Adv. Radio Sci., 8, 279–284, 2010www.adv-radio-sci.net/8/279/2010/doi:10.5194/ars-8-279-2010© Author(s) 2010. CC Attribution 3.0 License.

Advances inRadio Science

Attenuation correction for a high-resolution polarimetric X-bandweather radar

T. Otto and H. W. J. Russchenberg

Remote Sensing of the Environment, International Research Centre for Telecommunications and Radar (IRCTR), Departmentof Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands

Abstract. In 2007, IRCTR (Delft University of Technol-ogy) installed a new polarimetric X-band LFMCW radar(IDRA) at the meteorological observation site of Cabauw,The Netherlands. It provides plan position indicators (PPI) ata fixed elevation with a high range resolution of either 3 m or30 m at a maximum observation range of 1.5 km and 15 km,respectively. IDRA aims to monitor precipitation events forthe long-term analysis of the hydrological cycle. Due to thespecifications of IDRA, the spatial and temporal variabilityof a large range of rainfall intensities (from drizzle to heavyconvective rain) can be studied.

Even though the usual observation range of IDRA is lim-ited to 15 km, attenuation due to precipitation can be largeenough to seriously affect the measurements. In this contri-bution we evaluate the application of a combined method tocorrect for the specific and the differential attenuation, andin the same vein estimate the parameters of the raindrop-sizedistribution. The estimated attenuations are compared to aphase constraint attenuation correction method.

1 Introduction

Weather radars are a widely used measurement device toobserve the spatial distribution and the temporal evolutionof precipitation. In Europe over 150 operational C-bandweather radars are employed by the meteorological ser-vices1. Nowadays, the operational weather radar networksare complemented by compact X-band systems as gap fillers,McLaughlin et al. (2009). However, the attenuation of mi-crowaves by precipitation is stronger at X-band than at C-

Correspondence to:T. Otto(t.otto@tudelft.nl)

1OPERA – Operational programme for the exchange of weatherradar information, http://www.knmi.nl/opera

band. Radar measurements must be corrected for attenu-ation before they are used for a quantitative determinationof precipitation parameters. A first formulation of attenu-ation correction for weather radar measurements was pro-vided by Hitschfeld and Bordan (1954). However, withoutconstraining the path-integrated attenuation (PIA) by inde-pendent measurements, e.g. rain gauges or microwave links,the attenuation correction is unstable. Polarimetric weatherradars operating at linear horizontal/vertical polarisation ba-sis have the capability to measure the differential propaga-tion phase that is a forward scattering effect like attenuation.Scattering computations show that the differential propaga-tion phase is linearly related to the attenuation, Holt (1988),and can those be used to provide an estimate of the PIA.However, the relation between the differential propagationphase and the attenuation depends on the microphysics ofthe precipitation, Bringi et al. (1990). Testud et al. (2000) in-troduced an algorithm that uses the differential propagationphase to estimate the PIA that is subsequently distributedamong the range bins weighted by the reflectivity. Addi-tionally, self-consistency among the weather radar observ-ables involved in the attenuation correction may be imposedin order to account for the variability of the relation amongthe differential propagation phase and the attenuation, Bringiet al. (2001), Gorgucci and Baldini (2007).

Attenuation correction is also a prerequisite for IDRA,the polarimetric, horizontally scanning X-band weather radarof IRCTR installed at the meteorological observatory atCabauw2, The Netherlands. One purpose of IDRA is thelong-term monitoring of microphysics of precipitation. Themethod proposed in Chandra et al. (1990) is able to jointlyperform the attenuation correction and the raindrop-size dis-tribution retrieval for rain. It was successfully applied to C-band weather radar data. The purpose of this contribution isthe evaluation of this method for X-band weather radar data

2http://www.cesar-database.nl

Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V.

280 T. Otto and H. W. J. Russchenberg: Attenuation correction

Fig. 1. The radar geometry is shown in the upper part of this figure.The lower part shows rayplots of an IDRA measurement (26 May2009, 02:00 UTC) with heavy precipitation leading to a very strongspecific and differential attenuation that deteriorate the measuredreflectivityZhh,att and the differential reflectivityZdr,att (upper tworay plots). The measured differential propagation phase shows theexpected range-cumulative behaviour (ray plot at the bottom).

by applying it to IDRA data. Therefore, the attenuations de-rived by this method are compared to the phase constraint at-tenuation correction method with imposed self-consistency,Gorgucci and Baldini (2007).

2 Basics

The natural variability of rainfall can be described by thethree-parameter raindrop-size distribution (RDSD) that nor-malised with respect to the liquid water content can be writ-ten as, Bringi and Chandrasekar (2001),

N(D) = Nwf (µ)

(D

D0

)µ

e−(3.67+µ) D

D0 (1)

with

f (µ) =6

3.674

(3.67+µ)µ+4

0(µ+4)(2)

whereD is the equivolumetric raindrop diameter,D0 is themedian volume diameter,Nw is the concentration, andµ isthe shape parameter.

The measurements of an homogeneous ensemble of rain-drops by polarimetric weather radars can be expressed in

terms of the RDSD, and the scattering amplitudes of the rain-drops as follows:

Zhh= 10log10

(λ4

π5|K|2

∫D

σhh(D)N(D)dD

)(3)

Zdr = 10log10

∫D

σhh(D)(

DD0

)µ

e−(3.67+µ) D

D0 dD∫D

σvv(D)(

DD0

)µ

e−(3.67+µ) D

D0 dD

(4)

K1−waydp =

180

πλ

∫D

<[fhh(D)−fvv(D)]N(D)dD. (5)

The intrinsic weather radar observables in Eqs. (3) to (5) rep-resent the co-polarised reflectivity at horizontal polarisationZhh (dBZ), the differential reflectivityZdr (dB), and the spe-cific differential phaseK1−way

dp (◦/km) which is the rangederivative of the differential propagation phase9dp. Further-more,λ is the wavelength,|K|

2 is a dielectric factor,σhh/vvare the radar cross sections, andfhh/vv are the forward scat-tering amplitudes of the raindrops at linear horizontal andlinear vertical polarisations. For the purpose of this contribu-tion, numerical values of the radar cross sections and the for-ward scattering amplitudes of raindrops have been computedfor a frequency of 9.475 GHz (IDRA) by the Fredholm Inte-gral Method, Holt et al. (1978), assuming dielectric spheroidswith the axis ratio given by Illingworth et al. (2000), andthe complex permittivity of water at a temperature of 10◦C,Liebe et al. (1991).

The propagation of electromagnetic waves through rainleads to attenuation of the measured reflectivity and the dif-ferential reflectivity, Fig. 1:

Zhh,att(rn) = Zhh(rn)−2∫ rn−1

r1

α1−wayhh (r)dr (6)

Zdr,att(rn) = Zdr(rn)−2∫ rn−1

r1

α1−wayh−v (r)dr. (7)

The specific attenuationα1−wayhh (dB/km) and the differential

attenuationα1−wayh−v (dB/km) in the equations above are given

by

α1−wayhh = 8.686λ

∫D

=[fhh(D)]N(D)dD (8)

and

α1−wayh−v = 8.686λ

∫D

=[fhh(D)−fvv(D)]N(D)dD. (9)

A method to correct polarimetric weather radar measure-ments for attenuation has been introduced by Chandra et al.(1990). It is based on the estimation of the RDSD parame-ters that are subsequently used to determine the correspond-ing attenuations by scattering computations. The block di-agram of this method, shown in Fig. 2, is explained next.

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T. Otto and H. W. J. Russchenberg: Attenuation correction 281

Fig. 2. Block diagram of the method of Chandra et al. (1990) toextract the RDSD parameters, and, subsequently, to correct for at-tenuation.

A measured ray of the integrated weather radar observablesZhh,att, Zdr,att and 9dp, such as the one exemplary shownin Fig. 1, is divided into ray segments satisfying19

ra :rbdp =

9dp(rb)−9dp(ra) ≥ 5◦. A precondition for the applicationof this method is a given raindrop shape and a temperatureto calculate the complex permittivity of water. Starting atclose range to the radar, i.e.ra = r1, Fig. 1, the median vol-ume diameterDra :rb

0 is estimated via pre-calculated look-uptables from the measured differential reflectivityZ

ra :rbdr,att, as-

suming an initial shape parameterµra :rb = 0 (blue curve inFig. 3). After determiningN ra :rb

w again via pre-calculatedlook-up tables (red curve in Fig. 3), scattering computationswith the determined RDSD parameters are carried out in or-der to compute the expected differential propagation phase19

ra :rbdp,c for the ray segment. The optimum shape param-

eter µra :rb for the ray segment is found by minimising it-eratively the difference among the measured and the com-puted differential propagation phase of the ray segment, i.e.

min(|19

ra :rbdp,c −19

ra :rbdp |

). The range of possible shape pa-

0 0.5 1 1.5 2 2.50

1

2

3

4

D0 in mm

Zdr

in d

B

0 0.5 1 1.5 2 2.5−60

−40

−20

0

20

Zhhno

rm =

10l

og10

( z hh

/Nw

) in

dB

(mm

7 )

Fig. 3. Results of scattering computations to relate the differentialreflectivity (blue curve) and the normalised reflectivity at horizontalpolarisation (red curve) to the median volume diameter. The shapeparameter isµ = 0, and the raindrop axis ratio of Illingworth et al.(2000) was used.

rameters was limited within−2 ≤ µra :rb ≤ 10. Once theRDSD is characterised in this way, scattering computationsare carried out again in order to estimate the attenuations,Eqs. (8) and (9), for the ray segment. After correctingZ

ra :rNhh,att

andZra :rNdr,att for the attenuation, the method is applied to the

adjacent ray segment, i.e.ra = rb+1.This method is only suited for rain, i.e. it is likely to fail in

the presence of ground clutter or other hydrometeors such asgraupel, hail or snow. Furthermore, Otto et al. (2009) showedthat the application of this method is limited for IDRA to0.5 dB≤ Zdr ≤ 2.7 dB in order to estimate the median volumediameter within±0.15 mm. Thus, the method is not suitedfor light rain (rain rates<3 mm/h) as well as for strong rain(rain rates>25 mm/h). In the case of strong rain, scatter-ing computations show that the attenuation at X-band can bealternatively estimated by

αhh(dB/km) = 0.25Kdp(◦/km) (10)

and

αh−v(dB/km) = 0.05Kdp(◦/km). (11)

However, Eqs. (10) and (11) introduce uncertainties due tothe variability of the microphysics of precipitation, Bringiet al. (1990), and due to the estimation ofKdp, Georgiou et al.(2009).

For each ray segment the RDSD is estimated from at-tenuated reflectivity and differential reflectivity measure-ments which means that the median volume diameter willbe underestimated, blue curve in Fig. 3. This in turn re-sults in an underestimation ofZnorm

hh , red curve in Fig. 3,and an overestimation of the concentration sinceNw =

10(Zhh,att−Znormhh )/10(mm−1 m−3). At X-band this may yield

for µ = 0 to an underestimation of 0.3 mm forD0, and an

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282 T. Otto and H. W. J. Russchenberg: Attenuation correctionOtto and Russchenberg: Attenuation correction 5

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar Zhh

(dBZ)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

−20

−10

0

10

20

30

40

50

(a) Zhh,att (dBZ)

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar Zdr

(dB)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

−2

−1

0

1

2

3

4

(b) Zdr,att (dB)

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar LDR (dB)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

−30

−25

−20

−15

−10

−5

0

(c) LDR (dB)

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar Ψdp

(degrees)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

−20

−15

−10

−5

0

5

10

15

20

(d) Ψdp (◦)

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar Ahh, RDSD2−way (dB)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

0

0.5

1

1.5

2

2.5

3

3.5

(e) A2−way

hh,RDSD (dB)

W−E Distance from Radar (km)

S−

N D

ista

nce

from

Rad

ar (

km)

R2009−11−14/9−0−0OPar Ah−v, RDSD2−way (dB)

−15 −10 −5 0 5 10 15−15

−10

−5

0

5

10

15

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(f) A2−way

h−v,RDSD (dB)

Fig. 4. IDRA precipitation measurements from the 14th of November 2009 at 9:00UTC. Shown are PPI’s of (a) the reflectivityZhh,att

(dBZ), (b) the differential reflectivityZdr,att (dB), (c) the linear depolarisation ratioLDR (dB) and (d) the differential propagation phaseΨdp (◦). (e) and (f) show the 2-way cumulative attenuation at horizontal polarisation and the differential attenuation, respectively, derivedby the method of Chandra et al. (1990).

constraint method, followed by the estimation of the RDSDparameters. However it must be stressed, that the results ofthe comparison of the attenuation correction methods in thiscontribution can not be regarded as absolute. As a next step,we shall take advantage of the operational C-band weatherradar of the Royal Netherlands Meteorological Institute atDe Bilt that is situated in the vicinity of IDRA in a distanceof approximately 25km. The analysis and comparison of si-multaneous measurements of precipitation events shall en-able us to estimate the performance of attenuation correctionmethods.

References

Bringi, V. N. and Chandrasekar, V.: Polarimetric Doppler WeatherRadar, p. 410, Cambridge University Press, 1st edn., 2001.

Bringi, V. N., Chandrasekar, V., Balakrishnan, N., and Zrnic, D. S.:An Examination of Propagation Effects in Rainfall on RadarMeasurements at Microwave Frequencies, J. Atmos. OceanicTechnol., 7, 829 – 840, 1990.

Bringi, V. N., Keenan, T. D., and Chandrasekar, V.: Correcting C-Band Radar Reflectivity and Differential Reflectivity Data forRain Attenuation: A Self-Consistent Method With Constraints,IEEE Trans. Geosci. Remote Sens., 39, 1906 – 1915, 2001.

Chandra, M., Schroth, A., and Luneburg, E.: The Influence of Rain-dropsize Distribution on the Determination of Microwave Propa-

gation Properties by Polarimetric Radars, in: Geoscience and Re-mote Sensing Symposium, IGARSS 90, pp. 1041 – 1045, 1990.

Georgiou, S., Figueras i Ventura, J., and Unal, C. M. H.: Estima-tion of differential and specific differential phase with the IDRAX-band Doppler polarimetric radar for improving rain rate re-trieval, in: Proceedings of the 8th International Symposium oftropospheric profiling, Delft, The Netherlands, ISBN 978-90-6960-233-2, edited by Apituley, A., Russchenberg, H. W. J., andMonna, W. A. A., 2009.

Gorgucci, E. and Baldini, L.: Attenuation and Differential Atten-uation Correction of C-Band Radar Observations Using a FullySelf-Consistent Methodology, IEEE Geosci. Remote Sens. Lett.,4, 326 – 330, 2007.

Hitschfeld, W. and Bordan, J.: Errors inherent in the radar measure-ment of rainfall at attenuating wavelengths, J. Meteorol., 11, 58– 67, 1954.

Holt, A. R.: Extraction of differential propagation phase from datafrom S-band circularly polarized radars, Electron. Lett, 24, 1241– 1244, 1988.

Holt, A. R., Uzunoglu, N. K., and Evans, B. G.: An IntegralEquation Solution to the Scattering of Electromagnetic Radia-tion by Dielectric Spheroids and Ellipsoids, IEEE Trans. Anten-nas Propag., AP-26, 706 – 712, 1978.

Illingworth, A. J., Blackman, T. M., and Goddard, J. W. F.: Im-proved rainfall estimates in convective storms using polarisationdiversity radar, Hydrol. Earth Syst. Sci., 4, 555 – 563, 2000.

Liebe, H. J., Hufford, G. A., and Manabe, T.: A model for the com-plex permittivity of water at frequencies below 1 THz, Int. J.Infrared. Milli., 12, 659 – 675, 1991.

Fig. 4. IDRA precipitation measurements from the 14 November 2009 at 09:00 UTC. Shown are PPI’s of(a) the reflectivityZhh,att (dBZ),(b) the differential reflectivityZdr,att (dB), (c) the linear depolarisation ratio LDR (dB) and(d) the differential propagation phase9dp (◦). (e)and(f) show the 2-way cumulative attenuation at horizontal polarisation and the differential attenuation, respectively, derived by the methodof Chandra et al. (1990).

overestimation ofNw up to a factor of 100. For the compu-tation of the attenuations, Eqs. (8) and (9), this may yieldin turn to an over- or underestimation. In any case, theRDSD parameters are estimated again after the first run ofthis method from the attenuation corrected reflectivities. Thepresented method is applied in the next section to IDRA mea-surements in order to assess the accuracy of the estimatedattenuations. Therefore, they are compared to the attenua-tions derived by the phase constraint method with imposedself-consistency of Gorgucci and Baldini (2007).

3 Application to IDRA data

Figure 4 shows a precipitation measurement of IDRA fromthe 14 November 2009, 09:00 UTC. IDRA is located inthe centre of these plan-position indicators (PPI), that fromFig. 4a to d illustrate the measured weather radar observablesreflectivityZhh,att (dBZ), differential reflectivityZdr,att (dB),linear depolarisation ratio LDR (dB), and differential prop-agation phase9dp (◦). The presence of propagation effectsis not evident in the reflectivity and the differential reflectiv-ity measurement. However, the measured differential phase,

Fig. 4d, shows cumulative values of up to 20◦ over the rangeof 15 km in some sectors.

Using the measuredZhh,att, Zdr,att and9dp, the attenua-tions were determined by the method of Chandra et al. (1990)introduced in the preceding section. The resulting cumula-tive attenuation at horizontal polarisation and the differentialattenuation are shown in Fig. 4e and f.

For a comparison, the attenuations were also derived bythe method outlined in Gorgucci and Baldini (2007). Thismethod relies on a first estimation of the attenuations by theapplication of the phase constraint method of Testud et al.(2000). Then the self-consistency equations

αhh= a1zb1hhz

c1drK

d1dp (12)

and

αh−v = a2zb2hhz

c2drK

d2dp (13)

are imposed as outlined in Gorgucci and Baldini (2007), re-sulting in an adjustment of the estimated attenuations. Thereflectivitieszhh andzdr in Eqs. (12) and (13) are in linearunits, and the coefficients of these self-consistency equationsfor the frequency of IDRA can be found in Table 1. In thefollowing comparison of the attenuations, the subscriptSCPC

Adv. Radio Sci., 8, 279–284, 2010 www.adv-radio-sci.net/8/279/2010/

T. Otto and H. W. J. Russchenberg: Attenuation correction 283

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

1.2

1.4

αhh, RDSD1−way (dB/km)

α hh, S

CP

C1−

way

(dB

/km

)

0 0.05 0.1 0.150

0.05

0.1

0.15

αh−v, RDSD1−way (dB/km)

α h−v,

SC

PC

1−w

ay (

dB/k

m)

Fig. 5. Scatter plots comparing(a) the specific attenuations at hor-

izontal polarisationα1−wayhh , and (b) the differential attenuations

α1−wayh−v estimated by the methods of Chandra et al. (1990) (RDSD)

and Gorgucci and Baldini (2007) (SCPC) for 35317 range bins oftwo PPI’s measured by IDRA. The dashed black line correspondsto x = y. The red line is a power-law fit.

denotes attenuations derived by the self-consistency methodof Gorgucci and Baldini (2007), and the subscriptRDSD de-notes attenuations derived by the method of Chandra et al.(1990).

Figure 5 shows two scatter plots comparing the attenua-tionsα

1−wayhh andα

1−wayh−v estimated by the two methods pre-

sented above from IDRA data. The data comprise 35 317range bins from two PPI’s measured the 25 May 2009,20:23 UTC, and the 14 November 2009, 09:00 UTC, Fig. 4.The red lines in the scatter plots are power law fitsy = mxn

to the data withmhh = 1, nhh = 0.67, andmh−v = 0.22,nh−v = 0.58. The general tendency shows that for smallattenuationsα1−way

hh < 1.1 dB/km andα1−wayh−v < 0.03 dB/km,

the RDSD method is underestimating the attenuations com-pared to SCPC method, whereas larger attenuations are over-estimated. This non-linear correlation between the estimatedattenuations that is most notably in Fig. 5b may be attributedto the uncertainties introduced by estimating the RDSD pa-

Table 1. Coefficients for the self-consistency Eqs. (12) and (13)derived for a frequency of 9.475 GHz for a set of 1500 normalisedraindrop-size distributions with varyingNw, D0, µ, raindrop axisratios and temperatures.

a1 b1 c1 d14.95×10−3 0.463 −1.321 0.539

a2 b2 c2 d27.58×10−4 0.378 0.416 0.64

rameters from attenuated reflectivities. Depending on theactual values of the reflectivities, the resulting opposite er-rors ofD0 andNw do show non-linearities, Fig. 3. One maythink of additional iterations within the RDSD method to im-prove the estimated attenuations. However, this would yieldan increase of the processing time. Instead, at X-band it issuggested to perform the attenuation correction prior to theestimation of the RDSD parameters.

4 Conclusions

The purpose of this contribution was the evaluation of amethod to estimate the RDSD parameters and in the samevein to perform a correction for attenuation for polarimet-ric weather radar data at X-band, Chandra et al. (1990).The focus was laid on the estimated attenuations by com-paring them to a phase-constraint attenuation correctionmethod with imposed self-consistency, Gorgucci and Bal-dini (2007). Small attenuations were underestimated by theRDSD method compared to the SCPC method whereas largeattenuations were overestimated by the RDSD method. Theattenuations estimated by the RDSD method result from scat-tering computations with RDSD parameters that are esti-mated from attenuated reflectivities. This may result in anunderestimation of the median volume diameterD0 but anoverestimation of the concentrationNw that may explain theobserved deviations of the estimated attenuations. Since theRDSD method is only applicable for a limited differential re-flectivity range, no attenuation estimate is provided for weakand for strong rain. For X-band, this suggests to apply the at-tenuation correction and the RDSD estimation separately, i.e.first correct the reflectivities for attenuation using a phase-constraint method, followed by the estimation of the RDSDparameters. However it must be stressed, that the results ofthe comparison of the attenuation correction methods in thiscontribution can not be regarded as absolute. As a next step,we shall take advantage of the operational C-band weatherradar of the Royal Netherlands Meteorological Institute at DeBilt that is situated in the vicinity of IDRA in a distance ofapproximately 25 km. The analysis and comparison of simul-taneous measurements of precipitation events shall enable usto estimate the performance of attenuation correction meth-ods.

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284 T. Otto and H. W. J. Russchenberg: Attenuation correction

References

Bringi, V. N. and Chandrasekar, V.: Polarimetric Doppler WeatherRadar, p. 410, Cambridge University Press, 1st edn., 2001.

Bringi, V. N., Chandrasekar, V., Balakrishnan, N., and Zrnic, D. S.:An Examination of Propagation Effects in Rainfall on RadarMeasurements at Microwave Frequencies, J. Atmos. OceanicTechnol., 7, 829–840, 1990.

Bringi, V. N., Keenan, T. D., and Chandrasekar, V.: Correcting C-Band Radar Reflectivity and Differential Reflectivity Data forRain Attenuation: A Self-Consistent Method With Constraints,IEEE Trans. Geosci. Remote Sens., 39, 1906–1915, 2001.

Chandra, M., Schroth, A., and Luneburg, E.: The Influence of Rain-dropsize Distribution on the Determination of Microwave Prop-agation Properties by Polarimetric Radars, in: Geoscience andRemote Sensing Symposium, IGARSS 90, 1041–1045, 1990.

Georgiou, S., Figueras i Ventura, J., and Unal, C. M. H.: Estima-tion of differential and specific differential phase with the IDRAX-band Doppler polarimetric radar for improving rain rate re-trieval, in: Proceedings of the 8th International Symposium oftropospheric profiling, Delft, The Netherlands, ISBN 978-90-6960-233-2, edited by: Apituley, A., Russchenberg, H. W. J.,and Monna, W. A. A., 2009.

Gorgucci, E. and Baldini, L.: Attenuation and Differential Atten-uation Correction of C-Band Radar Observations Using a FullySelf-Consistent Methodology, IEEE Geosci. Remote Sens. Lett.,4, 326–330, 2007.

Hitschfeld, W. and Bordan, J.: Errors inherent in the radar mea-surement of rainfall at attenuating wavelengths, J. Meteorol., 11,58–67, 1954.

Holt, A. R.: Extraction of differential propagation phase fromdata from S-band circularly polarized radars, Electron. Lett., 24,1241–1244, 1988.

Holt, A. R., Uzunoglu, N. K., and Evans, B. G.: An IntegralEquation Solution to the Scattering of Electromagnetic Radia-tion by Dielectric Spheroids and Ellipsoids, IEEE Trans. Anten-nas Propag., AP-26, 706–712, 1978.

Illingworth, A. J., Blackman, T. M., and Goddard, J. W. F.:Improved rainfall estimates in convective storms using polar-isation diversity radar, Hydrol. Earth Syst. Sci., 4, 555–563,doi:10.5194/hess-4-555-2000, 2000.

Liebe, H. J., Hufford, G. A., and Manabe, T.: A model for the com-plex permittivity of water at frequencies below 1 THz, Int. J.Infrared. Milli., 12, 659–675, 1991.

McLaughlin, D. and Coauthors: Short-wavelength technology andthe potential for distributed networks of small radar systems, B.Am. Meteorol. Soc., 90, 1797–1817, 2009.

Otto, T., Figueras i Ventura, J., and Russchenberg, H. W. J.: Drop-size distribution retrieval of precipitation using a high-resolutionpolarimetric X-band weather radar, in: Proceedings of the 8thInternational Symposium of tropospheric profiling, Delft, TheNetherlands, ISBN 978-90-6960-233-2, edited by: Apituley, A.,Russchenberg, H. W. J., and Monna, W. A. A., 2009.

Testud, J., Le Bouar, E., Obligis, E., and Ali-Mehenni, M.:The Rain Profiling Algorithm Applied to Polarimetric WeatherRadar, J. Atmos. Oceanic Technol., 17, 332–356, 2000.

Adv. Radio Sci., 8, 279–284, 2010 www.adv-radio-sci.net/8/279/2010/