Методы повышения качества данных поляриметрических метеорологических радаров. Methods for Improving Data Quality of Polarimetric Weather Radars

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1 II Всероссийская научная конференция «Современные проблемы дистанционного зондирования, радиолокации, распространения и дифракции волн» - «Муром 2018» Методы повышения качества данных поляриметрических метеорологических радаров А.В. Рыжков,2, В.М. Мельников 1,2, Д.С. Зрнич 2 1 Университет Оклахомы, США; 2 Национальная лаборатория по исследованию сильных штормов, США, 120 David L Boen Blvd., Noman, Oklahoma, USA, Основные проблемы качества, обсуждаемые в докладе, включают в себя абсолютную калибровку радарной отражаемости Z и дифференциальной отражаемости ZDR, необходимость коррекции на ослабление/дифференциальное ослабление в осадках и устранения ошибок, связанных с частичной блокировкой радарного луча препятствиями. Предлагаются различные методологии для радаров, работающих в S, C, и X диапазонаx. Для калибровки Z рекомендуется метод, базирующийся на взаимной зависимости Z, ZDR и удельной дифференциальной фазы KDP в дожде. Обсуждаются пять методик абсолютной калибровки дифференциальной отражаемости. Коррекция на ослабление и блокировку луча осуществляется с использованием KDP и удельного ослабления А, на которые ослабление и блокировка не влияют Methods fo Impoving Data Quality of Polaimetic Weathe Radas Alexande V. Ryzhkov 1,2, Valey M. Melnikov 1,2, Dusan Znic 2 1 Univesity of Oklahoma, USA; 2 National Sevee Stoms Laboatoy, USA 120 David L Boen Blvd., Noman, Oklahoma, USA, The issues with data quality addessed in the pape include absolute calibation of ada eflectivity facto Z, absolute calibation of diffeential eflectivity ZDR, the need fo coection fo attenuation/diffeential attenuation in pecipitation, and mitigation of patial beam blockage of the ada. Vaious methodologies ae suggested fo utilization on weathe adas opeating at S, C, and X bands. A data-based method fo absolute calibation of Z capitalizes on the consistency between Z, ZDR, and specific diffeential phase KDP in ain. Diffeent techniques fo absolute calibation of ZDR ae discussed: (1) system intenal hadwae calibation, (2) bidbath calibation with vetically pointing ada, (3) Z ZDR consistency in light ain, (4) using dy aggegated snow as a natual calibato fo ZDR, and (5) using Bagg scatte as anothe natual taget fo calibation. Attenuation and ada beam blockage coection of Z and ZDR is pefomed using KDP and specific attenuation A which ae immune to these factos. 1. Intoduction Dual-polaization Dopple adas become a standad fo opeational netwoks of weathe adas. Weathe applications of dual-polaization adas ae summaized by Ryzhkov et al. [1]. Fist netwok of polaimetic weathe adas opeating at S band has been completed in the US in Since then, simila opeational weathe ada systems have been eithe implemented o emain unde development in Euope, Asia, and Austalia. The Russian Fedeation follows a tend and, stating fom 2011, а full-scale modenization of existing weathe ada netwok by eplacing old adas with C-band polaimetic Dopple adas (ДМРЛ-С) is undeway (Ефремов и др., [2]; Дядюченко и др., [3]; Жуков и Щукин, [4]. 35

2 Poviding high quality of weathe ada data is essential fo poducing eliable and obust hydological and meteoological infomation useful to the scientific and opeational communities. The accuacy of quantitative pecipitation estimation (QPE) and hydometeo classification diectly depends on the quality of diffeent ada vaiable estimates. Moden opeational Dopple polaimetic adas diectly measue ada eflectivity Z, diffeential eflectivity Z DR, diffeential phase Φ DP, coss-coelation coefficient ρ hv, Dopple velocity v, Dopple spectum width σ v, and linea depolaization atio LDR (in the LDR mode of opeation). Specific diffeential phase K DP is not diectly measued but deived fom Φ DP. The meaning of listed ada vaiables is explained in Bingi and Chandaseka [5], Ryzhkov et al. [1]. The estimates of all these ada vaiables ae obtained in the ada data pocesso fom the time seies of successive ada samples within the dwell time inteval and ae subject to andom fluctuations caused by the statistical natue of the ada signal. The uncetainty of such estimates is chaacteized by bias (o accuacy) and standad deviation (o pecision). The latte one is the measue of the noisiness of the estimate o the intensity of its tempoal and spatial fluctuations. Seveal factos may cause bias in the estimates of diffeent ada vaiables. These include (1) ada miscalibation, (2) impact of wet antenna adome, (3) attenuation in atmospheic gases and pecipitation, (4) patial beam blockage (PBB), (5) gound clutte contamination, (6) low signalto-noise atio (SNR), (7) nonunifom beam filling (NBF), (8) depolaization fom popagation in oiented ice cystals, and (9) multipath popagation (thee-body scatteing). These factos affect diffeently the biases of vaious ada vaiables. In this pape, a bief summay of the measuement eos and the methods to educe such eos is pesented. 2. Absolute calibation of Z Fo most impotant pactical applications of polaimetic weathe ada, the ada eflectivity facto Z should be calibated with the accuacy of 1 db, and diffeential eflectivity Z DR with the accuacy of 0.2 db. These geneally enable estimating ainfall within 15% accuacy (Ryzhkov et al., [6]). Bette accuacy of the Z DR calibation (0.1 db) might be needed fo measuements of light ain o snow. Polaimetic divesity povides a new method fo absolute calibation of Z which was a longstanding poblem fo single-polaization adas. This methodology ests on the idea that Z, Z DR, and K DP ae intedependent in ain and Z can be estimated fom K DP and Z DR which ae independent of absolute ada calibation. The diffeence between computed and measued values of Z is consideed to be the Z bias. The consistency of Z, Z DR, and K DP in ain can be fomulated as a dependence of the atio K DP /Z on Z DR : KDP f( Z ) DR Z. (1) In (1), Z and K DP ae in linea scale (i.e., mm 6 m -3 and deg km -1 espectively). The scatteplots of the atio K DP /Z vesus Z DR simulated fom lage DSD dataset in Oklahoma fo thee ada wavelengths and two tempeatues, 0 C and 30 C, ae illustated in Fig. 1. It is evident that the dependence in (1) on tempeatue is negligibly small at S band whee the effects of esonance scatteing ae insignificant. Howeve, the tempeatue becomes an impotant facto at C band fo Z DR > 2 db and should be taken into account fo all Z DR at X band. At S o C bands, Z can be estimated fom known K DP and Z DR with the accuacy bette than 1 db if ain does not contain many esonance-size dops. 36

3 Fig. 1. Scatteplots of K DP /Z vesus Z DR at S band (λ = 11.0 cm), C band (λ = 5.45 cm), and X band (λ = 3.2 cm) fo aindop tempeatue 0 C (blue dots) and 30 C (ed dots). The function f(z DR ) can be well appoximated by a fouth-ode polynomial fit in cetain ange of Z DR so that (1) can be pesented as KDP ( a0 a1z DR a2zdr a3zdr ). (2) Z In (2), Z DR is in decibels and the coefficients a 0 a 3 fo the S-, C-, and X-band ada wavelengths ae listed in Table 1. It is impotant, that (2) with coefficients fom the Table 1 is valid in the Z DR ange 0.2 db to 2 o 3 db and that diffeent consistency elations should be used fo diffeent tempeatues at X band. Because each of the thee polaimetic vaiables in (2) has statistical eos and K DP is notoiously noisy in light ain (especially at longe ada wavelengths) it is instumental to ewite (2) as 0.1 Z ( dbz ) KDP 10 f ( ZDR ) (3) and integate both sides of (3) ove a sufficiently lage spatial / tempoal domain Ω (Ryzhkov et al., [6]). The integal I1 KDPd (4) should be equal to the integal 0.1 I2 10 Z m f ( ZDR ) d, (5) if measued eflectivity Z m is pefectly calibated. The diffeence between I 1 and I 2 points to Z bias ΔZ which can be estimated as Z( db) 10log( I2 / I1). (6) if Z m = Z + ΔZ. Because appoximation (2) is valid only in the limited ange of Z DR listed in the Table 1, the integations (4) and (5) should be caied out only ove the pixels of data within the appopiate ange of Z DR (e.g., between 0.2 and 2.0 db at C band). It is also equied that data in the domain Ω ae not biased by low signal-to-noise atio o contaminated by scattees othe than aindops. These equiements ae satisfied if SNR > 25 db and ρ hv > Table 1. Coefficients a 0 a 3 in (2) fo S band (λ = 11.0 cm), C band (λ = 5.45 cm), and X band (λ = 3.2 cm). Fequency Tempeatue Z DR ange a 0 a 1 a 2 a 3 band ( C) (db) S C X X

4 X X The methodology of matching the integals I 1 and I 2 was fist tested at S band on a lage polaimetic dataset obtained duing the Joint Polaization Expeiment in Oklahoma and yielded an accuacy of Z calibation within 1 db (Ryzhkov et al., [6]). To mitigate the impact of attenuation (paticulaly at C and X bands), Z and Z DR should be eithe coected fo attenuation using total diffeential phase Φ DP accoding to the methods descibed in Section 4 o only the data adials with sufficiently small span of Φ DP should be used fo calibation. 3. Absolute calibation of Z DR 3.1. System intenal calibation. Relative intenal calibation of Z DR can be achieved by measuing the diffeences between gains / losses in the two othogonal channels. Because the tansmission path and eception path diffe, sepaate elative calibation of each is needed. Thus, the powe atio P h /P v downsteam of the components that can cause bias in each path needs to be monitoed. A change in eithe atio would cause a coesponding elative dift in the Z DR bias which is then coected (Znic et al., [7]). An additional step to account fo the absolute bias must be made. The pocedue is explained next by efeing to the diagam in Fig. 2. The elative values of the powe atios (in db) ae measued at two points. One is at the waveguide couples T ch and T cv on the tansmission side; these extact powes fom the coesponding H and V waveguides to establish the elative value in the tansmission path. The othe point is at the output of the two eceives when the signals ae injected into the eceiving couples R ch and R cv above the low noise amplifies. Let the powe atio of outputs at the couples T ch and T cv be Δ T (t 0 ) = 10log[P (Tc h )/P (Tc v )] (7) whee t 0 is a efeence time stamp; in its poximity few moe initial measuements must be made. Δ T (t 0 ) is measued using one eceive (say H) as in Fig. 2 by switching between the outputs of T ch and T cv. That way the eceive s tansfe function does not affect the measuement. The Δ T (t 0 ) should be stable ove many hous because thee ae no sepaate active components in the path up to the couples. In the eceive path, a simila pocedue is applied (Fig. 2). Note that the signal geneato powe is split (appoximately 50:50) and the exact value at the splitte output is immateial because the measuement is elative. Thus the powe atio is Δ R (t 0 ) = 10log[P(Rc h )/P(Rc v )], (8) and it is measued immediately afte (7) to avoid possible changes between the measuements. Afte these two measuements ae made, one needs to establish the absolute bias. This is moe challenging and few options have been tied. One is fom Bagg scattees (section 3.5) which poduce zeo Z DR, thus, the oveall coect bias is the value of Z DR measued fom Bagg scattees. Let that coect value be Δ C (t 0 ). It needs to be subtacted fom the biased estimates denoted with Ẑ to obtain the coected diffeential eflectivity Z DR : DR Z Z ˆ ( t ). (9) DR DR C 0 38

5 This coection is valid if (7) and (8) do not change. Δ T (t 0 ) nomally does not change and it suffices to check it at intevals of seveal hous (eight on the WSR-88D). If a change, denoted with Δ Tb = Δ T (t) - Δ T (t 0 ), does occu it should be subtacted, fom (9) i.e., ZDR Z ˆ DR ( ) ( ) ( ) C t0 T t T t. (10) 0 The same easoning applies to the eceiving pat of the bias which, howeve, changes moe often, and to catch these elatively fast changes, calibation of the eceiving path is made at the end of each volume scan. This, is automated, and poduces stable esult. Thus, the eceive bias is Δ Rb (t i ) = Δ R (t i ) - Δ R (t 0 ), at the times t i when volume scans end. The coection equies subtaction of Δ Rb (t i ) fom all the data within the subsequent volume scan, and so on. The sun can be a efeence souce and in case the tansmitting path is well balanced the Sun flux may be sufficient fo absolute calibation. Then the bias Δ Sb evealed fom the Sun scan can be substituted fo Δ C (t 0 ) in (9). Fig. 2. Tansmitte and eceive paths to the antenna. The couples in the tansmitte path Tc h, Tc v tap the signals fom the H, V waveguides close to the antenna; compaison is made sequentially, via Switch 2, in the H eceive. The signal geneato s output is split and injected into the eceive couples Rc h, Rc v located above the low noise amplifies in the H, V waveguides. Duing data collection the Switch 1 is open; it closes at the end of volume scans to enable automatic calibation of the eceive path Bidbath calibation of Z DR. Because the mean canting angle of aindops is close to zeo, aindops appea spheical if viewed at vetical incidence and the measued Z DR in light ain with vetically pointing antenna should be close to 0 db. Such calibation technique ( bidbath calibation) is discussed in Gogucci et al. [8] and Fech et al. [9] among othes. This technique may wok well only in light ain and in the absence of contamination fom gound clutte via antenna sidelobes. Such contamination can cause azimuthal modulation of Z DR fo vetically looking otating antenna. If this is the case, azimuthal aveaging is needed fo detemining the Z DR bias o spectal filteing of the gound clutte components can be applied (Znic and Melnikov, [10]) Z Z DR consistency in light ain. Small aindops have nealy spheical shape and it is expected that Z DR in light ain dominated by small-size dops is elatively close to zeo db. Theefoe, light ain may seve as a natual calibato fo Z DR measuements. This, howeve, is valid only in a geneal sense because 39

6 aindop size distibutions associated with intense size soting within convective updafts ae skewed towads lage dops and high values of Z DR may be measued in the aeas of elatively low Z. Fig. 3 shows Z Z DR dependencies coesponding to diffeent pecentiles of Z DR fo a given Z in ain simulated fom DSDs measued in Oklahoma. The simulations ae fo S band at T = 20 C. The domain between two dashed cuves encompasses Z Z DR pais of the whole dataset. Thus, Z DR can be as high as 1 db fo Z = 20 db. Nevetheless, in 80% of cases, Z DR at Z = 20 dbz stays below 0.4 db with aveage value of 0.23 db. The Z Z DR dependencies in ain shown in Figs ae valid at S band. Simila analysis at shote ada wavelengths shows quite simila esults fo Z < 30 db (see Table 2). The pocedue fo Z DR calibation based on the ada measuements in ain can be easily automated so that the consistency between measued and expected values of Z DR in light ain is checked evey ada scan if appopiate data ae available. Accoding to the automatic calibation outine implemented on the MeteoFance opeational ada netwok, the measued median Z DR at Z = dbz is compaed with its efeence value 0.2 db. It is also possible to estimate the Z DR bias as 6 1 (m) (m) ΔZDR [ ZDR ( k) ZDR ( k) ] (11) 6 k 1 whee <Z DR (m) (k)> ae median climatological values of Z DR in the k th 2-dB bin of Z shown in Table 2 and Z DR (m) (k) its value estimated fom eal ada data. Similaly to the self-consistency calibation of Z, the data appopiate fo calibation of Z DR should be selected whee SNR is sufficiently high (SNR > db), diffeential attenuation is insignificant, and ain scattees ae dominant contibutos (i.e., ρ hv > ). Table 2. Median climatological values of Z DR (db) fo diffeent Z (dbz) at S, C, and X bands in ain (20 < Z < 30 dbz). Z Z DR (S) Z DR (C) Z DR (X) Fig. 3. Z Z DR dependencies coesponding to vaious pecentiles of Z DR fo a given Z in ain. Z and Z DR ae simulated at S band fom DSDs measued in Oklahoma Z DR calibation using dy aggegated snow Dy aggegated snow is known fo its small intinsic Z DR caused by vey low density. The study by Ryzhkov et al. [6] indicate that mean Z DR (i.e., aveaged ove a sufficiently lage spatial 40

7 / tempoal inteval) in aggegated snow usually does not exceed 0.2 db if Z > 30 dbz. Dy aggegated snow nea the suface does not occu in wam climatic zones. In addition, such a snow should be caefully sepaated fom wet aggegated snow and dy cystallized snow that ae chaacteized by a much highe and moe vaiable Z DR. Nevetheless, dy aggegated snowflakes ae commonly pesent above the melting laye in statifom clouds (povided that Z > 30 dbz). Numeous polaimetic ada measuements show that Z DR dops almost to 0 db 1 2 km above the 0 C level whee dy aggegated snow is most likely. Quasi-vetical pofiles (QVP, Ryzhkov et al., [11]) of Z DR in aggegates above the melting laye ae suitable fo monitoing deviation fom expected low values. Because QVPs made fom azimuthal aveages ove 360 o at high elevations, the accuacy of this measuement is bette than 0.1 db Using Bagg scatte fo absolute calibation of Z DR Melnikov et al. [12] suggest using clea-ai ada echoes associated with Bagg scatteing fo absolute calibation of Z DR. Bagg backscatte fom efactive index petubations at 5 cm scales ceates sufficiently stong echo in a convective bounday laye to be detected by 10-cmwavelength weathe adas. These echoes ae chaacteized by intinsic Z DR equal to 0 db and coss-coelation coefficient ρ hv vey close to 1 making them easily distinguishable fom the clea-ai echoes caused by biota which have vey lage Z DR and low ρ hv. An automated algoithm fo estimating Z DR bias fom the Bagg scatte was developed and extensively tested on the S-band WSR-88D adas (Richadson et al., [13]). The algoithm yields bette accuacy of the Z DR bias estimation than the methods based on the Z DR measuements in light ain and dy snow. Stong Bagg scatteing usually occus at the top of the bounday laye because thee the gadients of humidity ae lagest and mixing by tubulence poduces stongest etuns. This is seen in Fig. 4 as a distinct laye of enhanced Z and close to zeo Z DR. Application of thesholds (Z < 10 dbz, SNR < 15 db, ρ hv < 0.98, and v > 2 m s -1 ) and some othe citeia identifies data in the laye that ae due to the Bagg scatte (Fig. 4b, top left); the histogam of Z DR (Fig. 4, ight panel) is indeed centeed on 0 db. Fig. 4. Example of Bagg scatteing obseved by the KMKX WSR-88D ada on 10 Nov (a) The fields of Z (uppe left), Z DR (uppe ight), ρ hv (lowe left), and Dopple velocity (lowe ight) ae fom conical scans at the 3.5 elevation angle (1852 UTC). Maximum ange in the image is ~22 km. (b) The Z DR histogam (ight) is fom the data (top left cone) which have passed Bagg detection citeia. Data that have passed the SNR > 2 db theshold ae in the bottom left image. (Fom Richadson et al., [13]). 41

8 4. Attenuation coection. Attenuation of micowave adiation in pecipitation may significantly bias the measuements of Z and Z DR, especially at shote ada wavelengths. Reliable coection of Z and Z DR is equied befoe utilizing these ada vaiables fo quantitative ainfall estimation, hydometeo classification, micophysical etievals, etc. Attenuation and diffeential attenuation in ain cause negative biases in Z and Z DR (ΔZ and ΔZ DR espectively) which can be estimated fom the total span of diffeential phase Φ DP along the popagation path (ΔΦ DP ). Specific attenuation A and specific diffeential attenuation A DP ae geneally popotional to specific diffeential phase K DP : A KDP and ADP KDP. (12) Theefoe, and DP DP (13) 0 0 Z( ) 2 A( s) ds 2 K ( s) ds ( ) Z ( ) 2 A ( s) ds 2 K ( s) ds ( ) DR DP DP DP (14) if the factos α and β do not change much along the popagation path (0,) (Bingi et al., [14]).The fact that attenuation biases of Z and Z DR ae diectly popotional to the diffeential phase is an advantage of polaimetic adas because it enables accuate quantification of pecipitation in the pesence of stong attenuation at shote ada wavelengths (C and X bands). The factos α and β in (12) ae sensitive to the vaiability of aindop size distibutions and tempeatue. Typical ange of thei vaiability at diffeent ada wavelengths is shown in Table 3. Attenuation coection in the fist appoximation can be made using default o aveage values in the ight column in Table 3. It poduces substantial impovement in Z and Z DR compaed to the absence of coection. The efficiency of default linea coection using (13) and (14) at C band with <α> = 0.08 dbdeg -1 and <β> = 0.02 db deg -1 is demonstated in Fig. 5 fo the case of a tonadic stom in Oklahoma. The fields of Z and Z DR measued by the C-band OU-PRIME ada show lage negative biases befoe attenuation coection is applied (Fig. 5a,b). The biases ae lagest along azimuthal diections whee total diffeential phase is highest (Fig. 5c). The coected fields of Z and Z DR in Fig. 5e,f ae consistent with the ones measued by the collocated S-band ada (not shown). Table 3. Ranges of vaiability of the factos α and β in ain at S, C, and X bands. S band α = db/deg <α> = 0.02 db/deg β = db/deg <β> = db/deg C band α = db/deg <α> = 0.08 db/deg β = db/deg <β> = 0.02 db/deg X band α = db/deg <α> = 0.28 db/deg β = db/deg <β> = 0.05 db/deg 5. Mitigation of patial beam blockage. Beam blockage caused by teain and othe obstacles such as buildings and tees limits ada coveage and intoduces bias in measuements. Theefoe, the quality of the weathe ada

9 poducts such as quantitative pecipitation estimate (QPE) is compomised. One of the most common methods fo mitigation of patial beam blockage (PBB) uses a digital elevation map (DEM) to estimate the degee of beam blockage at paticula azimuths and elevations based on geomety of the beam and its occultation. The DEM-based coection method may not wok well if the degee of blockage exceeds 60%. In addition to lage-scale teain featues, small-scale anthopogenic stuctues (e.g., towes, buildings) and neaby tees that ae not accounted fo by DEMs can cause additional occultation of the ada beam. The poblem of the patial beam blockage can be esolved moe efficiently with the dualpolaization ada than with the single-polaization ada because the fome can diectly measue diffeential phase Φ DP and estimate specific attenuation A ove a popagation path ( 1, 2 ) as follows (Ryzhkov et al., [15]) b [ Za ( )] C( b, PIA) A () (15) I( 1, 2 ) C( b, PIA) I(, 2 ) whee 1 2 a 2 b I(, ) 0.46 b [ Z ( s)] ds, (16) 2 a 1 2 b I(, ) 0.46 b [ Z ( s)] ds, (17) C( b, PIA) exp(0.23 bpia) 1, (18) PIA [ ( ) ( )], (19) DP 2 DP 1 DP whee b is a constant and Z a is the measued ada eflectivity facto which can be biased. It is evident that the estimate of specific attenuation A fom a adial pofile of Z a and a total span of diffeential phase ΔΦ DP is totally immune to the Z biases caused by attenuation, ada miscalibation, patial beam blockages, and wet adome. Indeed, if attenuated Z (Z a in (15)) expessed in linea scale is multiplied by an abitay constant ζ along the popagation path ( 1, 2 ), then the value of A emains intact because the numeato and denominato in (15) ae multiplied by the same facto ζ b which is cancelled out in the atio. This popety of the A estimate by (15) poves to be vey beneficial fo quantification of ainfall in the patially blocked aeas of ada etuns if the A-based algoithm is used fo ainfall estimation. The ada eflectivity facto unbiased by PBB can be estimated fom A using the Z(A) elation which is an inveted elation A = az b. The pefomance of this technique is illustated in Fig. 6 whee the fields of the measued X- band Z and Z DR (befoe coection fo attenuation and beam blockage) at antenna elevation 1.5 ae displayed along with the fields of Φ DP and ada eflectivity coected fo attenuation and PBB. It is obvious that that the PBB-elated Z bias in a naow SE secto is completely eliminated in the panel (c) of Fig

10 Fig. 5. Composite plot of Z, Z DR, Φ DP, and ρ hv measued by the C-band OU-PRIME ada at elevation 0.5 in the tonadic stom in cental Oklahoma on May 10, 2010 at 2042 UTC (panels a d). The fields of Z and Z DR coected fo attenuation ae displayed in panels (e) and (f). 44

11 Fig. 6. Composite plot of measued Z and Z DR befoe coection fo attenuation and beam blockage ((a) and (b)), Z afte coection (c), and diffeential phase (d). The measuements ae made by the Univesity of Bonn X-band polaimetic ada on June 22, 2011 at 1126 UTC at elevation Statistical eos Rada signals eflected fom weathe objects ae andom. This intinsic andomness is caused by the motions of individual scattees in the ada esolution volume. Themal noise geneated by the ada itself and suounding atmosphee and gound suface also adds to the statistical uncetainty of the estimates of ada vaiables. To educe the uncetainty, the estimates of spectal moments and polaimetic vaiables ae calculated fom a pulse tain of M consecutive samples. These samples ae coelated and theefoe the eduction in the vaiance of estimates is smalle than what it would be if thee was no coelation between the samples. The vaiance is invesely popotional to the equivalent numbe of independent pulses M I which depends on the wavelength λ, Dopple spectum width σ v, and pulse epetition peiod T. The statistical accuacy of the polaimetic ada vaiables also depends on the coelation between the hoizontally and vetically polaized components of the signal which is quantified by the coss-coelation coefficient ρ hv. 45

12 Fig. 7. Standad deviations of the estimates of Z DR, Φ DP, and ρ hv as functions of Dopple spectum width fo diffeent values of ρ hv and SNR at S band (λ = 11 cm) fo PRF = 321 Hz and M = 17. Solid lines SNR = 20 db, dashed lines SNR = 10 db; thick lines ρ hv = 0.99, thin lines ρ hv = Relatively simple and compact fomulas fo the standad deviations of the estimates of ada eflectivity Z, mean Dopple velocity v, spectum width σ v, diffeential eflectivity Z DR, diffeential phase Φ DP, and coss-coelation coefficient ρ hv can be obtained fo high values of signal-to-noise atio (SNR > 20 db) if the ada simultaneously tansmits and eceives H and V waves: 3.24 SD( Z) (db) 1/2 ( M ), (20) SD v vn 1/2 v 1 ( ) 0.20 (m s ) MT 1/2 v 1 SD( v) 0.16 (m s ) MT 1/2, (21), (22) 2 1 hv SD( ZDR ) 4.62 (db), (23) vnm 1/2-2 hv 1 DP vnm SD( ) 30.3 (deg), (24) 46

13 1 SD( ) 0.53, (25) ( ) 2 hv hv 1/2 vnm whee vn 4 vt / is the nomalized spectum width, λ is the wavelength (in m), T is the pulse epetition peiod (in sec), and M is the numbe of pulses. The dependencies of the standad deviations of the estimates of Z DR, Φ DP, and ρ hv on the Dopple spectum width fo diffeent values of ρ hv and SNR at S band ae in Fig. 7. The calculations have been made fo a typical suveillance scan of the S-band WSR-88D ada with pulse epetition fequency PRF = 321 Hz and M = 17. The standad deviations of all thee vaiables ae quite high fo such a shot dwell time, theefoe additional spatial aveaging (typically along a adial) is needed to obtain obust estimates of Z DR, Φ DP, and ρ hv. Refeences 1. Ryzhkov A., Schuu T., Melnikov V., Zhang P., Kumjian M. Weathe applications of dualpolaization adas / Радиотехнические и телекоммуникационные системы, 2016, 2. C Ефремов В.С., Вовшин Б.М., Вылегжанин И.С., Лаврукевич В.В., Седлецкий Р.М. Поляризационный доплеровский метеорологический радиолокатор С-диапазона со сжатием импульсов / Журнал радиоэлектроники, 10, с. 3. Дядюченко В.Н., Вылегжанин И.С., Павлюков Ю.Б. Доплеровские радиолокаторы в России / Наука в России С Жуков В.Ю., Щукин Г.Г. Состояние и перспективы сети доплеровских метеорологических радиолокаторов / Метеoрология и гидрология, N 2, С Bingi, V. and V. Chandaseka, 2001: Polaimetic Dopple Weathe Rada: Pinciples and Applications. Cambidge Univesity Pess, 636 pp. 6. Ryzhkov, A.V., S.E. Giangande, V. M. Melnikov, and T.J. Schuu, 2005: Calibation issues of dual-polaization ada measuements. J. Atmos. Oceanic Technol., 22, Znic, D., V. Melnikov, and J. Cate, 2006: Calibating diffeential eflectivity on the WSR- 88D. J. Atmos. Oceanic Technol., 23, Gogucci, E., G. Scachilli, and V. Chandaseka, 1999: A pocedue to calibate multipaamete weathe ada using popeties of the ain medium, IEEE Tans. Geosci. Remote Sensing, 37, Fech, M., M. Hagen, and T. Mammen, 2017: Monitoing the absolute calibation of a polaimetic weathe ada. J. Atmos. Oceanic Technol., 34, Znic, D.S., and V.M. Melnikov, 2007: Gound clutte ecognition using polaimetic spectal paametes. 33 d Confeence on Rada Meteoology, AMS, Cains, Austalia, Ryzhkov, A., P. Zhang, H. Reeves, M. Kumjian, T. Tschallene, C. Simme, S. Toemel, 2016: Quasi-vetical pofiles a new way to look at polaimetic ada data. J. Atmos. Oceanic Technol., 33, Melnikov, V., R. Doviak, D. Znic, and D. Stensud, 2011: Mapping Bagg scatte with a polaimetic WSR-88D. J. Atmos. Oceanic Technol., 28, Richadson, L., J. Cunningham, W. Zittel, R. Lee, R. Ice, V. Melnikov, N. Hoban, and J. Gebaue, 2017: Bagg scatte detection by the WSR-88D. Pat I: Algoithm development. J. Atmos. Oceanic Technol., 34, Bingi, V.N., V. Chandaseka, N. Balakishnan, and D. S. Znic, 1990: An examination of popagation effects in ainfall on polaimetic vaiables at micowave fequencies. J. Atmos. Oceanic Technol., 7,

14 15. Ryzhkov, A., M. Diedeich, P. Zhang, and C. Simme, 2014: Utilization of specific attenuation fo ainfall estimation, mitigation of patial beam blockage, and ada netwoking. J. Atmos. Oceanic Technol., 31,