. To remove the clutter contamination in long-term accumulations, we change to the stricter filter that also excludes ΦDP measurements within 200 m of a rejected range bin and applies a median filter for smoothing instead of averaging. With this filter, R(KDP) is less affected by clutter for BoXPol (Fig. 4b), although JuXPol still shows some contamination near the radar (Fig. 5b). Clutter contamination now completely disappears in the combined R(KDP, ZC) estimator (Figs. 4e, 5e). Note that the accumulations shown in Figs. 4 and 5 only contain observations made when both radars were operational to make the totals in Figs. 4 and 5 comparable, while Fig. 3 also includes times when JuXPol was offline. The R(AH) accumulations in Figs. 4c and 5c do not include estimates in the melting layer, and the fields show some gaps at close range to the radar, where the stricter ΦDP filter suppressed some ZPHI estimates. Even close to the radars, the accumulations of pure R(KDP) (Figs. 4b, 5b) and pure R(AH) (Figs. 4c, 5c) are lower than those obtained from attenuation-, PBB-, and calibration-corrected R(ZC + C) (Figs. 4d, 5d), which is linked to the lowered sensitivity through stricter ΦDP filtering. When R(KDP) and R(AH) are complemented with ZH-based estimators (Figs. 4e,f and 5e,f), the accumulations become structurally consistent, with the exception of a stronger melting layer contamination for BoXPol because of the higher elevation angle.

Fig. 4.
Fig. 4.

Accumulated rainfall estimates from six of the algorithms described in section 3 applied to the 1.5° elevation scan of BoXPol from May to September 2011. Only observations during which both BoXPol and JuXPol were operational were included in the accumulations.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

Fig. 5.
Fig. 5.

Accumulated rainfall estimates from six of the algorithms described in section 3 applied to the 1.1° elevation scan of JuXPol from May to September 2011. Only observations during which both BoXPol and JuXPol were operational were included in the accumulations.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

The combined R(KDP, ZC) estimator applied to JuXPol (Fig. 5e) leads to strongly underestimated rainfall totals, caused by significant contributions to total rainfall from miscalibrated reflectivity measurements. This illustrates that, if the calibration error is unknown and not corrected for, the high number of rain-rate estimates of R(KDP) below 8 mm h−1 will strongly affect the combined R(KDP, ZC) estimator. In the combined R(AH, ZC + S, ZC) estimator (Figs. 4f, 5f), the scan-based calibration correction +S of ZH using Z(A) is applied (algorithm i) if enough ZPHI segments are present in the scan, and R(ZC) (which is not corrected for calibration errors) is only used if not enough suitable segments were present. Opposed to R(KDP, ZC) (Figs. 4e, 5e), this combination of R(A), R(Z), and Z(A) gave quantitatively consistent precipitation totals for both radars (Figs. 4f, 5f) and their calibration-corrected R(ZC + C) counterparts (Figs. 4e, 5e). We conclude that a combined R(A) and R(Z) algorithm that uses strict ΦDP processing as described, together with a Z(A)-based real-time calibration correction, gave the best results in terms of quantitative consistency and structural plausibility in long-term accumulated rainfall fields. To achieve similar quantitatively consistent results with a combined R(KDP, ZC) estimator, it would be necessary to know the calibration error beforehand, or to also use a scan-based calibration correction using ZHZDRKDP consistency or ZHKDP consistency.

5. Validation using rain gauges

QPE is now investigated by comparison of radar-based estimates with hourly rain gauge accumulations for BoXPol and daily accumulations for BoXPol and JuXPol. Throughout these comparisons it should be kept in mind that, because of different measuring principles and volume–time sampling in radar and rain gauge measurements, their statistical distributions cannot be expected to be identical even if both rainfall estimates were perfect, although most QPE data users would want their statistical properties to be conveniently similar. For hourly accumulations we applied the liberal ΦDP processing routine for R(A) and R(KDP); thus, the use of stricter processing would lead to somewhat lower sums by pure R(A) and pure R(KDP) estimators.

The box–whisker plots in Fig. 6 compare the quintiles of hourly BoXPol estimates in pure rain, using temperature-based hydrometeor-phase discrimination and filtering. The gauge measurements are used to separate the observation pairs into three precipitation rate ranges (0.03–1.5, 1.5–5, or above 5 mm in 1 h). The necessity of attenuation correction at X band for Z-based estimators is evident from the strong underestimation by the R(ZH) estimator of algorithm a, especially for the moderate and high precipitation rates. The attenuation-corrected estimators R(ZH + IAH) (algorithm b) and R(ZC = ZH + IAH + BB) (algorithm c) underestimate rainfall in most cases compared to gauges (see 50% percentiles in all classes) but also show more extremely high values than R(KDP) (algorithm d), R(AH) (algorithm g), and rain gauges (see 91% percentiles and maxima). The probable cause is Mie scattering occurring for large hydrometeors at X-band wavelengths, causing enhancement of both ZH and IAH (the latter through δ peaks). If R(Z) is capped to be not higher than 100 mm h−1 (corresponding to 55 dBZ for this ZR relation), the maxima of hourly accumulations achieved through algorithms b and c become similar to those of the rain gauges. The pure R(KDP) algorithm d has the broadest quintile spectrum for low and medium rainfall because of the noisiness of KDP, but it does very well in heavy rain.

Fig. 6.
Fig. 6.

Box–whisker plots of hourly rain totals from gauge observations and different radar rainfall estimators from May to September 2011. The data are separated into three intervals of hourly gauge totals ranging between 0.03 and 1.5 mm, 1.5 and 5 mm, or above 5 mm (highest sum measured by gauges was 59 mm). The variable S is the percentage of total rainfall that each interval contains, and N is the number of measurements in the interval.

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

The pure R(AH) algorithm g performs similarly well at high rain rates (with the exception of slightly lower maxima, probably also linked to Mie scattering, as expected in RAL14) and shows much less scatter than R(KDP) at lower rain rates, combined, however, with a clear overestimation of the latter. The RFIT(ZC) relations that were fitted to R(AH) on a scan-to-scan basis (algorithm l) do not show the overall underestimation typical of the standard R(Z) relation, but they also exhibit too extreme estimates like the standard R(Z) relation if the R(A) segments are not directly included as in algorithm i.

The results displayed in Fig. 6—as discussed above—suggest that a combination of R(KDP) or R(AH) during heavy rain with R(Z) dynamically adjusted with R(A) during light rain exhibit the best overall performance (see algorithms d, i, and l). We also tried substituting R(A) by R(KDP) in cases of extremely high ZC or RFIT(Z) to mitigate the detrimental impact of hail and Mie scattering on R(A) predicted by RAL14, but no significant change or improvement was obtained in any of the comparisons, probably because of the scarcity of these cases and the fact that X-band radar returns are completely extinguished in most cases of hail anyway.

Correlation coefficient, mean bias, and RMSD of the hourly estimates from the 12 radar algorithms listed in section 3 toward rain gauges are summarized in Table 1, using different temperature-dependency assumptions and a separation between rain-only and “all included” applications in three columns. The best and second best scores are in boldface. For rain-only cases, slightly smaller biases are obtained by the algorithms that take variable temperature dependencies into account. However, the difference is smaller than the precision expected from the rain gauge measurements.

Table 1.

Correlation coefficients, bias, and RMSE between hourly rainfall accumulations as derived by different radar rainfall estimators and rain gauges (ZC = ZH + IAH + BB). The best and second best scores are in boldface.

Table 1.

The highest correlation coefficients between hourly rain totals from gauges and their radar estimates are obtained for the R(AH,V) algorithms. The pure R(KDP) algorithm yields the lowest bias while the mixed algorithms R(KDP, ZC) and R(AH, ZC) produce a slight overestimation between 1% and 4% compared to the gauges. The pure R(AH,V) algorithms generate larger positive biases of 13% and 17% due to persistent rain overestimation within the segments with low ΔΦDP. The regionally optimized fixed RBONN(ZC) relation leads to much better correlations and RMSD than the Marshall–Palmer relation, but it is still outperformed by the R(A)-based estimators.

The RFIT(ZC) algorithm that adapts the ZR relation in every scan [which is analogous to calibrating ZH with +S derived from Z(A) in every scan] also produces significantly better results than the Marshall–Palmer relation, as long as miscalibration and Mie scattering are not corrected in R(ZC). Thus, a potentially miscalibrated ZH can be corrected in real time on a scan-by-scan basis using R(A) or Z(A) without the need to accumulate over time. The better performance of RFIT(ZC) compared to R(ZC) is also an encouraging indication that the closer correlation of specific attenuation A or KDP and rain rate (compared to the correlation between ZH and rain rate) is reflected in R(A). The best result for a pure R(Z)-based estimator was achieved when corrections for calibration, PBB, and attenuation were applied to the standard relation and the rain rate was constrained to stay below 60 mm h−1 to compensate for Mie scattering effects (bottom row of Table 1). However, a better result could still be achieved by combining R(AH) and RFIT(ZC).

Assuming a constant temperature of 15°C instead of using extrapolated measured temperature changes the overall bias of the R(A) estimators by about 2% (bias columns in Table 1), but does not affect correlation toward rain gauges. To test the resilience of the algorithms with respect to possible contamination with mixed-phase hydrometeors, we did the same comparisons without excluding observations from beam segments colder than 6°C (thus increasing the sample size from 77 999 to 123 536 pairs; RMSE columns in Table 1). Correlation coefficients and RMSD decrease for the R(AH,V) and R(AH,V, ZC)-based estimates compared to the rain-only cases but are still better than the R(KDP), R(KDP, ZC), and R(ZH,V) estimates. The biases of per-scan optimized RFIT(AH, ZC) and RFIT(ZC) estimators increase to 13% and 17%, respectively, under these circumstances. Thus, in our case, ignoring hydrometeor type did not change the outcome significantly with the exception of a compromised RFIT(ZC) estimate. More severe consequences for higher elevation angles or during winter are expected.

The results summarized in Table 1 are based on the comparison at all gauge locations. As shown in section 4, certain locations suffer more heavily from error sources such as clutter, PBB, and range-dependent effects (Zawadzki 1984; Ryzhkov 2007). The evaluation scores calculated for each gauge individually are displayed as functions of range in Fig. 7, provided that the filtering of melting layer cases left more than 50 observation pairs. The attenuation and PBB effects visible in the biases shown in Fig. 7a are obviously well compensated by the estimators in Figs. 7b–f. For all estimators, correlation and RMSD deteriorate with range, which can be explained by the radar beam gaining height over the gauge at greater distance, and potentially imperfect attenuation correction due to a complete loss of radar signal, or poor estimates of the factor α. At close range from the radar, the R(KDP) (Fig. 7c), and to some extent the R(AH) algorithms (Fig. 7e), suffer from ground clutter contamination. The R(AH) estimates that include segments with ΔΦDP below 4° tend to produce too high rain rates within the first 40 km from the radar. This bias is reduced when the estimates for these segments are replaced by R(ZC) or RFIT(ZC) (Fig. 7f). Overall, the R(AH,V, ZC)-based algorithms perform better than the R(KDP) or R(KDP, ZC) and much better than the R(Z)-based algorithms for these hourly rain totals.

Fig. 7.
Fig. 7.

Correlation coefficient, mean bias, and RMSD as functions of range from the radar for six radar rainfall estimators and individual rain gauges. All values are from May to September 2011 and are restricted to observations for which estimates of the temperature in a ZPHI beam segment did not drop below 6°C. Different degrees of PBB are visualized by symbols (dots for BB < 2 dB, crosses for 2 > BB > 5 dB, asterisks for BB = 8 dB, and diamonds for BB = 19 dB).

Citation: Journal of Hydrometeorology 16, 2; 10.1175/JHM-D-14-0067.1

Finally, daily accumulations obtained from the most relevant estimators applied to BoXPol and JuXPol are compared to rain gauges, using the stricter ΦDP processing (see section 3), as opposed to the hourly gauge comparisons that used liberal ΦDP processing. The calibration errors deduced for BoXPol and JuXPol in DAL1 are selectively applied to the R(Z)-based estimators. Table 2 shows their correlation, bias, and RMSDs from comparison with gauge measurements. The pure R(KDP) and R(AH) now display negative biases between −7% and −20% because of signals rejected by the stricter ΦDP filter. The R(ZC) of BoXPol and JuXPol without calibration correction show negative biases of −22% and −64%, respectively, which are transformed into +5% and +10% if the constant calibration corrections of +2 dB (BoXPol) and +8 dB (JuXPol) are applied to ZC in R(ZC + C). If R(KDP) is replaced with R(ZC) without calibration correction for measurements where R(KDP) < 8 mm h−1, the bias of R(KDP, ZC) is improved to −9% for BoXPol but degraded to −34% for JuXPol because of strong miscalibration. When the calibration corrections deduced in DAL1 are applied in R(KDP, ZC + C), the biases improve to +5% and +7%. To substitute R(AH) in areas lacking a reliable ΔΦDP segment, we used R(ZC + S), or if not enough Z(A) values were available to calculate S in a scan, R(ZC). This combined estimator had a bias of −6% against gauges for BoXPol and +2% for JuXPol. Using R(ZC + C) instead of uncalibrated reflectivity measurements during very light rain changed these biases to −5% and +7%, respectively, showing that the total contribution of scans that cannot produce a rough estimate of +S to total rainfall is very small. In contrast to this, the amount of R(ZC) used in the R(KDP, ZC) estimator is high enough to also compromise the combined estimator in the case of strong miscalibration, as for JuXPol.

Table 2.

Correlation, bias, and RMSD between daily rainfall accumulations as derived by different radar rainfall estimators and rain gauge observations. The rainfall estimators use observed extrapolated temperature assumptions and rain-only filtering. The best and second best scores are in boldface.

Table 2.

The overall performance in terms of QPE was best for estimators that combined R(AH) or R(KDP) with attenuation, PBB, and calibration-corrected reflectivity measurements. Similarly to the RFIT(ZC) estimator, the per-scan based Z(A) calibration correction applied in R(ZC + S) provided rain estimates apparently more accurately than R(ZC). We conclude that the R(AH,V) method yields better results than both R(ZH,V) and R(KDP) estimators for hourly precipitation sums and demonstrates a performance that is comparable to the R(KDP) method for daily accumulations or higher, if both methods are complemented with ZH-based estimators. Although scan-by-scan calibration using Z(A) was not sufficiently reliable to keep ZH calibrated within a 3-dB precision (unlike calibration corrections derived from accumulations of several rain events; see DAL1), the scan-by-scan calibration corrections through RFIT(ZC) and R(ZC + S) were precise enough to improve quantitative precipitation estimators over their uncorrected counterpart R(ZC).

6. Summary and conclusions

The R(A) method for rainfall estimation was tested on a large dataset at X band using two dual-polarization radars and 133 rain gauges, together with other algorithms utilizing ZH and KDP. If ΔΦDP along the propagation path is lower than 4°–6° or potentially contaminated with clutter, the R(A) estimate should be complemented by R(Z) estimates, provided that Z is corrected for possible radar miscalibration, attenuation, and partial beam blockage (PBB). As confirmed by the gauge validation, the Z bias associated with radar miscalibration, and PBB can be deduced and corrected with sufficient accuracy using the Z(A) relations and estimates of A obtained from the ZPHI method, as done in DAL1. The precision of the ZH bias estimate encompassing miscalibration and PBB appeared to be excellent when the Z and A data are accumulated over a long period of time. If the miscalibration-related bias is determined by accumulating the ZH + IAH and R(AH) [or ZH(AH)] data over all unblocked sectors in a single scan for real-time applications, the precision is still sufficient to improve QPE totals with hourly or higher accumulation times for the analyzed radar systems. The latter application has the advantage of compensating radar miscalibration in real time without the need for previous calculations/accumulations or additional data and is believed to also mitigate, to some extent, effects of DSD variability that occur in ZR relations (Hazenberg et al. 2011b).

Accumulated rainfall fields obtained from BoXPol, JuXPol, and the Offenthal C-band radar, which exhibit large differences in R(ZH) estimates due to miscalibration and PBB, could be merged into a nearly seamless composite when using R(AH) instead of R(ZH). Accumulated 5-month rainfall maps obtained from R(AH) showed that (apart from being less noisy than single scans and storm total accumulations, as shown by RAL14) the R(AH) algorithm is also less affected by ground clutter contamination than R(KDP). Adapting the ΦDP processing to avoid clutter contamination lowered the sensitivity of R(AH) and R(KDP) in light rain. The resulting biases can, however, be alleviated using R(ZH) in those cases. Therefore, combining R(AH) with R(ZH) is recommended, as well as using an appropriate ΦDP processing.

The comparison with gauges indicates that R(AH) complemented by R(ZH) in very light rain outperforms all other algorithms, including R(KDP) in terms of the correlation coefficient, mean bias, and RMSE for hourly accumulations. The statistical distributions of hourly totals in light–heavy rain of combined R(AH, ZC) or R(KDP, ZC) were also conveniently similar to those of rain gauge observations. Taking into account the temperature dependence of the parameters of the R(AH) relation at X band results in only very slight changes in the comparisons with the gauges; the R(AH) algorithm still outperforms other algorithms if the temperature dependence is ignored, even in the presence of melting layer contaminations. However, a melting layer detection algorithm [as described in Qi et al. (2013)] should still be used to avoid contamination from mixed-phase hydrometeors, as for the other rainfall estimators. We have not yet found evidence (at least for the examined dataset in the Bonn area), that an adaptation of the factor α to rain type in the ZPHI formula, for example, by using the self-consistency method by Bringi et al. (2001), would improve results. Using default α values for typical temperatures [e.g., α = 0.3 dB (°)−1 for 15°C] and standard AH(ZH) and R(AH) relations listed in Tables 3 and 4 of DAL1 does not compromise the R(AH) performance noticeably and makes the method simpler and more straightforward.

The QPE accuracy of the R(AH) algorithm evaluated by rain gauge observations appears to be very good, and the ZH calibration offsets of 2 dB for BoXPol and 8 dB for JuXPol, which were derived from ZH(AH) and ZHZDRKDP consistency in DAL1, are also confirmed by the gauge comparisons. Our results were in good agreement with the independent work described in Tabary et al. (2011) and Figueras i Ventura and Tabary (2013), where polarimetric rainfall estimators managed to outperform even well-calibrated radars and climatologically tuned ZR relations. The 5-month gauge validation and the experiences gained concerning long-term accumulations, ground clutter contamination, ΦDP processing, and synergy of ZH and ΦDP encourage the use of the R(A) technique for operational QPE monitoring and radar networking.

Acknowledgments

This research was carried out in the Hans Ertel Centre for Weather Research, a network of universities, research institutes, and the Deutscher Wetterdienst, funded by the BMVBS (Federal Ministry of Transport, Building and Urban Development). The work was also supported by the D5 project of TR32 “Patterns in Soil–Vegetation–Atmosphere Systems,” funded by the Deutsche Forschungsgemeinschaft (DFG). X-band weather radar data were provided by the ABC/J Geoverbund, TR32, and the TERENO project of the Helmholtz Association. The C-band weather radar of Offenthal was provided by the Deutscher Wetterdienst (DWD). The topography map that the DEM-derived PBB calculations are based on was obtained from NASA and the Shuttle Radar Topography Mission. Special thanks to Kai Mühlbauer, Martin Lennefer, Normen Hermes, and Heye Bogena for providing the X-band data and to Kathrin Wapler and Patrick Tracksdorf for providing the C-band radar data. Rain gauge data were provided by the Erftverband, Landesumweltamt Nordrhein-Westfalen, and the city of Bonn. Funding for A. Ryzhkov and P. Zhang was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–OU Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce, and by the U.S. National Weather Service, Federal Aviation Administration, and U.S. Department of Defense program for modernization of NEXRAD radars.

REFERENCES

  • Brandes, E. A., and Ikeda K. , 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 15411553, doi:10.1175/JAM2155.1.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Chandrasekar V. , Balakrishnan N. , and Zrnic D. S. , 1990: An examination of propagation effects in rainfall on polarimetric variables at microwave frequencies. J. Atmos. Oceanic Technol., 7, 829840, doi:10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Keenan T. D. , and Chandrasekar V. , 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, doi:10.1109/36.951081.

    • Search Google Scholar
    • Export Citation
  • Diederich, M., Ryzhkov A. , Simmer C. , Zhang P. , and Trömel S. , 2015: Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part I: Radar calibration and partial beam blockage estimation. J. Hydrometeor., 16, 487502, doi:10.1175/JHM-D-14-0066.1.

    • Search Google Scholar
    • Export Citation
  • Figueras i Ventura, J., and Tabary P. , 2013: The new French operational polarimetric radar rainfall rate product. J. Appl. Meteor. Climatol., 52, 18171835, doi:10.1175/JAMC-D-12-0179.1.

    • Search Google Scholar
    • Export Citation
  • Giangrande, S. E., McGraw R. , and Lei L. , 2013: An application of linear programming to polarimetric radar differential phase processing. J. Atmos. Oceanic Technol., 30, 17161729, doi:10.1175/JTECH-D-12-00147.1.

    • Search Google Scholar
    • Export Citation
  • Gourley, J. J., and Calvert C. M. , 2003: Automated detection of bright band using WSR-88D data. Wea. Forecasting, 18, 585598, doi:10.1175/1520-0434(2003)018<0585:ADOTBB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Leijnse H. , and Uijlenhoet R. , 2011a: Radar rainfall estimation of stratiform winter precipitation in the Belgian Ardennes. Water Resour. Res., 47, W02507, doi:10.1029/2010WR009068.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Yu N. , Boudevillain B. , Delrieu G. , and Uijlenhoet R. , 2011b: Scaling of raindrop size distributions and classification of radar reflectivity–rain rate relations in intense Mediterranean precipitation. J. Hydrol., 402, 179192, doi:10.1016/j.jhydrol.2011.01.015.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Torfs P. J. J. F. , Leijnse H. , Delrieu G. , and Uijlenhoet R. , 2013: Identification and uncertainty estimation of vertical reflectivity profiles using a Lagrangian approach to support quantitative precipitation measurements by weather radar. J. Geophys. Res. Atmos., 118, 10 24310 261, doi:10.1002/jgrd.50726.

    • Search Google Scholar
    • Export Citation
  • Maesaka, T., Iwanami K. , and Maki M. , 2012: Non-negative KDP estimation by monotone increasing ΦDP assumption below the melting layer. Extended Abstracts, Seventh European Conf. on Radar in Meteorology and Hydrology, Toulouse, France, ERAD, QPE-233. [Available online at www.meteo.fr/cic/meetings/2012/ERAD/extended_abs/QPE_233_ext_abs.pdf.]

  • Matrosov, S. Y., Kropfli R. A. , Reinking R. F. , and Martner B. E. , 1999: Prospects for measuring rainfall using propagation differential phase in X- and Ka-radar bands. J. Appl. Meteor., 38, 766776, doi:10.1175/1520-0450(1999)038<0766:PFMRUP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., Clark K. A. , Martner B. E. , and Tokay A. , 2002: X-band polarimetric radar measurements of rainfall. J. Appl. Meteor., 41, 941952, doi:10.1175/1520-0450(2002)041<0941:XBPRMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nespor, V., and Sevruk B. , 1999: Estimation of wind-induced error of rainfall gauge measurements using a numerical simulation. J. Atmos. Oceanic Technol., 16, 450464, doi:10.1175/1520-0426(1999)016<0450:EOWIEO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Otto, T., and Russchenberg H. W. J. , 2011: Estimation of specific differential phase and differential backscatter phase from polarimetric weather radar measurements of rain. IEEE Geosci. Remote Sens. Lett., 8, 988992, doi:10.1109/LGRS.2011.2145354.

    • Search Google Scholar
    • Export Citation
  • Pellarin, T., Delrieu G. , Saulnier G.-M. , Andrieu H. , Vignal B. , and Creutin J.-D. , 2002: Hydrologic visibility of weather radar systems operating in mountainous regions: Case study for the Ardèche catchment (France). J. Hydrometeor., 3, 539555, doi:10.1175/1525-7541(2002)003<0539:HVOWRS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Qi, Y., Zhang J. , Zhang P. , and Cao Q. , 2013: VPR correction of bright band effects in radar QPEs using polarimetric radar observations. J. Geophys. Res. Atmos.,118, 3627–3633, doi:10.1002/jgrd.50364.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24, 729744, doi:10.1175/JTECH2003.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., Diederich M. , Zhang P. , and Simmer C. , 2014: Utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage, and radar networking. J. Atmos. Oceanic Technol., 31, 599619, doi:10.1175/JTECH-D-13-00038.1.

    • Search Google Scholar
    • Export Citation
  • Schneebeli, M., and Berne A. , 2012: An extended Kalman filter framework for polarimetric X-band weather radar data processing. J. Atmos. Oceanic Technol., 29, 711730, doi:10.1175/JTECH-D-10-05053.1.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., Boumahmoud A.-A. , Andrieu H. , Thompson R. J. , Illingworth A. J. , Le Bouar E. , and Testud J. , 2011: Evaluation of two “integrated” polarimetric Quantitative Precipitation Estimation (QPE) algorithms at C-band. J. Hydrol., 405, 248260, doi:10.1016/j.jhydrol.2011.05.021.

    • Search Google Scholar
    • Export Citation
  • Testud, J., Le Bouar E. , Obligis E. , and Ali-Mehenni M. , 2000: The rain profiling algorithm applied to polarimetric weather radar. J. Atmos. Oceanic Technol., 17, 332356, doi:10.1175/1520-0426(2000)017<0332:TRPAAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Trömel, S., Kumjian M. , Ryzhkov A. , Simmer C. , and Diederich M. , 2013: Backscatter differential phase—Estimation and variability. J. Appl. Meteor. Climatol., 52, 25292548, doi:10.1175/JAMC-D-13-0124.1.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., and Chandrasekar V. , 2009: Algorithm for estimation of the specific differential phase. J. Atmos. Oceanic Technol., 26, 25652578, doi:10.1175/2009JTECHA1358.1.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., 1984: Factors affecting the precision of radar measurements of rain. Preprints, 22nd Radar Meteorology Conf., Zurich, Switzerland, Amer. Meteor. Soc., 251–256.

Save
  • Brandes, E. A., and Ikeda K. , 2004: Freezing-level estimation with polarimetric radar. J. Appl. Meteor., 43, 15411553, doi:10.1175/JAM2155.1.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Chandrasekar V. , Balakrishnan N. , and Zrnic D. S. , 1990: An examination of propagation effects in rainfall on polarimetric variables at microwave frequencies. J. Atmos. Oceanic Technol., 7, 829840, doi:10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bringi, V. N., Keenan T. D. , and Chandrasekar V. , 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, doi:10.1109/36.951081.

    • Search Google Scholar
    • Export Citation
  • Diederich, M., Ryzhkov A. , Simmer C. , Zhang P. , and Trömel S. , 2015: Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part I: Radar calibration and partial beam blockage estimation. J. Hydrometeor., 16, 487502, doi:10.1175/JHM-D-14-0066.1.

    • Search Google Scholar
    • Export Citation
  • Figueras i Ventura, J., and Tabary P. , 2013: The new French operational polarimetric radar rainfall rate product. J. Appl. Meteor. Climatol., 52, 18171835, doi:10.1175/JAMC-D-12-0179.1.

    • Search Google Scholar
    • Export Citation
  • Giangrande, S. E., McGraw R. , and Lei L. , 2013: An application of linear programming to polarimetric radar differential phase processing. J. Atmos. Oceanic Technol., 30, 17161729, doi:10.1175/JTECH-D-12-00147.1.

    • Search Google Scholar
    • Export Citation
  • Gourley, J. J., and Calvert C. M. , 2003: Automated detection of bright band using WSR-88D data. Wea. Forecasting, 18, 585598, doi:10.1175/1520-0434(2003)018<0585:ADOTBB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Leijnse H. , and Uijlenhoet R. , 2011a: Radar rainfall estimation of stratiform winter precipitation in the Belgian Ardennes. Water Resour. Res., 47, W02507, doi:10.1029/2010WR009068.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Yu N. , Boudevillain B. , Delrieu G. , and Uijlenhoet R. , 2011b: Scaling of raindrop size distributions and classification of radar reflectivity–rain rate relations in intense Mediterranean precipitation. J. Hydrol., 402, 179192, doi:10.1016/j.jhydrol.2011.01.015.

    • Search Google Scholar
    • Export Citation
  • Hazenberg, P., Torfs P. J. J. F. , Leijnse H. , Delrieu G. , and Uijlenhoet R. , 2013: Identification and uncertainty estimation of vertical reflectivity profiles using a Lagrangian approach to support quantitative precipitation measurements by weather radar. J. Geophys. Res. Atmos., 118, 10 24310 261, doi:10.1002/jgrd.50726.

    • Search Google Scholar
    • Export Citation
  • Maesaka, T., Iwanami K. , and Maki M. , 2012: Non-negative KDP estimation by monotone increasing ΦDP assumption below the melting layer. Extended Abstracts, Seventh European Conf. on Radar in Meteorology and Hydrology, Toulouse, France, ERAD, QPE-233. [Available online at www.meteo.fr/cic/meetings/2012/ERAD/extended_abs/QPE_233_ext_abs.pdf.]

  • Matrosov, S. Y., Kropfli R. A. , Reinking R. F. , and Martner B. E. , 1999: Prospects for measuring rainfall using propagation differential phase in X- and Ka-radar bands. J. Appl. Meteor., 38, 766776, doi:10.1175/1520-0450(1999)038<0766:PFMRUP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Matrosov, S. Y., Clark K. A. , Martner B. E. , and Tokay A. , 2002: X-band polarimetric radar measurements of rainfall. J. Appl. Meteor., 41, 941952, doi:10.1175/1520-0450(2002)041<0941:XBPRMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nespor, V., and Sevruk B. , 1999: Estimation of wind-induced error of rainfall gauge measurements using a numerical simulation. J. Atmos. Oceanic Technol., 16, 450464, doi:10.1175/1520-0426(1999)016<0450:EOWIEO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Otto, T., and Russchenberg H. W. J. , 2011: Estimation of specific differential phase and differential backscatter phase from polarimetric weather radar measurements of rain. IEEE Geosci. Remote Sens. Lett., 8, 988992, doi:10.1109/LGRS.2011.2145354.

    • Search Google Scholar
    • Export Citation
  • Pellarin, T., Delrieu G. , Saulnier G.-M. , Andrieu H. , Vignal B. , and Creutin J.-D. , 2002: Hydrologic visibility of weather radar systems operating in mountainous regions: Case study for the Ardèche catchment (France). J. Hydrometeor., 3, 539555, doi:10.1175/1525-7541(2002)003<0539:HVOWRS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Qi, Y., Zhang J. , Zhang P. , and Cao Q. , 2013: VPR correction of bright band effects in radar QPEs using polarimetric radar observations. J. Geophys. Res. Atmos.,118, 3627–3633, doi:10.1002/jgrd.50364.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24, 729744, doi:10.1175/JTECH2003.1.

    • Search Google Scholar
    • Export Citation
  • Ryzhkov, A., Diederich M. , Zhang P. , and Simmer C. , 2014: Utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage, and radar networking. J. Atmos. Oceanic Technol., 31, 599619, doi:10.1175/JTECH-D-13-00038.1.

    • Search Google Scholar
    • Export Citation
  • Schneebeli, M., and Berne A. , 2012: An extended Kalman filter framework for polarimetric X-band weather radar data processing. J. Atmos. Oceanic Technol., 29, 711730, doi:10.1175/JTECH-D-10-05053.1.

    • Search Google Scholar
    • Export Citation
  • Tabary, P., Boumahmoud A.-A. , Andrieu H. , Thompson R. J. , Illingworth A. J. , Le Bouar E. , and Testud J. , 2011: Evaluation of two “integrated” polarimetric Quantitative Precipitation Estimation (QPE) algorithms at C-band. J. Hydrol., 405, 248260, doi:10.1016/j.jhydrol.2011.05.021.

    • Search Google Scholar
    • Export Citation
  • Testud, J., Le Bouar E. , Obligis E. , and Ali-Mehenni M. , 2000: The rain profiling algorithm applied to polarimetric weather radar. J. Atmos. Oceanic Technol., 17, 332356, doi:10.1175/1520-0426(2000)017<0332:TRPAAT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Trömel, S., Kumjian M. , Ryzhkov A. , Simmer C. , and Diederich M. , 2013: Backscatter differential phase—Estimation and variability. J. Appl. Meteor. Climatol., 52, 25292548, doi:10.1175/JAMC-D-13-0124.1.

    • Search Google Scholar
    • Export Citation
  • Wang, Y., and Chandrasekar V. , 2009: Algorithm for estimation of the specific differential phase. J. Atmos. Oceanic Technol., 26, 25652578, doi:10.1175/2009JTECHA1358.1.

    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., 1984: Factors affecting the precision of radar measurements of rain. Preprints, 22nd Radar Meteorology Conf., Zurich, Switzerland, Amer. Meteor. Soc., 251–256.

  • Fig. 1.

    (a) Radar reflectivity bias of BoXPol caused by PBB, as simulated with the use of a DEM. (b) Radar reflectivity bias caused by the combined effects of radar miscalibration and PBB, as estimated by calculating BA along uninterrupted ZPHI segments. Locations of the rain gauges are marked by dots.

  • Fig. 2.

    Maps of 4-h rainfall totals at 1000–1300 UTC 22 Jun 2011. Shown are estimates of R(ZH + IAH) from the (a) 0.5° elevation scan of JuXPol, (b) 1.5° elevation of BoXPol, and (c) 0.5° elevation of Offenthal radars; (d)–(f) the corresponding scans using R(AH); and (g),(h) a composite of these scans composed of values measured at the lowest altitude at each pixel.

  • Fig. 3.

    Accumulated BoXPol rainfall estimates from May to September 2011 computed by six of the algorithms described in section 3, applied to 1.5° elevation PPI scans.

  • Fig. 4.

    Accumulated rainfall estimates from six of the algorithms described in section 3 applied to the 1.5° elevation scan of BoXPol from May to September 2011. Only observations during which both BoXPol and JuXPol were operational were included in the accumulations.

  • Fig. 5.

    Accumulated rainfall estimates from six of the algorithms described in section 3 applied to the 1.1° elevation scan of JuXPol from May to September 2011. Only observations during which both BoXPol and JuXPol were operational were included in the accumulations.

  • Fig. 6.

    Box–whisker plots of hourly rain totals from gauge observations and different radar rainfall estimators from May to September 2011. The data are separated into three intervals of hourly gauge totals ranging between 0.03 and 1.5 mm, 1.5 and 5 mm, or above 5 mm (highest sum measured by gauges was 59 mm). The variable S is the percentage of total rainfall that each interval contains, and N is the number of measurements in the interval.

  • Fig. 7.

    Correlation coefficient, mean bias, and RMSD as functions of range from the radar for six radar rainfall estimators and individual rain gauges. All values are from May to September 2011 and are restricted to observations for which estimates of the temperature in a ZPHI beam segment did not drop below 6°C. Different degrees of PBB are visualized by symbols (dots for BB < 2 dB, crosses for 2 > BB > 5 dB, asterisks for BB = 8 dB, and diamonds for BB = 19 dB).

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1220 430 56
PDF Downloads 559 111 12