Validation of composite polarimetric parameters and rainfall rates from an X-band dual-polarization radar network in the Tokyo metropolitan area

This paper aims to determine the accuracy of composite polarimetric variables, horizontal polarization (ZH), differential reflectivity (ZDR), and specific differential phase shift (KDP), and rainfall rates derived from a network of four Xband polarimetric radar stations during localized convective precipitation over Tokyo on 28 September 2010 by comparison with data from a Joss–Waldvogel disdrometer and a surface rain gauge network. The four X-band polarimetric radars were complementary with respect to signal extinction, and they yielded composite maps of the polarimetric radar parameters and rainfall rates. The composite maps were validated by cross-comparison of data from the four individual radar stations, and by groundtruthing with surface observations. The raindrop size distribution (median volume diameter and normalized number concentration) was estimated from the composite maps of polarimetric parameters, and validated by the disdrometer data. We found that composite polarimetric radar parameters can provide useful information, not only for hydrological applications, but also for microphysical analysis.


INTRODUCTION
Dual-polarized weather radar provides valuable data for hydrological and meteorological studies, including quantitative precipitation estimation (QPE), raindrop size distributions (DSD), hydrometeor types, and information regarding the microphysical processes that take place within precipitation systems (Zrnić and Ryzhkov 1999;Gorgucci et al., 2002).QPE with high temporal and spatial resolution is especially important if we are to improve the accuracy and efficacy of nowcasting, water resource management, and warning systems for urban disasters.
QPE using X-band (wavelength: 3 cm) dual-polarized radars has received recent attention because it has several advantages compared to the long wavelength radars.One of the advantages is that the specific differential phase (K DP ) is much larger in the X-band than at longer wavelengths for a given rainfall rate (Matrosov et al., 1999;Chandrasekar et al., 2002;Maki et al., 2005b); this is advantageous when attempting to accurately measure rainfall rates during lowintensity events.However, a significant disadvantage at X-band wavelengths is the signal extinction area, which is defined as the area where rainfall attenuation causes the backscattered signal to fall below the receiver noise level.In a signal extinction area the radar cannot detect precipitation, and because such signal extinction is common in the X-band, adequate countermeasures are required in meteorological and hydrological applications of X-band polarimetric radar.Maki et al. (2012) proposed the use of supplementary Cband conventional weather radar to fill the signal extinction area.An alternative countermeasure involves the radar network itself.An X-band polarimetric radar network was developed by the engineering center for Collaborative Adaptive Sensing of the Atmosphere (CASA) in Oklahoma to study severe storms (Junyent andChandrasekar, 2009, 2010).The National Research Institute for Earth Science and Disaster Prevention (NIED) implemented this X-band polarimetric radar network (X-NET) in the Tokyo metropolitan area to study severe storms, and to develop a prediction system for meteorological disasters in urban areas (Maki et al., 2008).NIED successfully used X-NET to monitor, in real time, a heavy rainfall event that occurred in Zoshigaya, Tokyo in 2008 (Kato and Maki, 2009;Hirano and Maki, 2010).The potential impacts of urban flash floods, together with the success of the X-NET observations and previous research into QPE using X-band polarimetric radar at NIED (e.g., Park et al., 2005;Maki et al., 2005aMaki et al., , 2005b)), encouraged the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) to begin construction of operational X-band polarimetric radars across urban areas in Japan.
Preliminary results of the validation of composite rainfall maps derived from MLIT X-band radar networks with rain gauge data showed that this approach achieves better results than conventional C-band radar QPE (Tsuchiya, 2011;personal communications).However, detailed validation analyses have not been completed on the polarimetric radar variables that are essential for microphysical studies of precipitation.
The present study aims to answer two questions: 1. How accurate is a composite map of polarimetric radar parameters? 2. Can such maps be used for the retrieval of precipitation parameters?In the following sections, an algorithm used to generate composite maps of the polarimetric variables (Z H , Z DR , and K DP ) and rainfall intensity (R) using the X-NET data deployed by NIED and MLIT in the Tokyo Metropolitan Area is described, and the composite maps are evaluated by comparison with scattering simulations derived from ground-based disdrometer data and rain gauge data.In addition, the composite DSD parameters, median volume diameter (D 0 ), and normalized number concentration (log 10 N W ), were retrieved from the X-band polarimetric radar network and preliminary results are presented.

Observations
A localized heavy rainfall event over the suburbs of Tokyo on 28 September, 2010, associated with a fast-moving cold front that passed through the Kanto region, was observed by four X-band polarimetric radars located in Ebina (EBN), Kisarazu (KSR), Saitama (SAT), and Yokohama (SYK).Ground truth data was provided by an impact type Joss-Waldvogel disdrometer (JWD) located between the SAT and SYK radars, and 10 rain gauges operated by the Tokyo Metropolitan Government. Figure 1 shows the locations of the radar stations, JWD, and rain gauges.Specifications and descriptions of radars at SAT and SYK, operated by MLIT, are given in Maesaka et al. (2011), and those at EBN and KSR, operated by NIED, are given in Maki et al. (2008).
The radar variables derived from the four radars were Z H , Z DR , the total differential phase (Φ DP ), and the copolar correlation coefficient (ρ HV ), as well as Doppler velocity (V D ), and spectral width (W S ).The radars used PPI scans with different elevation angles.EBN and KSR used 10-tilt PPI scans to obtain 3D data every 5 minutes, and nearsurface polarimetric variables and the rainfall rate were estimated every 5 minutes from a 1.7° PPI scan.SAT and SYK used 12-tilt PPI scans every 5 minute, and near-surface polarimetric variables and the rainfall rate were estimated every minute.To obtain the radar variables every minute at SAT and SYK, PPI scans at two low elevation angles (1.4°a nd 2.4° at SAT; 1.7° and 2.6° at SYK) were used in a staggered way: 12-tilt scans were arranged such that either lower elevation angle (i.e., 1.4° and 2.4° for SAT) should scan the lower atmosphere every minute.

Processing of disdrometer measurements
The number of drops counted by the JWD was initially processed using the quality-control procedures described by Kim et al. (2010).Drop spectra were also corrected for the dead-time (Sheppard and Joe, 1994).To derive the polarimetric variables, T-matrix scattering simulations were performed using these quality-controlled drop spectra under the following conditions: 1) a temperature of 15℃; 2) an elevation angle of 0°; 3) the mean axis ratios (Thurai et al., 2007); and 4) a Gaussian canting angle distribution with a mean of 0° and standard deviation of 7°.

Processing of radar data
Prior to data analysis, noise, ground clutter, and nonmeteorological echoes were removed (Maesaka et al., 2011).Then, Z H , Z DR , Φ DP , and K DP were derived using the following procedure: 1) filtering of the total differential phase (Ψ DP ) and estimation of K DP , then 2) bias estimation, and 3) attenuation correction for Z H and Z DR , 4) calculation of the radio wave extinction area, 5) estimation of rainfall intensity, and 6) interpolation and compositing of variables.
To separate the scattering differential phase (δ) from the Ψ DP profiles, the range profiles of the Ψ DP were iteratively filtered in the range using the finite-impulse response (FIR) filter, and K DP was computed using the procedures described by Maesaka et al. (2011).
Z H and Z DR measured at X-band wavelengths are subject to rainfall attenuation, and it is important that this be corrected.We used the shifted self-consistent method (SSCM; Kim et al., 2010), which considers variability in the optimum coefficient α (A H = αK DP ) along the radar slantrange.
X-band weather radar sometimes misses precipitation echoes behind heavy rainfall due to severe rainfall attenuation in the signal extinction area.We identified the signal extinction area using the method proposed by Iwanami et al. (2007).
Rainfall intensity was derived from the composite estimator of the relationships R − K DP and R − Z H : where R, Z H , and K DP are in mm h −1 , mm 6 m −3 , and °km −1 , respectively.The coefficients and exponents in Equation 1were derived from scattering simulations under the conditions described in Section 2b using quality-controlled drop spectra collected during the analyzed storm that passed over the JWD site.The threshold value of 0.3 km −1 for K DP is the standard error of K DP calculated by Park et al. (2005), and confirmed by Kim et al. (2010).The estimated rainfall rates and the polarimetric variables from each radar were composited into a Cartesian coordinate system with a horizontal grid interval of 0.5 km, and we used a modified Cressman-type weighting function that applied an altitudinal weighting, with the observations from lower altitudes being more heavily weighted (Maesaka et al., 2011).

RESULTS
A convective precipitation line associated with a cold front passed over the observation area between 1100 and 1400 LST on 28 September, 2010.The core region of the convective system passed over the disdrometer site.Figure 2 shows PPI images of attenuation corrected Z H (a-d) and Z DR (e-h), measured K DP (i-l), and radar-rainfall intensity R (m-p) from the four radars at 1140 LST when severe attenuation occurred.The curved high reflectivity region (dotted line) ≥ 40 dBZ, which moved northeastwards, is located over the disdrometer.In general, the reflectivity patterns from each radar image were similar.However, due to the strong rainfall attenuation, signal extinction (gray area) occurred on the north side of the rainband for EBN, KSR, and SYK, but on the south side of the rainband for SAT.The signal extinction area was calculated as 13.8%, 8.2%, 22.5%, and 32.6% for EBN, KSR, SAT, and SYK, respectively.The Z DR from the four radars followed a similar pattern.The boundary patterns of high K DP near the signal extinction area of each radar are quite different, especially from EBN.An abrupt decrease in K DP values, behind a large K DP area, with increasing distance from the radar in Figure 2i is the result of a decreasing signal to noise ratio (SNR) (K DP filtered in low SNR area) caused by severe attenuation.Also notable is the K DP noise in the weak rainfall region of KSR.The speckled K DP south of the strong rainband (close to the radar station) was observed by KSR, but not by the other radars.This speckled K DP could lead to an over attenuation correction of Z H , and thus Z DR , and consequent over-estimation of the rainfall rate.
Rainfall intensity (Figure 2m-2p) was estimated using attenuation corrected Z H and K DP .The spatial variation in R is similar to that in K DP in the strong rainband region, and similar to Z H in the weak rainfall region (<10 mm h −1 ).The higher rainfall rates (≥80 mm h −1 ) were located around the disdrometer site for all radars.R was also affected by severe attenuation, and signal extinction occurred for all radars.Figure 2 demonstrates that observation by single radar is insufficient, and that the use of multiple radars is essential for rainfall measurements.
The areal composite of the attenuation corrected Z H , Z DR , K DP , and R are shown in Figure 3.The extinction area was successfully compensated for (signal extinction 0%) by the other radars in the overlapping observation area, and the precipitation echo was completely identified.In the core of the precipitation echo over the disdrometer, Z H and Z DR were >55 dBZ and 2 dB, respectively.A high K DP of 2.5-7.0 °km −1 was observed in the core of the echo, and the pattern of K DP was consistent with that of the rainfall rate (Figure 3d).The value of R in the core of the precipitation echo was estimated to be 60-80 mm h −1 .
Comparisons of composite map data and Z H , Z DR , K DP , and R from the four radars, with data calculated from the JWD are shown in Figure 4.The radar data were averaged within a 1 km radius of the JWD site.In addition, a five minute moving average was calculated for the simulated values using the JWD data, and for radars SAT and SYK, because the PPI scan at EBN and KSR was repeated every five minutes.The four variables from each radar, and the composite values, show good agreement with the values derived from the disdrometer.The corresponding slopes (correlation coefficients) of composite data for the four variables Z H , Z DR , K DP , and R were 1.03 (0.92), 1.08 (0.88), 1.07 (0.94), and 1.04 (0.90), respectively.
The accuracy of the polarimetric parameters and rainfall rate measured and composited by the four radars, compared with those calculated from disdrometer DSD data, was quantified by calculating the normalized error (NE) and normalized bias (NB) (Table I).Radar SYK showed the best agreement with the disdrometer data, and corresponding NE (NB) of Z H , Z DR , K DP , and R were 3.5% (2.0%), 16.8% (3.3%), 16.2% (−2.4%), and 12.8% (−1.4%), respectively.In contrast, radar KSR had poor NE and NB for all variables.
In particular, Z DR was over-estimated, with a corresponding NE and NB of 33.9% and 33.7%, respectively; conversely the Z DR of EBN was under-estimated, with a corresponding NE and NB of 26.3% and −12.4%, respectively.This overestimation (under-estimation) of the Z H and Z DR at KSR (EBN) was caused by noise (excessive filtering) in K DP as explained previously (Figure 2).The composite Z H , Z DR , K DP , and R produced NE (NB) values of 6.0% (3.8%), 19.9% (14.0%), 23.9% (−2.2%), and 21.8% (1.4%), respectively.These results are within the ranges quoted in previous studies, despite the relatively poor results from KSR (e.g., Kim et al. (2010) reported an NE of 5.3% and 17.2% for Z H and Z DR , respectively, while Park et al. (2005) reported an NE of 21.1% for R, and Seliga et al. (1981) an NE of 14%-26% for R).
To further examine the accuracy of the radar composite rainfall estimates, we compared the radar derived rainfall amounts with totals from 10 rain gauges for the period between 1100 and 1300 LST (Figure 5).The rainband passed over the disdrometer and the 10 rain gauges during this period, and more than 30 mm of rainfall was recorded at the center of the rainband (Figure 5a).The composite QPE tended to underestimate the rainfall amount by around 20% compared with the rain gauges (Figure 5b).Matrosov et al. (2005) and Kato et al. (2009) report similar underestimates, and this may be caused by the difference in temporal sampling volume between the radars and the rain gauges.Other possible explanations include assumptions such as the axis ratio, canting angle etc. for the R-K DP relationship that was derived from the scattering simulation, and the sliding window interval used for estimation of K DP from Φ DP .
The composite map of polarimetric radar parameters can be used to retrieve rain DSD. Figure 6 shows the retrieved rain DSD parameters, D 0 and log 10 N w , that were calculated using the algorithm proposed by Kim et al. (2010).The validation of D 0 and log 10 N w were accomplished by comparison with simulated DSD parameters from the JWD data (Figure 6c, 6d).The comparison showed good agreement; for D 0 the corresponding NE and NB were 13% and 7%, respectively, and for log 10 N w they were 9.2% and −3.3%, respectively.Successive rain DSD parameters, without the occurrence of signal extinction areas, can provide invaluable information for many meteorological applications, such as the analysis of microphysical properties, quantitative estimates of precipitation, and the initialization and verification of cloud models.

SUMMARY AND CONCLUSION
This paper presents the results of the validation of a composite map of four X-band polarimetric radar parameters and rainfall amounts using data from a surface disdrometer and a rain gauge network.We analyzed a locally heavy rainfall event that occurred over the suburbs of Tokyo on 28 September, 2010.Due to severe rainfall attenuation, all four X-band radars suffered a loss of received signal power (signal extinction).The extinction area was compensated for by the multiple radar observations and validation with a disdrometer.
A comparison between radar-composited and disdrometer-simulated data revealed good agreement on the values of Z H , Z DR , K DP , and rain rate R. The normalized error (NE) associated with the composite Z H , Z DR , K DP , and R values  was 6.0%, 19.9%, 23.9%, and 21.8%, respectively, and the normalized bias (NB) was 3.8%, 14%, −2.2%, and 1.4%, respectively.The correlation coefficients of these parameters were 0.92, 0.88, 0.94, and 0.90, respectively.The statistical errors associated with these parameters were acceptable for most meteorological and hydrological applications.From the inter-comparisons of the four radars, Z H and Z DR from STA and SYK showed better results when compared with the disdrometer, but K DP and R showed similarly good results from all stations.Comparing the composite radar rainfall map with the surface rain gauge data showed that the composite QPE underestimated the rainfall amount by around 20%.The possible reasons for this underestimation were briefly considered in the results section, but further research is required.
We conclude that a network of radars is essential when X-band polarimetric radar is used to observe heavy rainfall events.Composite polarimetric radar parameters can provide useful information, not only for hydrological applications, but also for microphysical studies.

Figure 4 .
Figure 4. Scatter plots of polarimetric variables and rainfall rate obtained from radar observations versus the simulated values (JWD) over the disdrometer site from 1100 to 1300 LST on 28 September, 2010: (a) Z H , (b) Z DR , (c) K DP , and (d) R. Gray dots are data from the composite map of the four radars.COM = composite data.

Figure 6 .
Figure 6.(a) Median volume diameter (D 0 ), and (b) normalized number concentration (log 10 N W ) from the composite radar data at 1140 LST on 28 September, 2010.Comparisons of these variables over the disdrometer site are shown in (c) and (d).The block dots (•) denote mean values from the composite radar data within a 1 km radius of the disdrometer.

Figure 5 .
Figure 5. (a) Accumulated rainfall amounts estimated from composite radar observations, and (b) comparison of rainfall intensity obtained from rain gauges (R_RG) and composite radar observations (R_COM) from 1100 to 1300 LST on 28 September, 2010.

Table I .
The normalized error (NE) and normalized bias (NB) percentages associated with values of Z H , Z DR , K DP , and R from the four radar stations and in the composite data (COM)