high-resolution rainfall estimation from x-band ...friedrik/experiments/...speciﬁcations of the...

110 VOLUME 5J O U R N A L O F H Y D R O M E T E O R O L O G Y

q 2004 American Meteorological Society

High-Resolution Rainfall Estimation from X-Band Polarimetric Radar Measurements

EMMANOUIL N. ANAGNOSTOU AND MARIOS N. ANAGNOSTOU

Department of Civil and Environmental Engineering, University of Connecticut, Storrs, Connecticut

WITOLD F. KRAJEWSKI, ANTON KRUGER, AND BENJAMIN J. MIRIOVSKY

IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, Iowa

(Manuscript received 28 March 2003, in final form 3 July 2003)

ABSTRACT

The paper presents a rainfall estimation technique based on algorithms that couple, along a radar ray, profilesof horizontal polarization reflectivity (ZH), differential reflectivity (ZDR), and differential propagation phase shift(FDP) from X-band polarimetric radar measurements. Based on in situ raindrop size distribution (DSD) data andusing a three-parameter ‘‘normalized’’ gamma DSD model, relationships are derived that correct X-band re-flectivity profiles for specific and differential attenuation, while simultaneously retrieving variations of thenormalized intercept DSD parameter (Nw). The algorithm employs an iterative scheme to intrinsically accountfor raindrop oblateness variations from equilibrium condition. The study is facilitated from a field experimentconducted in the period October–November 2001 in Iowa City, Iowa, where observations from X-band dual-polarization mobile radar (XPOL) were collected simultaneously with high-resolution in situ disdrometer andrain-gauge rainfall measurements. The observed rainfall events ranged in intensity from moderate stratiformprecipitation to high-intensity (.50 mm h21) convective rain cells. The XPOL measurements were tested forcalibration, noise, and physical consistency using corresponding radar parameters derived from coincidentallymeasured raindrop spectra. Retrievals of Nw from the attenuation correction scheme are shown to be unbiasedand consistent with Nw values calculated from independent raindrop spectra. The attenuation correction basedonly on profiles of reflectivity measurements is shown to diverge significantly from the corresponding polari-metric-based corrections. Several rain retrieval algorithms were investigated using matched pairs of instantaneoushigh-resolution XPOL observations with rain rates from 3-min-averaged raindrop spectra at close range (;5km) and rain-gauge measurements from further ranges (;10 km). It is shown that combining along-a-ray(corrected ZH, ZDR, and specific differential phase shift) values gets the best performance in rainfall estimationwith about 40% (53%) relative standard deviation in the radar–disdrometer (radar–gauge) differences. The case-tuned reflectivity–rainfall rate (Z–R) relationship gives about 65% (73%) relative standard deviation for the samedifferences. The systematic error is shown to be low (;3% overestimation) and nearly independent of rainfallintensity for the multiparameter algorithm, while for the standard Z–R it varied from 10% underestimation to3% overestimation.

1. Introduction

Modern flood and flash flood warning systems andthe efficient management of water resources call forimproved quantitative measurements of precipitation attemporal scales of minutes and spatial scales of a fewsquare kilometers. Urban catchments and small water-sheds, characterized by particularly fast response, re-quire even higher resolution of the rainfall products(Dabbert et al. 2000). The capability provided by weath-er radar in monitoring precipitation at high spatial andtemporal scales has stimulated great interest and supportwithin the hydrologic community. The U.S. National

Corresponding author address: Emmanouil N. Anagnostou, Civiland Environmental Engineering, University of Connecticut, Storrs,CT 06269.E-mail: [email protected]

Weather Service (NWS) is using an extensive networkof Weather Surveillance Radar-1988 Doppler (WSR-88D) systems (Heiss et al. 1990), which has broughtadvancements to a range of hydrometerological appli-cations. Nevertheless, research has shown that rainfallestimates based on these classical single-polarization ra-dar observations have severe quantitative limitations(e.g., Smith et al. 1996; Anagnostou et al. 1999; Younget al. 2000). These limitations arise mainly from un-certainties associated with 1) lack of a unique transfor-mation from reflectivity to rainfall intensity; 2) radartransmitter, receiver, and antenna gain calibration prob-lems; and 3) contamination by ground returns, partialbeam occlusion, and vertical precipitation profile ef-fects. These limitations and other issues, such as atten-uation of short-wavelength radar signals in rain, havebeen discussed and documented by several investigatorsin the past (e.g., Austin 1987). Rainfall products from

FEBRUARY 2004 111A N A G N O S T O U E T A L .

operational weather radar systems have a spatial reso-lution in the range of 4–16 km2, and a temporal scaleof 1 h. This is often not sufficient to drive distributedrainfall-runoff models, in particular those simulating ur-ban basin responses (Capodaglio 1994; Norreys andCluckie 1997; Dabbert et al. 2000; Sharif et al. 2002)and for situations of extremely intense convective raincells embedded within larger regions of rainfall (Marketet al. 2001).

In an effort to reduce some of the above uncertainties,research radar systems use polarization diversity tech-nology, which consist of simultaneous measurements ofreflectivity and signal phase at horizontal (H) and ver-tical (V) polarization (Zhrai and Zrnic 1993; Zrnic andRyzhkov 1999; Scott et al. 2001). The physical conceptbehind polarization diversity is that falling raindropstake oblate shape, which under equilibrium conditioncan be related to their volume (Pruppacher and Beard1970). This nonspherical raindrop geometry impactsboth propagation and backscatter of an incoming H andV polarization electromagnetic radar wave. The mostcommon polarimetric radar measurements are the re-flectivity factors at H and V polarization (ZH, ZV, mm6

m23); the differential reflectivity factor (ZDR, dimen-sionless), which is defined as the ratio of ZH to ZV; andthe propagation differential phase shift (FDP, degrees).Over a certain radial distance (Dr) one can calculate thespecific differential phase shift (KDP, degrees km21) asone-half of FDP gradient. Estimation of KDP is subjectto random errors in FDP measurements, and the back-scattering phase shift effect (also known as ‘‘d’’ effect)that cannot be readily separated from FDP data (e.g.,Keenan et al. 2001; Zrnic and Ryzhkov 1996; Hubbertand Bringi 1995). The d value can be significant at shortradar wavelengths, especially when sufficient concen-tration of large (.6 mm at C band and .3.5 mm at Xband) raindrops is encountered in the radar samplingvolume, which is more common in high rainfall inten-sities (Zrnic et al. 2000). This non-Rayleigh effect mayintroduce serious complications at C- and X-band fre-quencies, and requires careful consideration when KDP

is used in quantitative applications such as for attenu-ation correction of reflectivity and differential reflectiv-ity measurements (Matrosov et al. 2002; Keenan et al.2001).

Many studies on radar polarization diversity haveconcentrated primarily on nonattenuating (S band) fre-quency. Starting from the early study of Seliga and Brin-gi (1976) to the most recent work by Brandes et al.(2003) and Bringi et al. (2002), investigations haveshown that multi-parameter radar observations at S bandcan be used to derive raindrop size distribution param-eters and thereby estimate rainfall rate. The majority ofstudies, though, have been based on power-law radarparameter–rainfall relationships derived through simu-lated or observed raindrop spectra (e.g., Ryzhkov andZrnic 1995; Aydin et al. 1995; Jameson 1991). A gen-erality to be drawn from these various studies is that

KDP-based estimation techniques would provide the mostaccurate estimates of high rain rates (.50 mm h21),while for moderate to low rain rates definitive mea-surements of precipitation is possible through averagingin range and combining with other measured radar pa-rameters (e.g., ZDR). Other great advantages of KDP-based estimators is that they are not affected by radarcalibration errors or partial beam occlusion, and are lesssusceptible to ground clutter effects (Vivekanandan etal. 1999; Zrnic and Ryzhkov 1996). As shown in thosestudies, the differential phase shift at S band is char-acterized by relatively low sensitivity to rainfall rate,which impacts the resolution of rain products derivedfrom KDP estimators. For example, Blackman and Il-lingworth (1997) have shown that to retrieve a rainfallrate of 8 mm h21 from KDP at S band would require Drof at least 5 km at 25-km radar range. Since FDP sen-sitivity to the raindrop size is proportional to the radarfrequency, at X band, these limiting values are loweredby a factor of 3. Consequently, the use of X-band wave-length should allow more detailed, and potentially moreaccurate estimation of light to moderate rainfall rates.

These improvements are primarily important for theaccurate prediction of floods in small to medium size(,100 km2) watersheds that are associated with a rapidresponse to high rain rates, and for real-time urban watermanagement. The partial signal attenuation, which issignificant at X band, is not an issue for the KDP mea-surements unless there is complete attenuation (i.e., sig-nal drops below a minimum detection threshold). Thereare two main complications in using polarimetric pa-rameters (ZDR and KDP) at X band that require carefulinvestigation: 1) the presence of d effect in cases ofsignificant concentration of large drops, and 2) the var-iability in raindrop size distribution and in the equilib-rium relationship between oblate raindrop shape andsize. Zrnic et al. (2000) and Keenan et al. (2001), whostudied the sensitivity of C-band polarimetric variablesto the form of raindrop axial ratio and the tail of raindropsize distribution, have exemplified the effect of bothissues on the accuracy of rainfall estimation. Currently,research on the use of polarimetric radar measurementsat X band has been limited to a few theoretical (Jameson1994, 1991; Chandrasekar and Bringi 1988; Chandra-sekar et al. 1990) and experimental studies (Tan et al.1991; Matrosov et al. 1999; Matrosov et al. 2002).

The experimental study by Matrosov et al. (1999),although valuable from the viewpoint of polarimetrictechnique development, did not provide adequate quan-titative evaluation of the estimators. In their most recentstudy, however, Matrosov et al. (2002) provided a quan-titative error analysis of the various rain estimatorsbased on field data. They concluded that a multiparam-eter algorithm consisting of ZH, ZDR, and KDP measure-ments provides the least standard error compared to oth-er single-parameter estimators. According to the au-thors, the combined polarimetric parameter algorithmintrinsically accounts for the variability in equilibrium


TABLE 1. Dates, times, duration, rain accumulations, and maximumminute-rain rates of the storm cases observed jointly by XPOL andthe IIHR gauge/disdrometer network during the experiment in IowaCity.

Storm period(Date and time in UTC)

Duration(h:min)

Accumula-tion

(mm)

Max rainrate

(mm h21)

1833–2113 UTC 4 Oct0115–0323 UTC 5 Oct1647–1829 UTC 10 Oct1859–2016 UTC 13 Oct1659 UTC 22 Oct–0344 UTC

23 Oct1439–1739 UTC 24 Oct1250–1523 UTC 30 Oct0520–0731 UTC 19 Nov

2:402:081:521:17

10:453:002:432:11

2.311.07

10.271.63

38.505.421.580.80

3.481.16

43.0519.75

47.597.954.632.44

TABLE 2. Specifications of the National Observatory of Athens X-band Polarimetric and Doppler Radar on Wheels.

Transmitter system A 2.98-cm radar wavelength, 50-kW peak transmit power, and selectable pulse length (38–150-m resolutionvolumes).

Polarization diversity Simultaneous transmission of signal at horizontal and vertical polarization.Antenna system An ;0.98 3-dB beamwidth (8.5-ft antenna) and a maximum of 308 s21 azimuth rotation. During operation,

antenna center is about 8 ft from the ground.Antenna control system Plan position indicator, range height indicator, and survey scan modes. Programmable azimuth and elevation

boundaries and step angles and rates. Solar calibration mode.Radar measurables Horizontal and vertical polarization reflectivity, Doppler velocities, spectral width, and differential phase

shift.Radar calibration Use of a signal generator to calibrate the antenna gain. Use of solar calibration and GPS for exact radar

positioning.Mobile platform Radar system mounted on a flatbed truck with radar operations cabin, a hydraulic leveling system, and a

diesel power generator.

drop shape–size relationship, thus offering a more stableestimator.

In this paper, we are concerned with the same issues,but follow a different approach. We attempt to explicitlyresolve the raindrop size distribution and equilibriumshape–size relationship parameter variations using po-larimetric measurements. Our rainfall estimation tech-nique is based on algorithms that couple profiles of ZH,ZDR, and FDP taken along a radar ray, following a schemeproposed by Testud et al. (2000). Based on in situ rain-drop size distribution (DSD) data and using an assumedthree-parameter normalized gamma model for DSD, wederive relationships applied to ZH and FDP ray-profilemeasurements to correct for ZH and ZDR attenuation,while simultaneously retrieving variations of one of theDSD parameter values. The retrieved DSD parameterand corrected ZH and ZDR profiles are combined withKDP profiles derived from the filtered FDP data to retrieverainfall rates at high resolution.

Our study was facilitated by a field experiment con-ducted in the period October–November 2001 in IowaCity, where we collected X-band polarimetric obser-vations simultaneously with high-resolution in situ dropsize distribution data. The polarimetric radar measure-ments were performed with the National Observatoryof Athens X-band dual-polarization mobile radar (here-after named XPOL), while the in situ facilities include

three disdrometers located within a 5-km range fromthe XPOL, and a network of dual tipping-bucket raingauge platforms located at further ranges (;10 km).The facilities are under the umbrella of the KDVNWSR-88D in Davenport, Iowa, about 80 km from theradar.

In the following section we describe the field exper-iment and the data collected. In section 3, we presentthe mathematical formulation of the proposed rain es-timation algorithm, and discuss issues relevant to DSDand shape–size variability effects. In section 4, we com-pare attenuation correction and rain estimation algo-rithms, including those based on single polarization ob-servations. In section 5, we evaluate the algorithm errorsbased on the in situ rain gauge and disdrometer rainfallmeasurements. We close the paper with our conclusionsin section 6.

2. Experimental data

a. Overview

We obtained high-resolution X-band polarimetric ra-dar data at the well-instrumented hydrometeorologicalsite of IIHR-Hydroscience and Engineering, a researchinstitute at the University of Iowa in Iowa City, Iowa.The experiment lasted 2 months, from early October tothe end of November 2001. Table 1 summarizes thestorm events measured coincidentally by all instrumentsduring the 2-month period of the experiment.

The XPOL system used in this research is a mobiledual-polarization radar unit with characteristics shownin Table 2. The XPOL was situated at a farm approx-imately 10 km west of Iowa City with a clear 1808 viewtowards the IIHR facility. The in situ instruments usedin this experiment included three disdrometers locatedwithin a 5-km range from XPOL, and three clusters ofdouble-gauge tipping-bucket (0.25 mm) rain gauges lo-cated between 5 and 10 km from XPOL. The disdro-meters included a two-dimensional video disdrometer(2DVD) discussed in detail by Kruger and Krajewski(2002), a Precipitation Occurrence Sensing System(POSS), which is a bistatic, continuous wave, X-bandradar developed by the Atmospheric Environment Ser-


FIG. 1. Aerial photography of the experimental domain overlaid by the XPOL and nearest NEXRAD samplinggrids, and of the dual-gauge and disdrometer locations.

vice of Canada (Sheppard 1990), and a Joss–Waldvogel(JW) disdrometer (Joss and Waldvogel 1967), a long-time community standard. A detailed discussion of theDSD data collected by the disdrometers in our experi-ment is given in Miriovsky et al. (2004). A view of theinstrument locations overlaid on an area map andXPOL’s sampling grid is shown in Fig. 1. The nearestNext Generation Doppler radar (NEXRAD) samplinggrids are also shown.

b. Calibration of XPOL

The XPOL scanning strategy was set to a three-ele-vation (0.58, 1.58, and 3.08) sector (;1008) volume scansfollowed by range–height indicator (RHI) scans overthe dual-gauge and disdrometer locations, with scanningcycles requiring about 3 min. To determine the XPOLZH, ZDR, and FDP measurement noise statistics we usedmultiple fixed-antenna samples (100 bins per sample)taken during low precipitation intensity periods. In ZH

the evaluated noise standard deviations (STDs) rangedbetween 0.15 and 0.25 dBZ, while in ZDR the STDs werea little higher, between 0.22 and 0.46 dB. In differentialphase shift, the noise STDs ranged between 18 and 58,with a mode at 1.88. To determine reflectivity (ZH) mea-surement calibration we used in situ DSD data, which

showed a 0.9-dB positive bias. We show later that re-moving this ZH bias consistently provides unbiased es-timates of one of the DSD parameters from the com-bination of ZH and FDP measurements. To determine ZDR

calibration we used measurements collected with ver-tically (908) pointing and rotating antenna in light pre-cipitation. These indicated a low positive bias of nearly0.3 dB. Matrosov et al. (2002) has explained some ofthis bias through simulation showing that ZDR measure-ments based on a slant 458 transmission with two re-ceivers (like the ones XPOL is using) can be biased by0.1–0.3 dB for canted drops in the range of 58–108 ofvertical.

We also devised a scheme for correcting differentialphase (FDP) measurements from range folding, and im-plemented an iterative filter for removing noise and deffect, based on Hubbert and Bringi (1995). Applicationof this filter to XPOL ray measurements (Fig. 2) showsthat the algorithm works well and that the differentialphase measurements have low noise. Furthermore, noobvious d effect is shown in these profiles, which wewill discuss in a later section. From the filtered FDP

profile data, we can now readily derive KDP estimates.As the final stage of checking the XPOL data, we

compared the calibration-adjusted ZH and ZDR measure-ments and KDP estimates against coincident 3-min time-


FIG. 2. XPOL single ray profile of measured and filtereddifferential phase shift (FDP) for a rain sample case.

FIG. 3. Scatterplots of (top) horizontal polarization effective reflectivity (ZH) vs differentialreflectivity (ZDR), and (bottom) ZH versus specific differential phase shift (KDP) determined fromattenuation corrected XPOL observations and radar observables calculated from measured rain-drop spectra.

averaged polarimetric parameters derived from three insitu disdrometer measurements. Figure 3 shows scat-terplots of ZH versus ZDR and ZH versus KDP as observedby the XPOL (left) and calculated from raindrop spectra

measurements (right). The scatterplots show that XPOLmeasurements give almost identical ZH–ZDR and ZH–KDP

relationships compared to the relationships derived fromDSD data. The scatter is higher in XPOL data, whichis a result of the additional noise included in the mea-surement of radar parameters and the sampling differ-ence between point (disdrometer) and volume average(XPOL) measurements. This analysis demonstrates astrong physical consistency in XPOL measurements. Italso shows that there is a degree of added variabilitydue to measurement noise, which should be consideredwhen developing rain estimation techniques.

3. Rainfall estimation algorithm

a. Polarimetric radar parameters

The XPOL measurements at each range bin are theattenuated radar reflectivity in H and V polarization, ZaH

and ZaV (mm6 m23), from which we derive the attenuateddifferential reflectivity, ZaDR 5 ZaH/ZaV (decibels, dB);and the differential phase shift between H and V po-larization, FDP (degrees). These measurements are re-lated to the nonattenuated parameters as follows:


r

Z (r) 5 Z (r) 3 exp ln10 20.2 A (s) dsaH eH E H5 6[ ]0

r

Z (r) 5 Z (r) 3 exp ln10 20.2 A (s) ds (1)aV eV E V5 6[ ]0

r

Z (r) 5 Z (r) 3 exp ln10 20.2 A (s) ds (2)aDR DR E DR5 6[ ]0

r

F (r) 5 d(r) 1 2 K (s) ds, (3)DP E DP

0

where ZeH, ZeV, and ZDR are the H and V equivalent(nonattenuated) radar reflectivity and differential reflec-tivity parameters, AH, AV, and ADP (dB km21) are the Hand V specific attenuation and differential attenuationparameters, respectively, and KDP is the specific differ-ential phase shift (degrees km21). These parameters arerelated to the hydrometeor size distribution (DSD) with-in a radar sampling volume through the following in-tegral equations (Bringi and Chandrasekar 2002):

Dmax4 2l m 1 2Z 5 s (D )N(D ) dD (4)eH,V E bH,V e e e5 2) )p m 2 1 0

Dmax

A 5 2l Im[ f (K , K ; D )]N(D ) dD (5)H,V E H,V 1 1 e e e

0

K 5 l {Re[ f (K , K ; D )]DP E H 1 1 e

2 Re[ f (K , K ; D )]}N(D ) dD (6)V 1 1 e e e

Dmax

d 5 arg f (K , 2K ; D )E H 1 1 e[0

3 f *(K , 2K ; D )N(D ) dD , (7)V 1 1 e e e]where De is the equivolumetric spherical diameter,N(De) the number of drops in [De, De 1 dDe] range, lis the radar wavelength, and m the complex refractiveindex of the hydrometeors. The H and V polarizationbackscattering cross sections, sbH,V(De), and the for-ward, f H,V(K1, K1; De), and backward, f H,V(K1, 2K1;De), scattering coefficients can be calculated for an as-sumed DSD using the T-matrix method (Barber and Yeh1975). The backscattering phase shift parameter (d) isexpected to be negligible when FDP measurements arefiltered through the iterative approach of Hubbert andBringi (1995) as discussed in the previous section.

Estimation of these polarimetric radar parameters andconsequently rainfall from the XPOL measurables is aninverse problem that involves the earlier physicallybased equations, (1)–(7). We want to solve this systemof equations for the values of equivalent radar param-eters based on the measured ones. From the derivedparameters we should be able, in principle, to find es-

timates of rainfall variables. Before we discuss our strat-egy for finding the solution, in the following section wepresent theoretical relationships between the various in-tegrated radar and rainfall parameters derived on thebasis of assumed DSD and raindrop shape–size models.

b. Relationships between integrated radar andrainfall parameters and DSD

As shown by the integral equations in the previoussection, information on the DSD, as well as hydrometeorphase (liquid, solid, mixed) and shape is key to relatepolarimetric radar measurements to precipitation andother radar parameters (e.g., specific and differentialattenuation, KDP, liquid water content, rain rate, etc.) Asindicated by past investigations based on models andobservations, the shape of raindrops can be well ap-proximated by oblate spheroids (e.g., Pruppacher andBeard 1970; Beard and Chuang 1987; Bringi et al.1998). The spheroid minor-to-major axis ratio (r) canbe approximately related to the equivolumetric sphericaldiameter (De) through a linear relationship (Pruppacherand Beard 1970). In this study we follow a generalformulation of this relationship as in Matrosov et al.(2002), assuming that axis ratio (ra) diverges from onewhen raindrops are larger than 0.5 mm:

r 5 (1.0 1 0.05beta) 2 betaDa c

for D . 0.5 mm, (8)e

where parameter beta is the slope of the shape–sizerelationship (dr/dDe). The value of 0.062 mm21 ap-proximated by Pruppacher and Beard (1970) for param-eter beta brings (8) close to the equilibrium shape–sizerelation thereby denoted as the equilibrium shape pa-rameter (betae). Nevertheless, a number of raindrop ob-lateness-size studies have shown varying degrees of di-vergence from the preceding relation, especially in largedrops (Keenan et al. 2001).

The raindrop size distribution used in this research isthe ‘‘normalized gamma distribution’’ model as pre-sented in recent polarimetric radar rainfall studies (e.g.,Testud et al. 2000):

m41mG(4) (3.67 1 m) DN(D) 5 Nw 4 1 23.67 G(4 1 m) D0

D3 exp 2(3.67 1 m) , (9)[ ]D0

where D0 (mm) is the raindrop median volume diameter,while m is the shape parameter, and Nw (m24) a ‘‘nor-malized’’ form of the intercept parameter (N0) of theclassic gamma distribution model (Ulbrich 1983). It canbe shown that Nw (mm21 m23) is related to liquid watercontent (W, gr m23) in the following form:

WN 5 , (10)w 40.055pr DW 0


FIG. 4. Statistics of normalized gamma DSD model parameter (shape parameter, m, mediandrop diameter, D0, and intercept coefficient, Nw) values determined from 1780 measured raindropspectra.

where rw is the density of water. As shown in Testudet al. (2000) all of the integrated radar (except ZDR andd) and precipitation parameters derived based on thenormalized gamma model are proportional to Nw. Con-sequently, relationships between any two of those pa-rameters, if normalized by Nw, would lead to reducedscatter, and low sensitivity to variations in m (see Testudet al. 2000). The relationships considered in this studyto support our algorithm development are given next.

In terms of radar parameters the relationships are12b bA 5 aN Z , (11)H w eH

A 5 gK , (12)H DP

12d dA 5 cN A . (13)DP w H

In terms of rainfall rate these relationships are12n nR 5 mN A , (14)w H

c zbR 5 aZ · Z K , (15)eH DR DP

tR 5 sZ . (16)eH

A linear relationship is assumed between AH and KDP,which is a good approximation for X-band frequency.Most of the preceding relationships have been used inprior studies of C-band and X-band polarimetric rainfall

estimation and corresponding parameters (power andmultipliers a, b, g, c, and d for radar parameters, andm, n, a, b, c, z, s, and t for rainfall parameters, re-spectively) derived based on both simulations and ex-perimental data (e.g., Testud et al. 2000; Le Bouar etal. 2001; Matrosov et al. 2002).

In this study, we evaluated these relationships basedon radar (ZeH, AH, ADP, KDP) and precipitation (rainfallrate, R) parameters derived experimentally from in situ3-min average raindrop spectra (1780 spectra). The me-dian mass diameter (Dm, mm) and water content (W, grm23) were calculated from each 3-min DSD spectra,after which D0 (mm) was obtained from Dm(3.67 1 m)/(4 1 m) and Nw(mm21 m23) on the basis of Eq. (10).The shape parameter m was then determined by mini-mizing (with respect to m) the least squares differenceof calculated [from Eq. (9)] versus sampled (from the3-min averaged spectra) counts over a range of 20 dropdiameter bins. Statistics of the estimated normalizedgamma DSD model parameters are presented in Fig. 4,which shows frequency histograms for the median dropdiameter (D0), Nw, and m parameter values, and a scat-terplot of D0 versus Nw. For each fitted DSD parameterset the radar variables (ZH, ZDR, KDP) at X-band fre-quency were computed on the basis of T-matrix cal-


TABLE 3. Relationship parameter values determined based on 3-min time-averaged measured raindrop spectra for 78C air temperature, anda range of oblateness coefficient (beta) values. In this table we present the parameter values for the upper/lower and equilibrium beta valuesused in the study.

Beta

Parameter

a b g c d m n a b c z s t

0.0320.0620.092

4.6E-64.5E-64.3E-6

0.7780.7740.770

0.430.230.17

2.785.207.56

1.211.211.21

2.071.761.43

0.790.780.77

154.163.735.1

20.1820.1620.14

20.06520.07020.076

1.141.121.09

8.78E-58.01E-57.10E-5

0.6080.5990.589

culations (Barber and Yeh 1975), assuming 1) the axisratio of Eq. (8) for a range of beta values (0.032–0.092mm21), 2) a Gaussian canting angle distribution withzero mean and standard deviation 10, and 3) a 6-mmmaximum drop diameter. Table 3 shows the relationshipparameters determined based on the preceding raindropspectra for a mean air temperature of 78C and for threecharacteristic values (upper, lower, and equilibrium) ofthe shape–size relationship parameter beta.

c. The rainfall estimation algorithm

As we mentioned previously, due to XPOL’s shortwavelength (;3 cm), the path reflectivity attenuationAH and differential attenuation ADP can be significant atmoderate to high rainfall rates. The rainfall estimationtechnique we propose here is based on algorithms thatcouple along-the-ray profiles of ZaH(r), ZaV(r), andFDP(r), where r symbolizes the range bin along the ray.The starting point of the formulation is the algorithmpresented by Testud et al. (2000), where Eqs. (11) and(12) are jointly used to provide stable corrections forpath attenuation of ZH while simultaneously retrievingNw variations at discrete range intervals along a radarray. The equations adopted from this formulation are asfollows (for detailed derivations the interested reader isreferred to Testud et al. 2000):

bZ (r)aHA (r) 5H 0.1bgDFI(r , r ) 1 (10 2 1) · I(r, r )1 0 0

0.1bgDF3 (10 2 1) (17)1/(12b)

20.1bgDF1 (1 2 10 )N (r , r ) 5 · , (18)w 1 0 [ ]a I(r , r )1 0

whererj

I(r , r ) 5 0.46b Z (s) ds. (19)i j E aH

ri

The r1 and r0 are range boundaries of an along-a-radar-ray interval in which Nw is assumed to be constant.The DF 5 FDP(r0) 2 FDP(r1) within that range intervalis determined from the filtered FDP data and thus ex-pected to have negligible d effect. The intervals aredetermined so that DF noise is reduced, which conse-quently minimizes uncertainty in Nw estimation. First,we identify the rain cell boundaries within a radar ray

using a low-reflectivity threshold value (14 dBZ) forrain–no rain separation. A rain cell is subsequently di-vided in subintervals if both DF . 88 and the rain cellwidth is larger than 4 km. In this case the subintervalsare selected so that both inequalities are fulfilled, thatis, DF $ 48 and r0 2 r1 $ 2 km. These thresholds areparameters that can be altered as part of the algorithmcalibration. The values were subjectively selected to bal-ance between noise reduction in FDP and the need fora detailed representation of DSD variability.

The preceding approach is accurate only if we assumethat the AH–KDP relationship is not sensitive to variationsin raindrop shape–size parameter beta. As shown by theAH–KDP scatterplot and fitted relationships at the top ofFig. 5 there is strong dependence between the slope ofAH–KDP relationship (g parameter) and the shape–sizeparameter (beta) value. This dependence has conse-quences on the attenuation correction as shown by thereflectivity profile plots at the middle and bottom of Fig.5, where beta values on either side of the equilibriumvalue betae yield significantly different ZeH and ZDR pro-files using Eqs. (17)–(19). It was observed, though, thatfor every range interval (ri, ri11) where Nw is deter-mined, there can be a beta value that minimizes thedifference between the filtered FDP data and a theoretical

profile simulated from the path attenuation esti-thFDP

mates (AH). Consequently, the algorithm was expandedso that for every range interval, Eqs. (17)–(19) are it-erated with respect to beta until they minimize the fol-lowing function:

r5ri11

th 2min [F (r) 2 F (r, beta)] ,O DP DP5 r5ri

beta 5 beta(r , r ) , (20)i i11 6where

thF (r, beta)DP

r25 F (r ) 1 [A (s, beta) · Ds], (21)ODP i Hg(beta) ri

where g (beta) and AH(s, beta) indicate that the rela-tionships used in Eqs. (17)–(19) and (12) are beta de-pendent. This approach leads to stable attenuation cor-rection profiles and estimates of Nw that are consistentwith the measured FDP data.


FIG. 5. (top) Scatterplot and fitted regression lines of specific attenu-ation (AH) vs specific differential phase shift (KDP) determined for a rangeof shape–size relationship b parameter values (0.032–0.092 mm21 withstep of 0.010). (middle), (lower) Ray profiles of measured (thick darkgray line) and corrected (shaded region) for attenuation ZH and ZDR values.The attenuation correction is based on parameterizations derived fromthe equilibrium (black line) and the upper- and lowermost b values forthe shape–size relationship (shaded region bounds).

The uncertainty in attenuation correction of ZH andZDR profiles and Nw retrieval can be statistically relatedto the measurement noise, assuming independence, as(Testud et al. 2000):

dA (r) dZ (r) d(DF[r , r ])H H 1 02Var 5 b Var 1 Var5 6[ ] [ ]A (r) Z (r) DF[r , r ]H H 1 0

(22)

dA (r) dZ (r)DP H2Var 5 (bd) Var[ ] [ ]A (r) Z (r)DP H

21 2 bd d(DF[r , r ])1 01 Var (23)1 2 5 61 2 b DF[r , r ]1 0

dN [r , r ] 1 d(DF[r , r ])w 1 0 1 0Var 5 Var , (24)21 2 5 6N [r , r ] (1 2 b) DF[r , r ]w 1 0 1 0

where dX/X defines the relative error of a radar mea-surement or retrieved variable X, while the rest of theparameters and variables have been previously defined.The relative error variance of XPOL’s ZH measurementswas determined to be 0.23 for 150-m gate size, whilethe DF relative error variances for range intervals [r1,r0] of 2, 4, and 5 km are 0.194, 0.053, and 0.029, re-spectively. Based on these measurement error statisticswe determined that AH (ADP) estimates are associatedwith a 0.168 (0.203) relative error variance, while fora range interval of 2 km (5 km) the Nw estimation rel-ative error variance would be 3.8 (0.568). An assump-tion made in this error analysis is that beta can be ac-curately determined from (20). In case of erroneous betaestimation the uncertainty in attenuation correction andNw retrieval can be significantly higher as discussed ear-lier in this section (Fig. 5).

d. Examples of XPOL ray profile measurements ofprecipitation

In this section we present examples of two charac-teristic ray profile measurements that contain both in-tense and moderate precipitation areas. The profileswere taken from sweeps at around 0.88 elevation, andpresented up to 34-km range where the whole beamsampling volume is well below 1.0 km. At that height,we can safely assume that all hydrometeors are waterdroplets following the DSD and shape–size parameter-izations presented in the previous section. Figure 6 il-lustrates the two examples showing range profiles of 1)the XPOL measured (attenuated) H-polarization reflec-tivity, 2) the corresponding measured (attenuated) dif-ferential reflectivity, and 3) differential phase shift. Inthe ZH ray profile plot, we show the effective reflectivityestimates determined based on the presented polari-metric method versus the standard Hitchfeld and Bordan(1954) approach, assuming Nw 5 8.0E6 (Marshall andPalmer 1948). In the ZDR ray profile we present the


FIG. 6. Two examples of ray profiles of horizontal polarization reflectivity (ZH), differentialreflectivity (ZDR), differential phase shift (FDP), and the normalized gamma DSD intercept (Nw).(top) The shaded region centered on the black line denotes 1 std dev uncertainty bound of polar-imetric correction (P), the dark gray line denotes standard attenuation correction (S), and the lightgray line denotes the measured values. Similar convention applies to other frames. Here, AH isspecific attenuation; Nw is integrated over 5-km intervals.

attenuation correction performed using the differentialattenuation estimates from Eq. (13) for a retrieved AH

and Nw profile. In those panels we overlay the correctedZH and ZDR profiles associate with AH(1 6 )Ï0.168and ADP (1 6 ) one standard deviation errorÏ0.203bounds in the attenuation estimates. In the FDP ray pro-file plot we also present profiles evaluated from theprFDP

retrieved AH profiles (from both polarimetric and stan-dard approach) as follows:

rprF (r) 5 F (r ) 1 (2/g) [A (s) · Ds]. (25)ODP DP i H

s5ri

Finally, at the bottom of Fig. 6 we present the re-trieved variations of Nw at discrete range intervals (5km), along with its one standard deviation error bounds,and the Nw value calculated from coincident 3-min rain-drop size spectra. Several observations can be madefrom the previous sample ray profiles of polarimetric


radar parameters. First, the standard and polarimetricattenuation correction schemes give different rain-pathattenuation estimates, where in cases of intense rainrates this divergence can be significant. From the FDP

ray profile plots we observe that the FDP predictionsderived from the standard AH retrieval are biased com-pared to the measured FDP profile, while the polarimetricretrieval consistently follows the measured FDP profile.Noticing concurrently that the retrieved Nw value at thediscrete interval containing the disdrometer is similarto the value calculated from the measured raindrop spec-tra supports the argument that polarimetric informationis critical to achieve stable and definitive attenuationcorrection estimates at X-band frequency. Another note-worthy point concerns the ZDR attenuation correction.The corrected ZDR profile values seem to be at reasonablelevels and, as was shown by comparisons with shortradar-range disdrometer data (see Fig. 3), they are con-sistent with the corrected ZH profile values. This studylacks reference ZH and ZDR measurements from furtherranges (.5 km) to support more definitive statementsabout the polarimetric attenuation correction efficiency,but future research based on coincident S-band and X-band polarimetric ray profile measurements would ad-dress this aspect. The error in ZH and ZDR correctedprofiles due to the attenuation correction sensitivity tomeasurement noise is shown to be as high as 2–3 dB.We also observe that the ZH profile corrected on thebasis of the standard method falls within the one stan-dard deviation error bounds of the polarimetric atten-uation correction. The disdrometer-determined Nw val-ues are shown to be outside the error bounds of the Nw

retrieval as part of the polarimetric attenuation correc-tion technique. A major source of this difference is theresolution of Nw retrieval (5 km), but could also be anindication of error in beta parameter estimate.

Finally, we would like to reinforce an observationmade by Matrosov et al. (2002) where they noted thelack of significant d effect in rain-rate profile measure-ments during a winter experiment at Wallops Island. Thed effect would appear in the data as a rapid increase/decrease (i.e., a ‘‘bump’’ that would stand above therandom FDP noise variations) in the FDP profile. Al-though we have implemented a FDP correction filter toalleviate potential d effects, visual observation (notshown here) of several moderate to heavy rain-rateXPOL ray profile measurements indicated insignificantd effect in the data. We note that the d effect at X bandis small for drop diameters below 3 mm, while it onlygradually and monotonically increases at larger dropdiameters (see Matrosov et al. 2002, their Fig. 6, anddiscussion therein on this issue). That we could not findsignificant d effect in the FDP data from this experimentcould be because the type of storm systems observedwere typically stratiform with few very intense raincells. Another reason for lack of significant d discussedin the conclusions of a study by Zrnic et al. (2000) isthat the increased attenuation occurring when large rain-

drop are present compensates the resonance effect at 3-cm wavelength.

The radar parameters measured or estimated in thisstudy are consistent with prior experimental studies onX-band polarimetric measurements of rainfall (e.g., Ma-trosov et al. 1999; Matrosov et al. 2002). In intense rain(;10 km radar range) where reflectivity exceeds 50 dBZfor a few kilometers range interval, the differential re-flectivity takes on values of about 2.5 dB, and the FDP

slope (i.e., KDP) is in the range of 3.28–3.78 km21. Inthe range of intense rain cells the Nw parameter of anormalized gamma DSD model takes on values around2 3 106 m24, which is 4 times lower than the Marshall–Palmer value (8 3 106 m24). In the regions where thereflectivity is moderate to low (around 30 dBZ), whichis associated with light rainfall (see Fig. 6), the ZDR isabout zero, while the KDP is consistently below 18 km21.It is noteworthy that the low noise in FDP data, even inthe case of low reflectivity (,30 dBZ) and short rangeintervals (,1 km), can provide a measure of the KDP

signal in rain. This is the major advantage of X-bandpolarimetric measurements over S-band systems, whichfor low rainfall intensities would require long-range in-tervals (.5 km) to provide a reliable KDP measure inrain.

The ray profiles of the retrieved rain rates associatedwith the profiles of Fig. 6 are presented in Fig. 7. Thepolarimetric rain estimates are derived from Eq. (14),while the standard rain estimates are evaluated usingthe Z–R relationship of Eq. (16). Both algorithms usethe attenuation corrected radar parameters as determinedby the corresponding polarimetric and standard meth-ods. The one standard deviation error bounds of thepolarimetric retrieval are overlaid on the plot. The rainestimation relative error variance (0.13) of Eq. (14) wasderived from the corresponding error variances of AH

and Nw estimates as described in section 3a. The rain-rate values calculated from coincident 3-min raindropsize spectra for the two example cases are also presentedin the plot. Observe that the divergence between po-larimetric and standard rain retrieval is consistent withthe corresponding differences shown in ZH attenuationcorrection. However, note that those differences can bemore significant in rain rates due to the nonlinear trans-formation. Nevertheless, as in ZH attenuation correctionthe standard Z–R rain profile is consistently within theerror bound of the polarimetric rain profile. Althoughno gauge or disdrometer data are available at far rangesto verify those estimates, at the short range (;5 km)we observe that the polarimetric retrieval has closeragreement with the observed rain-rate value, which isalso within its error bounds. Ongoing research based onrecent field experiments that provided joint S- and X-band polarimetric measurements would support inves-tigation of XPOL retrievals at further ranges (http://www.joss.ucar.edu/ihop).


FIG. 7. Rain-rate profiles corresponding to the ray profiles shown in Fig. 6, that is, left (right) frames correspondsto Fig. 6 left (right). The rain-rate estimates are derived from the combined AH and Nw [Eq. (14)] algorithm and thestandard Z–R approach [Eq. (16)]. The shaded region denotes uncertainty due to AH and Nw estimation.

4. Comparison of XPOL-derived rain rates withground-based data

The objective in this section is to assess the high-frequency (1–3-min temporal and 150-m spatial reso-lution) estimation of rain rates and raindrop size distri-bution parameters (Nw) by the polarimetric precipitationretrieval approach. In terms of rain rates, we comparethe multiparameter polarimetric algorithm [Eq. (15)]with the (Nw, AH)-based [Eq. (14)] and equilibrium dropshape KDP-based [Eq. (14) with AH derived from KDP

using Eq. (12)] estimators, as well as rain-rate estimatesderived from standard [nonpolarimetric, Eq. (16)] radarmeasurements. The rain estimation algorithm parame-ters are shown in Table 3 and as discussed in a previoussection were determined from theoretical calculationsbased on 3-min measured raindrop spectra.

Figure 8 shows uncertainty statistics of the differentestimators applied to radar parameters derived from bothXPOL observations (Fig. 8, top) and measured raindropspectra (Fig. 8, bottom), using as reference the rain ratescalculated from the measured raindrop spectra. The sta-tistics presented here are the mean and standard devi-ation of the relative difference («) defined as

R 2 Rdsd est« 5 , (26)Rdsd

where Rdsd is the rain rate (mm h21) calculated from themeasured 3-min raindrop spectra, and Rest is the rainfallrate (mm h21) estimated from the different radar al-gorithms. The statistics are presented for varying KDP

threshold values representing different levels of rainfallintensity. Figure 8 (left) shows the mean relative dif-ference (MRD), while Fig. 8 (right) shows the standarddeviation. It is shown that the estimators’ MRD is con-

sistently small (within 5%) for the whole range of KDP

thresholds. Application to XPOL measurements,though, shows that for some estimators, MRD becomesKDP (or rainfall intensity) magnitude dependent; in par-ticular the (Nw, AH)-based retrieval where MRD varieswithin 15%. The best estimates in terms of MRD areshown to be the ones retrieved from the multiparameterand KDP-based estimators, while the standard Z–R re-lationship seems to consistently underestimate rainfall.We note that XPOL measurements are unbiased withrespect to the radar parameters derived from raindropspectra (see Fig. 9) and as shown in the lower-left ofFig. 8, the Z–R estimator has very low bias in terms ofthe DSD calculated radar parameters and rain rates.Consequently, an explanation of this underestimation isthe imperfect standard ZH-based attenuation correction,which was shown to be quite different from the atten-uation correction derived based on polarimetric mea-surements (FDP constraint). In terms of STD we showthat the (Nw, AH)-based and KDP-based estimator uncer-tainties strongly depend on the magnitude of KDP. Thisis expected, since both estimators are very sensitive tothe uncertainty in KDP estimation propagated from noisein FDP data. In particular, for the (Nw, AH)-based al-gorithm, the STD in DSD calculated radar and rainfallparameters drops from about 40% at KDP threshold of0.18 km21 to 15% at KDP values greater than 0.58 km21.This effect is more significant (67% decrease in STD)when the estimator is applied on XPOL measurements.This is expected because radar-based retrievals are af-fected by measurements noise in radar parameters, inaddition to the estimator uncertainty. In particular, FDP

measurement noise decreases relative to the increase ofrainfall intensity (i.e., KDP). The multiparameter and


FIG. 8. Uncertainty statistics (mean and std dev) of different polarimetric algorithms and thestandard Z–R estimator based on (top) XPOL observations and (bottom) raindrop spectra mea-surements for various KDP thresholds. (left) For the means ratio; (right) dR is the difference betweenthe DSD-based and a given estimate, and R is estimated from the DSD.

FIG. 9. Scatterplot of horizontal polarization reflectivity (ZH) ob-served by XPOL and calculated by coincident measured raindropspectra.

standard Z–R estimators’ uncertainties are less sensitiveto the KDP threshold, which is shown consistently in boththe DSD calculated and XPOL measured radar param-eters. Note that the multiparameter estimator is asso-ciated with about 38% (70%) less standard deviationestimate (STDE) than the standard Z–R estimator whenapplied to XPOL (DSD calculated) radar parameters.

Figure 10 shows scatterplots of instantaneous mul-tiparameter and standard Z–R estimates versus rain ratescalculated from corresponding 3-min raindrop spectra,for algorithms applied to XPOL measured and raindropspectra calculated radar parameters. The multiparameterretrieval is associated with less scatter (higher corre-lation) in the DSD-based estimate–rain-rate comparison.Nevertheless, the decrease (increase) in scatter (corre-lation) from standard Z–R to multiparameter estimatesis not as significant in the XPOL measurements, whichis consistent with the STDE error statistics presentedpreviously in this section. Figure 11 shows time seriesplots of coincident DSD calculated versus XPOL atten-uation corrected ZH and retrieved Nw values along with


FIG. 10. Scatterplots of rainfall rates calculated from raindrop spectra vs coincident rain-rateestimates determined based on polarimetric (ZH, ZDR, Nw) and standard (ZH) parameters derivedfrom (left) XPOL observations and (right) raindrop spectra.

rain rates derived from the multiparameter and standardZ–R methods for a 5-h storm event passing over thePOSS disdrometer. There is good agreement betweendisdrometer and XPOL reflectivity values. The multi-parameter and standard Z–R rain rates determined fromthe same reflectivity values seem to perform similarly,but at high intensities (;2 h) the multiparameter tech-nique estimates are closer to the disdrometer rain rates.The retrieved Nw values are within 2.5 times the dis-drometer derived values, which is nearly one standarddeviation of the relative Nw retrieval error (2-km inter-vals were used in this case). The correlation of disdro-meter and retrieved Nw values is low, which could bedue to random effects associated with the retrieval errorand spatial resolution. Alternatively, we compare thefrequency histograms of the retrieved Nw values withthe corresponding values derived from the measuredraindrop spectra for all coincident XPOL–disdrometerpairs (see Fig. 12). It is apparent that the XPOL esti-mated Nw values span a larger range than those calcu-lated from disdrometer measurements. This is anotherindication of the significant random effects on the re-trieval associated with measurement noise in the XPOLdata. Nevertheless, we see no systematic difference inthe two histograms, and the bulk of XPOL retrieved Nw

values are within the ones determined from disdrometermeasurements.

Figure 13 shows scatterplots of XPOL instantaneousrainfall-rate estimates versus 3-min rainfall rates mea-sured by three clusters of dual rain gauge platformslocated at about 10 km from XPOL. Figure 13 (left andright) show the polarimetric and standard Z–R retrievals,respectively. The figure also shows histograms of theNw estimated by the polarimetric algorithm (at right).The comparison between polarimetric and standard Z–R approach is consistent with what we discussed earlierin this section; that is, the scatter decreases in polari-metric retrieval, while the standard Z–R estimator isslightly biased with respect to gauge rainfall. The overallmean and standard deviation of the relative differencesare 24% (215%) and 53% (73%) for the polarimetric(standard Z–R) estimates, while correlation (r2) is 0.70and 0.51 for the multiparameter and standard Z–R, ac-cordingly. These differences reduce significantly atcoarser spatial and temporal scales (Matrosov et al.2002). The DSD intercept parameter (Nw) values eval-uated over the gauge locations are in the same range asin Fig. 12, with a mode around 2 3 106. Comparisonof cumulative rainfall for a 5-h storm event over thethree gauge clusters is presented in Fig. 14. Consistently


FIG. 11. Time series of reflectivity, Nw, and rainfall rates determinedfrom POSS-measured raindrop spectra vs XPOL retrievals for a 5-hstorm event 22 Oct 2001.

FIG. 12. Frequency histogram of the normalized gamma DSD mod-el intercept parameter (Nw) values determined from XPOL KDP-basedattenuation correction algorithm and from coincident measured rain-drop spectra.

to the statistics shown in this section, the multiparametercumulative values correlate better to gauge rainfall thanthe standard Z–R estimates for all gauge clusters.

It is expected that local (measurement) random errorsat gauge locations associated with the discrete time sam-pling, the wind effects, and the area-point representa-tiveness problem can introduce discrepancies in arearainfall estimation by gauges (Ciach and Krajewski1999; Anagnostou et al. 1999; Ciach 2003). Given thesmall size of XPOL cells over the gauges (about 1503 150 m2) and the nature of the rainfall regime in Iowa(Krajewski et al. 2003; Miriovsky et al. 2004) we con-sidered only the local random error effect in XPOL–gauge difference statistics. After Ciach (2003), the stan-dard deviation (sm, mm h21) of the relative gauge mea-surement error at 3-min accumulation scale can be rep-resented using the following formula:

s (R ) 5 0.02 1 0.4/R .m G G (27)

Consequently, every 3-min gauge rain rate RG associatedwith a standard error sm can be used to statisticallyevaluate XPOL rain estimates as follows. We determinethe relative difference («) between XPOL estimate andgauge rain rate as in Eq. (26), and then compute theratio of « to sm. The cumulative probability of «/sm

calculated for two XPOL estimators (multiparameterand standard Z–R) are presented in Fig. 15. The figureillustrates several important points. First, radar-basedestimates are clearly less accurate than the ground-basedreference at the given time and space scales. Second,the multiparameter method seems to consistently out-perform the single-parameter method. For example, ifwe consider error ratios of 4, the Z–R method leads to50% of estimates with errors smaller than that while themultiparameter methods result in over 60% such esti-mates. Considering other sources of uncertainty, suchas the horizontal and vertical scale mismatches, wouldsomewhat lower the presented error statistics for bothretrievals, but we prefer to avoid speculating on therespective amounts.

5. Conclusions

We presented an experimental investigation of a rain-fall estimation algorithm for X-band polarimetric radarmeasurements. In developing the algorithm, we ad-dressed estimation of specific attenuation jointly withretrieving the intercept parameter (Nw) of the ‘‘normal-ized’’ gamma DSD model. This was achieved in a man-ner similar to the profiling algorithm presented by Tes-tud et al. (2000), where differential propagation phaseshift and attenuated reflectivity are combined withinsegments along a radar ray to retrieve the specific at-tenuation profile, and a mean Nw value along each seg-


FIG. 13. Scatterplots of gauge 3-min-averaged rainfall rate vs rain rate estimated based on (left) XPOL polarimetricand (middle) standard Z–R algorithms for the three rain gauge clusters. (right) Frequency histograms of the normalizedgamma DSD model intercept parameter (Nw) determined over the gauge locations.

ment. The differential reflectivity values were subse-quently corrected via estimation of the differential at-tenuation profile from the specific attenuation and Nw

retrieved profiles. Several algorithms for rainfall esti-mation were investigated, including power-law algo-rithms relating rainfall rate to 1) specific attenuation andNw; 2) specific attenuation, differential attenuation, andspecific differential phase shift (multiparameter); 3) spe-cific differential phase shift alone; and 4) the standardreflectivity–rainfall-rate relationship. It was shown thatthe Nw retrieval, attenuation correction, and rainfall al-gorithm parameter values are sensitive to the assumedlaw for raindrop shape–size relationship. Consequently,uncertainty exists due to the natural variability of rain-drop oblateness, which can deviate from the assumedrelationship. The proposed algorithm addresses theproblem by selecting the raindrop oblateness model forwhich a measured FDP profile matches best with theprofile determined from the specific attenuation and Nw

retrievals. Using an equilibrium shape–size relation

would result in biased ZH measurements with respect todisdrometer observations.

The field experiment on which this study is basedemployed an X-band polarimetric radar, XPOL, col-lecting data over densely instrumented sites with threedisdrometers and several tipping-bucket dual-gaugeplatforms. We collected data for the months of Octoberand November 2001. The observed rainfall eventsranged in intensity from moderate stratiform precipi-tation to high-intensity (.50 mm h21) convective raincells. The XPOL reflectivity calibration bias was de-termined to be about 1 dB based on reflectivity datadetermined from coincident 3-min averaged raindropspectra. The differential reflectivity was evaluated usingvertical pointing measurements in a low-intensity strat-iform event, showing a bias less than 0.3 dB. The bias-adjusted XPOL measurements were subsequently testedfor physical consistency using corresponding radar pa-rameters derived from coincidentally measured raindropspectra.


FIG. 14. Cumulative rainfall plots of gauge rainfall vs XPOL mul-tiparameter and standard Z–R retrievals for a 5-h storm event 22 Oct2001 over three gauge clusters.

FIG. 15. Cumulative probabilities of «/sm ratios for themultiparameter and standard Z–R estimators.

The attenuation correction was shown to be associ-ated with unbiased Nw retrievals with respect to Nw val-ues determined from coincident raindrop spectra. Theattenuation correction based on profiles of only reflec-tivity measurements was shown to diverge significantlyfrom the corresponding polarimetric-based corrections.We investigated the rain retrieval algorithms usingmatched pairs of instantaneous high-resolution XPOL

observations and rain rates from 3-min averaged rain-drop spectra and rain gauge measurements. Our inves-tigations show that the multiparameter (ZH, ZDR, ZDP)retrieval has the optimum rain estimation performancewith about 40% relative difference standard deviation.For comparison, the case-tuned reflectivity–rainfall rate(Z–R) relationship gave about 65% relative differencestandard deviation. Here we show that the systematicdifference is low (;3% overestimation) and nearly in-dependent of rainfall intensity for the multiparameteralgorithm, while for the standard Z–R it varied from10% underestimation to 3% overestimation (13%change).

Further research investigations are under way, usinga large number of acquired field data, including jointX-band and S-band polarimetric radar measurementsfrom the International H2O Project. Those studies areaimed at 1) continuing the investigation on specific at-tenuation, differential attenuation, and Nw profile re-trieval at X-band by further exploring the effect of rain-drop oblateness relation; 2) developing an X-band radarretrieval scheme for precipitation fluxes of different pre-cipitation phases (including snow and mixed phase); and3) developing a precipitation classification algorithm forX-band measurements.

Acknowledgments. The study was supported by theNSF Grants EAR00-03054 and EAR00-03046, andIIHR-Hydroscience and Engineering of The Universityof Iowa. B. Miriovsky was supported by an AMS In-dustry/Government Graduate Fellowship funded by theNSF Division of Atmospheric Sciences. The authorsappreciate expert help of Radoslaw Goska of IIHR withthe graphics. We are indebted to John Hruska, Mary


Ebert, Diana Thrift, Eilleen Eichinger, and Ching-LongLin for allowing us to use their land for instrumentdeployment. We also acknowledge Dr. Fred Ogden(University of Connecticut) for loaning us a JW dis-drometer, McGill University Radar Observatory forloaning and deploying the POSS, and Dr. DominiqueCreutin for taking care of the optical disdrometers. Ra-dar measurements were obtained with the mobile X-band Dual-Polarization and Doppler radar (XPOL)owned by the Institute for Environmental Research andSustainable Development, National Observatory of Ath-ens, Greece.

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high-resolution rainfall estimation from x-band ...friedrik/experiments/...speciﬁcations of the...

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