WU Chongand LIU LipingState Key Laboratory of Severe Weather,Chinese Academy of Meteorological Science,Beijing 100081

2Chengdu University of Information Technology,Chengdu 610225

1.Introduction

Phased-array radar(PAR)for meteorological observation with agile electronic beam steering has the capability of instantaneously and dynamically controlling beam position on a pulse-by-pulse basis,which allows a single radar to perform multiple functions,such as tracking multiple storms or weather and aviation surveillance.Many convective storms and tornadoes evolve on time scales shorter than those resolved by Weather Surveillance Radar-1988 Doppler(WSR-88D)in the USA and China’s New Generation Weather Radar(CINRAD).This beam agility makes PAR an ideal platform for performing rapid scan to catch severe weather phenomena such as microbursts,supercells and squall lines.The phased-array,f i xed-site,S-band Doppler radar in the National Weather Radar Testbed(NWRT)in Norman,Oklahoma,has been available to research communities since September 2003.Moreover,recent experiments have demonstrated that a better and more precise characterization of fast-evolving weather systems could be obtained with the fast updates provided by the NWRT PAR,compared to the WSR-88D(Zrnic′ et al.,2007;Heinselman et al.,2008).In 2009,X-band PAR(MWR-05XP)was used in the Second Veri fication of the Origins of Rotation in Tornadoes Experiment(VORTEX2),cooperated with mobile X-band Doppler radar and W-band cloud radar to observe the detailed structure of storms(Bluestein et al.,2010;Wurman et al.,2012).

In China,an S-band PAR,which scans electronically in elevation while scanning mechanically in azimuth,was built based on a military PAR.The S-band PAR transmits radar waves with wide beam width(about 9°in the vertical direction and 1.6°in the horizontal direction),and receives four beams simultaneously with four receivers.The S-band PAR scansfourelevationanglessimultaneouslybecauseithasfour receivers.The re fl ectivity structures of convective precipitation were compared with S-band operational radar(SA)at a distance of 50 km,and a mobile X-band Doppler radar at the same site of the PAR(Zhang and Liu,2011).

To test the expected advantages,explore and assess the utility of the phased-array technology in meteorology,a fi rst prototype airborne X-band planar PAR(XPAR)scanning electronically in both elevation and azimuth directions was built from a navigation phase-array radar in China.The XPAR will be used to observe the ref l ectivity and radial velocity of precipitation systems for research purposes.The radar should be calibrated carefully before conducting any quantitativestudy;for example,forQuantitativePrecipitation Estimate(QPE).Before the XPAR is installed on the aircraft,it was tested for precipitation observations on the ground,cooperated with classical X-band mobile Doppler radar(XDR)at the same site and the SA.The f i eld experiment was conducted in July and August 2012 to examine the observation capability of the XPAR,its calibration,data quality,and to improve its data processor.

In this study,the XDR at the same site as the XPAR and the SA in Nanjing were used to examine the ref l ectivity and radial velocity biases,the ref l ectivity sensitivity,and their horizontal and vertical structures by the XPAR.The cross comparisons of ref l ectivity with varying pulse width and scanning strategy were analyzed.

2.Characteristics of the radars and the f i eld experiment

The XPAR and XDR at the same site(31.9°N,119.2°E;54.6 m),and the SA,51 km away from the XPAR(32.2°N,118.7°E;138.8 m),conducted simultaneous observations from July to August 2012.

In order to test the different operating modes,the volume plan position indicator scan(VPPI)and range height indicator(VRHI)scan were set with varying pulse repetition frequency(PRF),the number of range samples and pulse width.The main technological characteristics and operating work modes are listed in Table 1.The XPAR antenna was f i xed and broadside pointed at the direction of 199°,and scanned electronically in the azimuth and elevation directions.Steeringthebeamby±37°fromtheaxis(normal)ofaplanararray was set to limit the effect of beam broadening.The scan increment in the elevation angle was set to an angle of 0.5°or 1°from 0.5°–8°with azimuthal resolution of 0.32°.The volumetric update time(from near the surface up to the highest elevation)was 7–12 min to gather enough independent samples to improve the sensitivity and to produce meaningful estimates of Doppler velocity.It takes 1 min to complete 240 beams in azimuth,which is two times longer than that by the SA.The XDR scanned mechanically in azimuth and elevation angles,and performed a volume scan with 11 elevation angles once every 5.5 min.The observation mode is similar to that used in the SA.The SA observed the precipitation with the operating mode of VCP21 with nine elevation angles once every 6 min.It takes 6 min to complete the full set of volume scans from elevation angles of 0.5°to 19.5°.The SA was calibrated in the radar company before it was used in operational observation.In operational observation,calibration was conducted at each volume scan,beginning with the inner calibration system.The transmitted peak power,sensitivity of receiver,noise f i gure and dynamic range were measured and ref l ectivity and Doppler velocity were calibrated by a frequency synthesizer,digital attenuator,noise generator and power sensor.The ref l ectivity observed by the SA radar is considered as“truth”and used to examine the bias of XPAR and XDR.The XDR was only calibrated in the company before operation;no calibration took place in each volume scan.

The database and operating modes are listed in Table 2.The four operating modes were tested in the f i eld experiment.Two convective precipitation cases were observed by the XPAR on 13 July and 2 August 2012 in the different operating modes.The XPAR worked in a larger pulse width and range compression in the 2 August case.

3.PRA radar equation and XDR data remap

The radar equation for classical meteorological radar can be expressed by(Probert-Jones,1962)

where Z(mm6m?3)is ref l ectivity,Ptis transmitter output power,Pris receiver input power,G is the antenna gain,λis wavelength,Risrangetotarget,θand?arehalfpowerbeam width;|K|2=|(m2?1)/(m2+1)|,m is complete refractionindex,c=3×108m s?1,andτis pulse width.

Table 1.Characteristics of the XPAR,XDR and SA.

Table 2.The database and operating modes.

The antenna gain and beam width of the PAR varies with the angle between the beam direction and axis normal to the array.The PAR with solid-state transmitters compresses the received wide band long pulse for achieving the desired range resolution and increasing the signal-to-noise ratio.According to Knorr(2007),letαbe the angle of the antenna beam with respect to the normal of the array face;θ0,?0the beam width in orthogonal planes(y?z and x?y planes)when the beam is pointed in the broadside direction;Gt0and Gr0the transmitting and receiving gains;and θu,?uthe beam widths on the orthogonal phase planes.In any arbitrary direction,the transmitting and receiving gains(Gt,Gr)and beam widths(θ,?)are expressed as:

The pulse compress function produces gain of Gp.The radar equation for PAR can be expressed by

Equation(6)was used to calculate the ref l ectivity.

The XPAR’s maximum squinted angles in the azimuth and elevation directions were 37°and 8°,respectively.The beam width in the azimuth direction increases from 3.7°to 4.7°,while the beam width in the elevation direction increases from 2.5°to 2.53°.The XDR’s beam width is 1.5°.In this case,one beam of XPAR could include several beams of XDR.In the broadening direction,one beam of XPAR is equivalent to three beams of XDR;at the maximum squinted angle,the number of equivalent beams increases to f i ve.The ref l ectivity data from the XDR in the same object volume of XPAR are averaged by

Here,Ziis re fl ectivity observed by XDR,Giis the antenna gain of XPAR,and N is the number of included beams.The Z is compared with the re fl ectivity by XPAR in the same gate.

4.Data processing and analysis scheme

For quantitative comparison,differences between the observation mode and radar locations among the three radars shouldbeconsidered.TheSAradarperformedvolumescans,with nine elevation angles,once every 6 min.The SA radar raw data were interpolated onto the gates of XPAR and XDR,and the matched ref l ectivity was used to analyze the ref l ectivity bias between SA and XPAR or XDR.Meanwhile,the ref l ectivity and velocity by XPAR and XDR in the same positions were compared to analyze the differences between XPAR and XDR.

To balance the spatial differences between XPAR and XDR due to the wide beam width of XPAR,and simplify the comparison,the ref l ectivity of XDR was averaged among the azimuthal direction in the beam width of XPAR to obtain the ref l ectivity data with similar observation space by using Eqs.(6)and(7).The pairs of ref l ectivity were used to examine the effect of wide beam width on the observed ref l ectivity biases and correlation.

4.1.Comparison of ref l ectivity structures by XPAR,SA and XDR

The plan position indicator(PPI)and vertical cross sections observed by XDR and interpolated from SA were chosen to examine the echo patterns observed by XPAR.The variations of ref l ectivity with range and azimuth are compared between both radars to examine the horizontal locations of precipitation observed by XPAR.The averaged vertical prof i les of ref l ectivity are also compared to examine the vertical locations of XPAR.

4.2.Sensitivity analysis

The ref l ectivity values at the same range in different azimuth and elevation angles were used to calculate the minimum ref l ectivity in different ranges.The variations of minimum ref l ectivity with range were used to calculate the ref l ec-tivity sensitivity for the three kinds of radars.

4.3.Ref l ectivity and velocity biases between XPAR and SA,and the difference between XPAR and XDR

The point-to-point matched re fl ectivity between XPAR and SA,and XPAR and XDR,were used to examine the refl ectivity bias or difference.To eliminate the effects of attenuation on re fl ectivity of XPAR and XDR,the pixels along the beam within 10 km from the edge of precipitation near the radar were chosen to analyze the re fl ectivity bias between SA and XPAR,and SA and XDR.The pairs of velocity and spectral width data observed by XPAR and XDR were compared to examine the XPAR velocity and spectral width.The average error(D),standard deviation(σ)and correlation coef fi cient(ρ)were calculated according to the following equations:

Here,Xiand Yiare pairs of re fl ectivity or radial velocity observed by two types of radars;X,Y are the average values of XiandYi;and n is the number of data pairs.

The probability distributions of re fl ectivity for SA and XPAR,and XDR and XPAR,were produced to analyze the re fl ectivity distribution and biases.

5.Observed ref l ectivity comparison between XPAR,XDR and SA

5.1.Ref l ectivity structures

The PPI for ref l ectivity at the elevation angles of 1.0°,3.0°and 5.0°at 1515 LST 2 August 2012 observed by XDR,SA and XPAR are shown in Fig.1.The PPI of velocity by XPAR and XDR are shown in Fig.2.It should be noted that the PPI for SA is interpolated from volume scanning data.We can see that the three types of radar were able to capture similar ref l ectivity and velocity structures at the elevation angles of 1.0°and 3.0°;the precipitation positions and strong ref l ectivity centers matched very well.The precipitation structures were smooth and their ref l ectivity values were underestimated by XPAR.The velocity spatial distributions observed by XPAR and XDR were also similar.These results suggested that the steering beam in the horizontal direction of the XPAR was correct.It should be noted that the spectral width values(not shown)by XPAR were larger than those by XDR and SA,possibly due to the wide beam width.

Fig.1.PPI of ref l ectivity by the XPAR,XDR and SA radar for elevation angles of 1°,3° and 5°at 1515 LST 2 August 2012.(a–c)Observed by the XPAR at 1°,3° and 5°,respectively;(d–f)are the corresponding PPI observed by the XDR;(g–i)are for the SA radar.The azimuths with+/?10°normal to the antenna plane are marked with a dotted line.The circles are in intervals of 15 km.The maximum range is 75 km.

Fig.2.The same as Fig.1,but for radial velocity by XPAR and XDR.

Fig.3.Vertical cross sections of(a)ref l ectivity and(b)velocity by XPAR at 1553 LST with the VRHI mode and those(c,d)by XDR at 1602 LST 2 August 2012.

The cross sections of ref l ectivity and velocity by XPAR with the VRHI mode and those by XDR with conventional volume scanning are shown in Fig.3.We can see that the XPAR was able to capture the detailed vertical structures of precipitation with the VRHI mode.XDR could not conduct the VRHI mode.

In order to analyze the differences of ref l ectivity in detail along the range direction and avoid the effects of azimuth position error on the observation,the variation of ref l ectivity with range was produced by averaging the beams within 10°in the azimuthal direction to eliminate the effects of antenna azimuthal direction error and difference of beam width between XDR and XPAR.Figure 4 shows the ref l ectivity and velocity variations with range for azimuth angles between 194°and 204°at different elevation angles observed by the XPAR and XDR.The ref l ectivity variations with range observed by XPAR and XDR were similar for all of the elevation angles;however,the averaged ref l ectivity difference was about 6.31 dB,and the bias of range position was about 3–5 km.For the velocity data in elevation angles from 2°–4°,in most of the range,the velocity values and variations with ranges observed by both of radars matched very well.However,the XPAR observed the severe sharp variations in the area of weak ref l ectivity at a range of 30 km for an elevation of 1°.The sharp variations are possibly due to the low signal-to-noise ratio(SNR).A higher percentage of the Doppler velocity values at an elevation angle of 1°and within 40 km from the radar observed by the XPAR were reported close to zero than that by XDR.This is possibility due to the ground clutter effects on velocity observed by the XPAR with wide width beam.

The ref l ectivity variations in the azimuthal direction were compared to analyze the smooth effect due to the wide beam of XPAR.The ref l ectivity variations in azimuthal directions for the ranges of 42–45 km and 60–63 km observed by both of the radars are shown in Fig.5.The precipitation structures were smoothed by the XPAR.Besides the ref l ectivity systematic bias,the strong re fl ectivity values were underestimated and the weak re fl ectivity values were overestimated.Comparison with the variation in range direction and the variations in azimuthal direction by both of the radars had obvious differences due to the different beam widths.

Fig.4.Ref l ectivity prof i les along the range direction for azimuths between 194° and 204° at elevation angles of(a)1°,(b)2°,(c)3° and(d)4° by the XPAR and XDR;(e–h)are the corresponding velocity prof i les.

Fig.5.Ref l ectivity variation along the azimuthal direction in the range of(a)42–45 km and(b)60–63 km.

The PPI of re fl ectivity observed by the XPAR and XDR at 1410 LST 13 July 2012 in different work modes are shown in Fig.6.In this case,the XPAR could also observe a similar precipitation pattern with that by the XDR.However,at distances beyond 60 km for an elevation of 4°and 45 km for an elevation of 6°,the XPAR could not detect weak echo due to the radar operating mode without pulse compression.We fi nd that the effect of attenuation on the re fl ectivity far from the radar site was obvious by comparing the re fl ectivity patterns by SA and both of the X-band radars.

The cross sections for re fl ectivity by XPAR,XDR and SA along azimuth angles of 199°and 179°are shown in Fig.7.The same as the PPI,the XPRA was able to capture similar vertical structures of re fl ectivity as the XDR and SA.However,the echo top was underestimated by the XPAR due to the wide beam width and low sensitivity.The XPAR could also capture a similar pattern of velocity vertical structures as XDR(not shown).These results examined the steering capability of the XPAR in the elevation direction.The results for the case on 13 July 2012(not shown)were consistent with those on 2 August 2012.

5.2.Radar sensitivity analysis

The XPAR will be installed in an airplane to observe the precipitation ref l ectivity and Doppler velocity to estimate the intensity and wind structures.It is import to know the radar sensitivity to design the observation targets and to evaluate the gain of pulse compression.The variations of minimum ref l ectivity observed by the three kinds of radars are analyzed to compare the radar sensitivities.The minimum ref l ectivity observed by XPAR is 2.1 dB higher than that by XDR on 2 August and 16.9 dB higher on 13 July.The pulse compression function used in XPAR on 2 August improved the radar sensitivity by 14 dB.The SA could observe minimum ref l ectivity 10.0 dB lower than that by XDR.The minimum ref l ectivity by XPAR,XDR and SA at 50 km are 15.4 dBZ,13.5 dBZ and?3.5 dBZ,respectively.

5.3.Ref l ectivity bias analysis

The pixels of original ref l ectivity and velocity with the same range,azimuth and elevation by XDR and XAR were used to compare the ref l ectivity and velocity differences between XDR and XPAR.The pixels of original ref l ectivity by SA and the nearest pixels of XPAR were chosen to produce the sequence of data pairs.The 11 volume scans by VPP1 during 1350–1450 LST 13 July and seven volume scans during1500–1540 LST 2 Augustwereused to analyzetheref l ectivity bias.The scatter graphs for pairs of ref l ectivity by XDR and XPAR,SA and XPAR,and SA and XDR on 13 July and 2 August are shown in Fig.8.These pairs of ref l ectivity for XDR and XPAR are close to the 1-to-1 line.Comparing the pairs of ref l ectivity for XDR and SA,we can see that there is a positive calibration bias of the XDR.This means that the ref l ectivity bias of XPAR is also positive,and the XDR and XPAR have not calibrated well for ref l ectivity measurements.The correlations between XDR and SA are better than that between XPAR and SA.In addition,the attenuation effectson XDR and XPAR and the different scattering volume between radars produce deviation of the pairs to the y=x line,especially for XPAR and SA.The scatter graphs for pairs of averaged re fl ectivity by XPAR and SA(not shown)suggests that the averaging of the SA data in the same scattering volume of XPAR could improve the correlations of pairs of refl ectivity between SA and XPAR.

Fig.6.The same as Fig.1,but for PPIs at elevations of 2°,4°and 6° at 1410 LST 13 July 2012.

The statistical biases between the three types of radars were calculated with these pairs of data.The averaged differences of re fl ectivity between XPAR and XDR for the cases on 13 July and 2 August were 0.4 dB and?4.5 dB,respectively.The averaged differences of re fl ectivity between XDR and SA for cases on 13 July and 2 August were 6.6 dB and 5.1 dB,respectively.The correlation coef fi cients between XPAR and XDR for the two cases were 0.5 and 0.36,and the standard deviations were 5.2 dB and 9.6 dB.The probability distributions of re fl ectivity by XPAR,XDR and SA and the probability distributions of velocity by XPAR and XDR are shown in Fig.9.The patterns of the probability distributions for re fl ectivity have obvious differences.The distributions of re fl ectivity by XDR and SA were wider than that by XPAR due to the different beam width between XPAR and XDR,and SA.Attenuation would shift the distribution of higher refl ectivity of XPAR and XDR to the left,which means that the difference between SA and XDR is larger than the statistical results and XDR is not correctly calibrated.For the velocity,the averaged difference for the two cases between XPAR and XDRwaslessthan0.22ms?1,thecorrelationcoef fi cientwas 0.57,and the standard deviation was 2.4 m s?1.The probability distributions of velocity for both of the radars matched very well.

XDR was operated with no pulse compression on 13 July and with pulse compression on 2 August.According to the comparisonresultsbetweenXPARandXDRon13Julyand2 August,thecalibrationforpulsecompressioncouldintroduce ref l ectivity differences of?4.6 dB.The calibration methods for ref l ectivity and gain of pulse compression should be improved.

6.Effects of wide beam width on the observed ref l ectivity f i elds

Theobservedtargetvolumeof XPARislargerthanthatof XDR,due to the wide beam width.The different beam width could introduce the differences of ref l ectivity structures and their values.For quantitative evaluation of the effects of wide beam width on the observed ref l ectivity,the XDR data were averaged in the azimuth and elevation directions with Eq.(7)to obtain the averaged ref l ectivity in similar target volume with XPAR.The number of averaged XDR beams depends on the coverage of each of XPAR beam,which vary with the intersecting angle between the steering direction and broadside of XPAR.

Fig.7.Vertical cross sections of ref l ectivity along 199°and 179°at 1515 LST 2 August 2012 by(a,b)XPAR,(c,d)XDR,and(e,f)SA.

Fig.8.Scatter graphs of original ref l ectivity by XPAR and XDR on(a)13 July and(b)2 August,by XPAR and SA on(c)13 July and(d)2 August,and by XDR and SA on(e)13 July and(f)2 August.

Figure 10 shows the comparison between raw ref l ectivity PPI observed by XDR,averaged PPI from XDR,and PPI observed by XPAR at an elevation angle of 1°.After averaging in the azimuth and elevation directions,the detailed structure of ref l ectivity by XDR was smoothed and the echo area was extended.The averaged PPI of XDR was closer to that observed by XPAR.The scatter graph for ref l ectivity by XPAR and averaged XDR is shown in Fig.11.There is still a significant difference between the probability distributions of the ref l ectivity.This suggests that resolution is not the main reason causing the difference between these two X-band radars.Compared to the raw XDR data,the correlation coeff i cient increased to 0.40 from 0.36,and the standard deviation decreased to 8.4 dBZ from 9.6 dBZ.

7.Discussion and conclusions

Fig.9.The probability distributions of original ref l ectivity by XPAR,XDR and SA on(a)13 July and(b)2 August,and probability distributions of radial velocity by XDR and XPAR on(c)13 July and(d)2 August.

Fig.10.The PPI of raw ref l ectivity by(a)XDR and averaged values by(b)XDR and(c)XPARat an elevation angle of 1°at 1515 LST 2 August 2012.

To analyze the observation capability and test the design principle and working mode of XPAR made in China,the XPAR and XDR were located at the same site and used for precipitation observations in Nanjing in conjunction with an SA.TheSAandXDRdata,collectedon2Augustand13July 2012,were analyzed to examine the observation capability of the XPAR and the calibration.The cross-comparison algorithm between different observation modes,spatial resolutions and observation site were presented.The horizontal and vertical precipitation structures by the three kinds of radars and the statistical parameters of observed ref l ectivity and velocity were analyzed.The effect of beam width on ref l ectivity was analyzed.The conclusions are as follows:

(1)The three types of radar can resolve similar locations and patterns of ref l ectivity structure.The XDR can capture the detail of ref l ectivity variation.The ref l ectivity variation by XDR with range is similar to that by XPAR.The smoothing of ref l ectivity in the azimuth direction by XPAR is obvious due to the wide beam width of the radar.The operating modesofXPARwithdifferentsamplespeedsandscansched-ules worked very well.

Fig.11.(a)Scatter graph of original ref l ectivity by XPAR and corresponding averaged XDR data;and(b)probability distributions of ref l ectivity by XDR,XPAR and corresponding averaged XDR data during 1500–1540 LST 2 August 2012.

(2)The quantitative analysis on ref l ectivity difference between the different radars showed that the ref l ectivity difference between XPAR and XDR,and XPAR and SA,are obvious for the two cases.The pulse compression function improves the ref l ectivity sensitivity by about 14 dB,but introduces a ref l ectivity bias of about 4.6 dB.The calibration method,data processor,and operating mode should be improved.

(3)It could improve the relationship between XPAR and XDR to average the XDR in the azimuth direction over the coverage of PAR.

This comparison study at the ground level before installing the radar on an aircraft examined the observation capability and the design principle of XPAR.However,the current operating mode of XPAR is not suitable for research purposes to observe precipitation systems in an aircraft.The calibration,data processor,and operating mode of XPAR should be improved before airborne observation.The peak transmitted power and range resolution should be improved to increase the radar sensitivity,and the azimuthal resolution shouldbeincreasedtoabout1°todecreasethevolumeupdate time.An agile scanning strategy should be used to observe 3D ref l ectivity and the Doppler wind prof i le.

Acknowledgements.The authors wish to thank the Jiangsu Meteorological Bureau for providing the SA radar data.This study was funded by National High-Tech Research and Development Projects(863;Grant No.2007AA061901),the National Key Program for Developing Basic Sciences(Grant No.2012CB417202),the National Natural Science Foundation of China(Grant No.41175038),and the Public Welfare Meteorological Special Project(Grant No.GYHY201106046).

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