• Bertalmio,M.,L. Vese,G. Spario, andS. Osher,2003:Simultaneous structure and texture image inpainting.IEEE Trans. Image Process.,12,882889, https://doi.org/10.1109/TIP.2003.815261.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluestein,H.,M. French,R. Tanamachi,S. Frasier,K. Hardwick,F. Junyent, andA. Pazmany,2007:Close-range observations of tornadoes in supercells made with a dual-polarization, X-band, mobile Doppler radar.Mon. Wea. Rev.,135,15221543, https://doi.org/10.1175/MWR3349.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi,V. N., andV. Chandrasekar,2001: Polarimetric Doppler Weather Radar Principles and Applications. Cambridge University Press, 636 pp.

    • Crossref
    • Export Citation
  • Bringi,V. N.,V. Chandrasekar,N. Balakrishman, andD. Zrnić,1990:An examination of propagation effects in rainfall on radar measurements at microwave frequencies.J. Atmos. Oceanic Technol.,7,829840, https://doi.org/10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi,V. N.,T. Kennan, andV. Chandrasekar,2001:Correcting C-band reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints.IEEE Trans. Geosci. Remote Sens.,39,19061915, https://doi.org/10.1109/36.951081.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey,L.,S. Rutledge,D. Ahijevych, andT. Keenan,2000:Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase.J. Appl. Meteor.,39,14051433, https://doi.org/10.1175/1520-0450(2000)039<1405:CPEICB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar,V.,H. Chen, andB. Philips,2018:Principles of high-resolution radar network for hazard mitigation and disaster management in an urban environment.J. Meteor. Soc. Japan,96A,119139, https://doi.org/10.2151/jmsj.2018-015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Criminisi,A.,P. Perez, andK. Toyama,2004:Region filling and object removal by exemplar-based image inpainting.IEEE Trans. Image Process.,13,12001212, https://doi.org/10.1109/TIP.2004.833105.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Errico,J.,2006: Data interpolation by image inpaiting. Version 1.1.0.0, MATLAB Central File Exchange, http://www.mathworks.com/matlabcentral/fileexchange/4551.

  • Diederich,M.,A. Ryzhkov,C. Simmer,P. Zhang, andS. Trömel,2015:Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part I: Radar calibration and partial beam blockage estimation.J. Hydrometeor.,16,487502, https://doi.org/10.1175/JHM-D-14-0066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doviak,R. J., andD. S. Zrnić,1993: Doppler Radar and Weather Observations. 2nd ed. Academic, 562 pp.

  • Doviak,R. J.,V. Bringi,A. Ryshkov,A. Zahrai, andD. Zrnic,2000:Considerations for polarimetric upgrades to operational WSR-88D radars.J. Atmos. Oceanic Technol.,17,257278, https://doi.org/10.1175/1520-0426(2000)017<0257:CFPUTO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Elad,M.,J. Starck,P. Querre, andD. Donoho,2005:Simultaneous cartoon and texture image inpainting using morphological component analysis.Appl. Comput. Harmonic Anal.,19,340358, https://doi.org/10.1016/j.acha.2005.03.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Figueras i Ventura,J.,2009: Design of a high resolution X-band Doppler polarimetric radar. Ph.D. thesis, Delft University of Technology, 162 pp.

  • Funk,T. W.,K. E. Darmofal,J. D. Kirkpatrick,V. L. Dewald,R. W. Przybylinski,G. K. Schmocker, andY.-J. Lin,1999:Storm reflectivity and mesocyclone evolution associated with the 15 April 1994 squall line over Kentucky and southern Indiana.Wea. Forecasting,14,976993, https://doi.org/10.1175/1520-0434(1999)014<0976:SRAMEA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giangrande,S. E., andA. V. Ryzhkov,2005:Calibration of dual-polarization radar in the presence of partial beam blockage.J. Atmos. Oceanic Technol.,22,11561166, https://doi.org/10.1175/JTECH1766.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giangrande,S. E.,R. McGraw, andL. Lei,2013:An application of linear programming to polarimetric radar differential phase processing.J. Atmos. Oceanic Technol.,30,17161729, https://doi.org/10.1175/JTECH-D-12-00147.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci,E., andV. Chandrasekar,2005:Evaluation of attenuation correction methodology for dual-polarization radars: Application to X-band systems.J. Atmos. Oceanic Technol.,22,11951206, https://doi.org/10.1175/JTECH1763.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci,E.,V. Chandrasekar, andL. Baldini,2006:Correction of X-band radar observations for propagation effects based on the self-consistency principle.J. Atmos. Oceanic Technol.,23,16681681, https://doi.org/10.1175/JTECH1950.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gourley,J. J.,P. Tabary, andJ. P. D. Chatelet,2006:Data quality of the Meteo-France C-band polarimetric radar.J. Atmos. Oceanic Technol.,23,13401356, https://doi.org/10.1175/JTECH1912.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grazioli,J.,M. Schneebeli, andA. Berne,2014:Accuracy of phase-based algorithm for the estimation of the specific differential phase shift using simulated polarimetric weather radar data.IEEE Geosci. Remote Sens. Lett.,11,763767, https://doi.org/10.1109/LGRS.2013.2278620.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang,H.,G. Zhang,K. Zhao, andS. E. Giangrande,2017:A hybrid method to estimate specific differential phase and rainfall with linear programming and physics constraints.IEEE Trans. Geosci. Remote Sens.,55,96111, https://doi.org/10.1109/TGRS.2016.2596295.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hubbert,J., andV. N. Bringi,1995:An iterative filtering technique for the analysis of copolar differential phase and dual-frequency radar measurements.J. Atmos. Oceanic Technol.,12,643648, https://doi.org/10.1175/1520-0426(1995)012<0643:AIFTFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jameson,A. R.,1992:The effect of temperature on attenuation correction schemes in rain using polarization propagation differential phase shift.J. Appl. Meteor.,31,11061118, https://doi.org/10.1175/1520-0450(1992)031<1106:TEOTOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim,D.-S.,M. Maki, andD.-I. Lee,2010:Retrieval of three-dimensional raindrop size distribution using X-band polarimetric radar data.J. Atmos. Oceanic Technol.,27,12651285, https://doi.org/10.1175/2010JTECHA1407.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumjian,M. R., andA. V. Ryzhkov,2008:Polarimetric signatures in supercell thunderstorms.J. Appl. Meteor. Climatol.,47,19401961, https://doi.org/10.1175/2007JAMC1874.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leijnse,H., andCoauthors,2010:Precipitation measurement at CESAR, the Netherlands.J. Hydrometeor.,11,13221329, https://doi.org/10.1175/2010JHM1245.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim,S., andV. Chandrasekar,2016:A robust attenuation correction system for reflectivity and differential reflectivity in weather radars.IEEE Trans. Geosci. Remote Sens.,54,17271737, https://doi.org/10.1109/TGRS.2015.2487984.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim,S.,R. Cifelli,V. Chandrasekar, andS. Y. Matrosov,2013:Precipitation classification and quantification using X-band dual-polarization weather radar: Application in the hydrometeorology testbed.J. Atmos. Oceanic Technol.,30,21082120, https://doi.org/10.1175/JTECH-D-12-00123.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,K. Clark,B. Martner, andA. Tokay,2002:X-band polarimetric radar measurements of rainfall.J. Appl. Meteor.,41,941952, https://doi.org/10.1175/1520-0450(2002)041<0941:XBPRMO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,D. E. Kingsmill,B. E. Martner, andF. M. Ralph,2005:The utility of X-band polarimetric radar for quantitative estimates of rainfall parameters.J. Hydrometeor.,6,248262, https://doi.org/10.1175/JHM424.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,P. C. Kennedy, andR. Cifelli,2014:Experimentally based estimates of relations between X-band radar signal attenuation characteristics and differential phase in rain.J. Atmos. Oceanic Technol.,31,24422450, https://doi.org/10.1175/JTECH-D-13-00231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLaughlin,D., andCoauthors,2009:Short-wavelength technology and the potential for distributed networks of small radar systems.Bull. Amer. Meteor. Soc.,90,17971817, https://doi.org/10.1175/2009BAMS2507.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Otto,T., andH. W. J. Russchenberg,2010: Estimation of the raindrop-size distribution at X-band using specific differential phase and differential backscatter phase. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology (ERAD 2010), Sibiu, Romania, Meteor Romania, 6 pp., https://www.erad2010.com/pdf/oral/thursday/xband/07_ERAD2010_0109.pdf.

  • Otto,T., andH. W. J. Russchenberg,2011:Estimation of specific differential phase and differential backscatter phase from polarimetric weather radar measurements of rain.IEEE Geosci. Remote Sens. Lett.,8,988992, https://doi.org/10.1109/LGRS.2011.2145354.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park,S.-G.,V. N. Bringi,V. Chandrasekar,M. Maki, andK. Iwanami,2005a:Correction of radar reflectivity and differential reflectivity for rain attenuation at X band. Part I: Theoretical and empirical basis.J. Atmos. Oceanic Technol.,22,16211632, https://doi.org/10.1175/JTECH1803.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park,S.-G.,M. Maki,K. Iwanami,V. N. Bringi, andV. Chandrasekar,2005b:Correction of radar reflectivity and differential reflectivity for rain attenuation at X band. Part II: Evaluation and application.J. Atmos. Oceanic Technol.,22,16331655, https://doi.org/10.1175/JTECH1804.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reinoso-Rondinel,R.,C. Unal, andH. Russchenberg,2018:Adaptive and high-resolution estimation of specific differential phase for polarimetric X-band weather radars.J. Atmos. Oceanic Technol.,35,555573, https://doi.org/10.1175/JTECH-D-17-0105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Russchenberg,H.,T. Otto,R. Reinoso-Rondinel,C. Unal, andJ. Yin,2010: IDRA weather radar measurements—All data. 4TU Centre for Research Data, Delft University of Technology. Subset used: IDRA processed data with standard range, accessed 12 October 2012, https://doi.org/10.4121/uuid:5f3bcaa2-a456-4a66-a67b-1eec928cae6d.

    • Crossref
    • Export Citation
  • Ryzhkov,A., andD. S. Zrnić,1995:Precipitation and attenuation measurements at 10-cm wavelength.J. Appl. Meteor.,34,21212134, https://doi.org/10.1175/1520-0450(1995)034<2120:PAAMAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov,A., andD. S. Zrnić,2005: Radar polarimetry at S, C, and X bands: Comparative analysis and operational implications. 32nd Conf. on Radar Meteor., Albuquerque, NM, Amer. Meteor. Soc., 9R3, https://ams.confex.com/ams/32Rad11Meso/webprogram/Paper95684.html.

  • Ryzhkov,A.,M. Diederich,P. Zhang, andC. Simmer,2014:Potential utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage, and radar networking.J. Atmos. Oceanic Technol.,31,599619, https://doi.org/10.1175/JTECH-D-13-00038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli,G.,E. Gorgucci,V. Chandrasekar, andT. A. Seliga,1993:Rainfall estimation using polarimetric techniques at C-band frequencies.J. Appl. Meteor.,32,11501160, https://doi.org/10.1175/1520-0450(1993)032<1150:REUPTA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli,G.,E. Gorgucci,V. Chandrasekar, andA. Dobaie,1996:Self-consistency of polarization diversity measurement of rainfall.IEEE Trans. Geosci. Remote Sens.,34,2226, https://doi.org/10.1109/36.481887.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneebeli,M., andA. Berne,2012:An extended Kalman filter framework for polarimetric X-band weather radar data processing.J. Atmos. Oceanic Technol.,29,711730, https://doi.org/10.1175/JTECH-D-10-05053.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneebeli,M.,J. Grazioli, andA. Berne,2014:Improved estimation of the specific differential phase shift using a compilation of Kalman filter ensembles.IEEE Trans. Geosci. Remote Sens.,52,51375149, https://doi.org/10.1109/TGRS.2013.2287017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snyder,J.,H. Bluestein, andG. Zhang,2010:Attenuation correction and hydrometeor classification of high-resolution, X-band, dual-polarized mobile radar measurements in severe convective storms.J. Atmos. Oceanic Technol.,27,19792001, https://doi.org/10.1175/2010JTECHA1356.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud,J.,E. L. Bouar,E. Obligis, andM. Ali-Mehenni,2000:The rain profiling algorithm applied to polarimetric weather radar.J. Atmos. Oceanic Technol.,17,332356, https://doi.org/10.1175/1520-0426(2000)017<0332:TRPAAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trömel,S.,M. R. Kumjian,A. V. Ryzhkov,C. Simmer, andM. Diederich,2013:Backscatter differential phase—Estimation and variability.J. Appl. Meteor. Climatol.,52,25292548, https://doi.org/10.1175/JAMC-D-13-0124.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang,Y., andV. Chandrasekar,2009:Algorithm for estimation of the specific differential phase.J. Atmos. Oceanic Technol.,26,25652578, https://doi.org/10.1175/2009JTECHA1358.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang,Y.,P. Zhang,A. V. Ryzhkov,J. Zhang, andP.-L. Chang,2014:Utilization of specific attenuation for tropical rainfall estimation in complex terrain.J. Hydrometeor.,15,22502266, https://doi.org/10.1175/JHM-D-14-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman,M., andR. Trapp,2003:Low-level mesovortices within squall lines and bow echoes. Part I: Overview and dependence on environment shear.Mon. Wea. Rev.,131,27792803, https://doi.org/10.1175/1520-0493(2003)131<2779:LMWSLA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    Methods associated with the estimation of (a) KDP and (b) A. The outputs related to the conventional KDP technique are indicated with red, while the outputs related to the adaptive high-resolution approach are indicated with green.

  • View in gallery

    A flowchart for the estimation of δhv. It consists of five steps, where steps 1 and 2 are processed in 1D (i.e., along a PPI radial), while steps 3–5 are processed in 2D (i.e., a complete PPI).

  • View in gallery

    Observations by IDRA radar at elevation angle of 0.5° in the NL at 1216 UTC 18 Jun 2011, event E1. Fields of (a) differential phase ΨDP, (b) z, (c) KDP(C) from the conventional approach, and (d) KDP(AHR) from the AHR approach. In (b)–(d), attenuation-corrected 30-dBZ levels are indicated by black contour lines; in (c) and (d), −1° km−1 levels are indicated by magenta contour lines. The red rings are at 5-km increments.

  • View in gallery

    (a) The KDP(C)–A(ZPHI) scatterplot resulting from event E1 at 1216 UTC is indicated by red dots, and the KDP(AHR)–A(ZPHI) scatterplot is indicated by green dots. In addition, the empirical relation KDP = (1/α)A is indicated by the black line, where α = 0.34 dB (°)−1. (b) As in (a), but for Z(DP, C)–Z(ZPHI) and Z(DP, AHR)–Z(ZPHI) scatterplots. Also, the relation Z(DP) = Z(ZPHI) is indicated by the black line. The biases are computed for Z(ZPHI) ≥ 35 dBZ.

  • View in gallery

    (a) Errors obtained from Eq. (3): EΦDP(C) (red) and EΦDP(AHR) (green) in the azimuth 288.1°, as a function of α [αmin;αmax]. (b) Profiles of ΨDP, ΦDP(C), and ΦDP(CZPHI) are shown as a function of range. In addition, upper and lower ΦDP(CZPHI) bounds (dashed lines) corresponding to αmin and αmax, respectively. (c) As in (b), but using ΦDP(AHR) rather than ΦDP(C). (d) Stemplots of selected αΦDP(C) (red) and αΦDP(AHR) (green) as a function of azimuth.

  • View in gallery

    (a) The A(CZPHI, C)–KDP(AHR) and A(CZPHI, AHR)–KDP(AHR) scatterplots resulting from event E1 at 1216 UTC are represented by the red and green dots, respectively. (b) As in (a), but for Z(CZPHI, C)–Z(DP, AHR) and Z(CZPHI, AHR)–Z(DP, AHR) scatterplots. In addition, the relation Z(CZPHI) = Z(DP) is indicated by the black line.

  • View in gallery

    Event E1 at 1216 UTC. Fields of (a) z, (b) zdr, (c) Z(CZPHI,AHR), and (d) ZDR are illustrated. The black contours represent the 30-dBZ level.

  • View in gallery

    Event E2 at 1450 UTC. Fields of (a) Z(CZPHI, AHR), (b) ZDR, (c) KDP(C), and (d) KDP(AHR) are shown. The black contours indicate the 30-dBZ level, and the magenta contours in (c) show the −1° km−1 level. In addition, the Z gradient along the inflow edge, the Z narrow appendage, and the ZDR arc signatures are indicated by arrows 1–3, respectively. The low-level inflow in (a) is represented by the three arrows.

  • View in gallery

    Event E2 at 1450 UTC. Selected values for α using ΦDP(C) and ΦDP(AHR) are given by the stemplots in red and green, respectively, as a function of azimuth.

  • View in gallery

    Event E3 at 1955 UTC. Fields of (a) Z(CZPHI, AHR), (b) ZDR, (c) KDP(C), and (d) KDP(AHR) are indicated. Various levels are shown: 40 dBZ (black contours), 1° km−1 (red contours), and −1° km−1 (magenta contours). The Z gradient along the inflow edge (arrow 4), the bow apex (arrow 5), and the weak-echo hole (arrow 6) are given in (a). The low-level inflow (white arrows) and the rotation pattern associated with the echo-weak hole (white circles) are also shown.

  • View in gallery

    As in Fig. 8, but for E4 at 0558 UTC.

  • View in gallery

    The resulting fields of δhv from E1 to E4 at (a) 1216, (b) 1450, (c) 1955, and (d) 0558 UTC. The white contours indicate the 30-dBZ level, whereas the black contours in (c) represent the 40-dBZ level.

  • View in gallery

    Event E1 at 1216 UTC. The δhvKDP(AHR) scatterplots resulting from steps 1 and 2 (blue) and steps 1–4 (green) of the δhv algorithm. The thick black line represents δ¯hv (i.e., mean values of δhv estimates as a function of KDP), while the thin lines represent δ¯hv±σδhv. The gray straight lines indicate two linear relations, L1 and L2, derived from scattering simulations in rain.

  • View in gallery

    Time series of quality measures from the CZPHI method for event E2. (a) Mean values e¯min (solid lines) related to ΦDP(C) (red) and ΦDP(AHR) (green). The corresponding variabilities e¯min±σemin (dashed lines). (b) ρAK (solid lines) and σAK (dashed lines) related to ΦDP(C) (red) and ΦDP(AHR) (green). (c) RMSE of Z associated with ΦDP(C) (red) and ΦDP(AHR) (green).

  • View in gallery

    (a) Histograms of optimal αΦDP(C) (red) and αΦDP(AHR) (green) for event E1. (b)–(d) As in (a), but for E2–E4, respectively.

  • View in gallery

    (a) Time series of quality measures from the δhv algorithm for event E1. Left y axis: MAE + 5° resulting from steps 1 and 2 (solid blue) and from steps 1–4 (solid green). The black line indicates the 5° shift. MSD from steps 1 and 2 (dashed blue) and from steps 1–4 (dashed green). Right y axis: I resulting from step 4 (magenta). (b)–(d) As in (a), but for E2–E4, respectively.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 43 43 9
PDF Downloads 41 41 13

Improved Estimation of the Specific Attenuation and Backscatter Differential Phase over Short Rain Paths

View More View Less
  • 1 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, Netherlands
© Get Permissions
Full access

Abstract

In radar polarimetry, the differential phase ΨDP consists of the propagation differential phase ΦDP and the backscatter differential phase δhv. While ΦDP is commonly used for attenuation correction (i.e., estimation of the specific attenuation A and specific differential phase KDP), recent studies have demonstrated that δhv can provide information concerning the dominant size of raindrops. However, the estimation of ΦDP and δhv is not straightforward given their coupled nature and the noisy behavior of ΨDP, especially over short paths. In this work, the impacts of estimating ΦDP on the estimation of A over short paths, using the extended version of the ZPHI method, are examined. Special attention is given to the optimization of the parameter α that connects KDP and A. In addition, an improved technique is proposed to compute δhv from ΨDP and ΦDP in rain. For these purposes, diverse storm events observed by a polarimetric X-band radar in the Netherlands are used. Statistical analysis based on the minimum errors associated with the optimization of α and the consistency between KDP and A showed that more accurate and stable α and A are obtained if ΦDP is estimated at range resolution, which is not possible by conventional range filtering techniques. Accurate δhv estimates were able to depict the spatial variability of dominant raindrop size in the observed storms. By following the presented study, the ZPHI method and its variations can be employed without the need for considering long paths, leading to localized and accurate estimation of A and δhv.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ricardo Reinoso-Rondinel, r.reinosorondinel@tudelft.nl

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JTECH-D-17-0105.1

Abstract

In radar polarimetry, the differential phase ΨDP consists of the propagation differential phase ΦDP and the backscatter differential phase δhv. While ΦDP is commonly used for attenuation correction (i.e., estimation of the specific attenuation A and specific differential phase KDP), recent studies have demonstrated that δhv can provide information concerning the dominant size of raindrops. However, the estimation of ΦDP and δhv is not straightforward given their coupled nature and the noisy behavior of ΨDP, especially over short paths. In this work, the impacts of estimating ΦDP on the estimation of A over short paths, using the extended version of the ZPHI method, are examined. Special attention is given to the optimization of the parameter α that connects KDP and A. In addition, an improved technique is proposed to compute δhv from ΨDP and ΦDP in rain. For these purposes, diverse storm events observed by a polarimetric X-band radar in the Netherlands are used. Statistical analysis based on the minimum errors associated with the optimization of α and the consistency between KDP and A showed that more accurate and stable α and A are obtained if ΦDP is estimated at range resolution, which is not possible by conventional range filtering techniques. Accurate δhv estimates were able to depict the spatial variability of dominant raindrop size in the observed storms. By following the presented study, the ZPHI method and its variations can be employed without the need for considering long paths, leading to localized and accurate estimation of A and δhv.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ricardo Reinoso-Rondinel, r.reinosorondinel@tudelft.nl

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JTECH-D-17-0105.1

1. Introduction

Conventional S- and C-band weather radars have been used for several decades to monitor the evolution of precipitation. In recent years the technology of those conventional radars has been upgraded to polarimetric technology in order to further improve weather radar measurements (Doviak et al. 2000). Severe weather can produce rapid and localized surface damage associated with, for example, heavy rain and tornadoes. In this context, a network of small polarimetric X-band weather radars may be suitable to obtain observations of fast-developing storms at close range and at resolutions higher than those from conventional radars (McLaughlin et al. 2009; Chandrasekar et al. 2018).

One of the advantages of polarimetric radars is given by the measurements of differential phase between the horizontally and vertically polarized signals caused by the delay of one with respect to the other as both signals propagate through hydrometeors. In this way, the differential phase ΨDP (°) is independent of attenuation, miscalibration, and partial beam blockage (PBB) effects (Doviak and Zrnić 1993). However, ΨDP measurements can include phase shifts in the backward direction as a result of Mie scattering, the so-called backscatter differential phase δhv (°), and random fluctuations ε (°) on the order of few degrees. In general, a ΨDP range profile is modeled as
ΨDP(r)=ΦDP(r)+δhv(r)+ε,
where ΦDP(r) (°) represents the differential phase in the forward direction and r (km) indicates the distance from the radar. Two useful variables that can be estimated from ΦDP are the specific differential phase KDP (° km−1) and the specific attenuation A (dB km−1), which are commonly used for the estimation of rainfall rate and attenuation correction (Bringi and Chandrasekar 2001).

The traditional method to estimate KDP (or ΦDP) from ΨDP when δhv is significant is given by Hubbert and Bringi (1995), and several attempts have been proposed to improve KDP estimates at X-band frequencies (Wang and Chandrasekar 2009; Giangrande et al. 2013; Schneebeli et al. 2014; Huang et al. 2017). The specific differential phase KDP has been used to correct measurements of reflectivity Z (dBZ) affected by radar calibration and PBB (Giangrande and Ryzhkov 2005). In addition, KDP has led to improved estimation of rainfall rate, mostly in heavy rain or mix rain, because of its quasi-linear relation to liquid water content (Lim et al. 2013). Although radar measurements seem to benefit from using KDP, comprehensive research on KDP is still needed because it is a challenge to provide accurate KDP from noisy measurements of ΨDP.

Existing methods to estimate A in rain assume that A = αKDP, where α is a constant for a given frequency (Bringi et al. 1990). Testud et al. (2000) also used the relation between A and KDP in their rain profiling ZPHI technique, to express A in terms of the difference of ΦDP and measurements of Z, avoiding KDP calculation. However, it is known that α is sensitive to temperature, drop size distribution (DSD), and drop size variabilities; therefore, Bringi et al. (2001) extended the ZPHI technique to avoid a priori value for α. These methods have been adapted to address attenuation problems at X-band frequencies (Matrosov et al. 2002; Park et al. 2005a; Gorgucci et al. 2006; Lim and Chandrasekar 2016). Moreover, Ryzhkov et al. (2014), Wang et al. (2014), and Diederich et al. (2015) modified the extended ZPHI method to improve rainfall-rate estimation and to demonstrate that A can be used to reduce issues related to radar calibration and PBB. Despite these promising benefits, the potential of using A might be limited depending on the approach to obtain ΦDP and α (Bringi et al. 2001; Ryzhkov and Zrnić 2005).

In contrast to KDP and A, limited research has been conducted on the applications of δhv. For example, δhv can be a suitable candidate to mitigate uncertainties related to the differential reflectivity ZDR (dB) because δhv and ZDR offer a correlated behavior (Scarchilli et al. 1993; Testud et al. 2000) and because δhv is independent of attenuation and radar calibration; see Eq. (1). These aspects of δhv could be useful to establish relations between δhv and the median drop diameter D0 (mm) (Trömel et al. 2013) because D0 is often expressed in terms of ZDR (Matrosov et al. 2005; Kim et al. 2010). Moreover, Otto and Russchenberg (2010) included δhv estimates to retrieve DSD parameters. Hubbert and Bringi (1995), Otto and Russchenberg (2011), and Trömel et al. (2013) estimated δhv by subtracting ΦDP from ΨDP, while Schneebeli and Berne (2012) included a Kalman filter approach. The effectiveness of estimating δhv at high resolution is rather complicated because of the cumulative and noisy nature of ΨDP and possible remaining fluctuations on ΦDP.

The purpose of this work is to 1) explore the role and impact of estimated ΦDP profiles on the performance of the extended ZPHI method at X-band frequencies to improve estimates of α and A over short paths and 2) develop a technique to compute δhv in rain while keeping the spatial variability of drop sizes. For such purpose, two KDP (or ΦDP) methods, by Hubbert and Bringi (1995) and Reinoso-Rondinel et al. (2018), are reviewed in section 2 as well as three attenuation correction approaches, by Bringi et al. (1990), Testud et al. (2000), and Bringi et al. (2001). In addition, the δhv algorithm is introduced, which integrates estimates of KDP and A. In section 3, the performances of the attenuation correction methods that assume a constant α are compared using four storm events. This comparison is extended in section 4 to examine the selection of α profile by profile and its impact on A and Z. In section 5, the δhv technique is evaluated. Section 6 focuses on the statistics of α, A, Z, and δhv to conduct further assessments of the presented methods. Finally, section 7 draws conclusions of this article.

2. Estimation techniques for ΨDP-based variables

a. Estimation of KDP

In the conventional technique given by Hubbert and Bringi (1995), a low-pass filter is designed such that gate-to-gate fluctuations at scales of the range resolution Δr (km) are filtered from a ΨDP(r) profile. Fluctuations at range scales larger than Δr (i.e., δhv “bumps”) are removed by applying the same filter multiple times to new generated ΨDPg profiles by combining a previous filtered and original ΨDP profile. In this manner the corresponding ΦDP profile is obtained and KDP is given by taking a range derivative of ΦDP. For the generation of ΨDPg, a predetermined threshold τ (°) is required, which is on the order of 1–2 times the standard deviation of ΨDP, hereafter σP (°). One of the limitations of this technique is that accurate estimates of ΦDP and KDP at Δr scales are hardly achieved (Grazioli et al. 2014).

An adaptive approach that estimates KDP at high spatial resolution while controlling its standard deviation σK (° km−1) is given by Reinoso-Rondinel et al. (2018). For notation purposes, the difference of a radar variable V over a given pathlength is expressed as ΔV. Besides ΨDP, attenuation-corrected Z and ZDR profiles are also required, as well as a predefined pathlength interval [Lmin;Lmax] (km). For gate i, located at range ri, a set of σK samples are obtained from [Lmin;Lmax] using a theoretical expression of σK. The pathlength that minimizes the σK set is selected and denoted as L(i). Assuming the correlated behavior between ZDR and δhv, ΔΨDP samples in the range [riL(i); ri+L(i)] that do not satisfy the condition |ΔZDR|<σZDR are filtered to avoid contamination from Δδhv. The standard deviation of the ZDR profile is denoted as σZDR. The spatial variability of ΨDP at Δr scales is captured by downscaling each remaining ΔΨDP sample from L(i) to Δr scale. A downscaling parameter w(i) [0, 1] is derived from Z and ZDR in the same interval [riL(i); ri+L(i)], and KDP(i) is estimated as
KDP(i)=1Mj=1MΔΨDP(j)w(j)(i)2Δr,withj=1,2,,M,
where M represents the number of ΔΨDP samples with negligible Δδhv. The actual σK(i) is calculated using the terms inside the sum operation in Eq. (2). The KDP and σK profiles are obtained by repeating the same procedure over the remaining gates, while the corresponding ΦDP profile is calculated by simply integrating KDP in range. In addition, a profile of the normalized standard error (NSE) of KDP is given by the ratio between actual σK and KDP. This approach was demonstrated for rain particles at X-band frequencies, and therefore any undetected Z and ZDR echoes from hydrometeors other than rain can lead to inaccurate KDP estimates. The two KDP methods will be referred to as the conventional (C) and the adaptive high-resolution (AHR) approaches, respectively. A diagram is presented in Fig. 1 to briefly indicate the inputs and outputs of each method.
Fig. 1.
Fig. 1.

Methods associated with the estimation of (a) KDP and (b) A. The outputs related to the conventional KDP technique are indicated with red, while the outputs related to the adaptive high-resolution approach are indicated with green.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

b. Estimation of A

For attenuation correction purposes, Z and ZDR profiles are represented as Z(r)=z(r)+PIA(r) and ZDR(r)=zdr(r)+PIADP(r), respectively, where z (dBZ) and zdr (dB) represent the attenuated reflectivity and the attenuated differential reflectivity, respectively; and PIA(r) (dB) indicates the two-way path-integrated attenuation in reflectivity and PIA(r)DP (dB) in differential reflectivity.

Bringi et al. (1990) introduced the differential phase (DP) approach such that A(r) = αKDP(r) and PIA(r)=αΦDP(r), where α [dB (°)−1] is assumed to be a constant coefficient. Gorgucci and Chandrasekar (2005) studied the accuracy of this method using simulated radar variables at X-band frequencies and showed that estimates of A are very sensitive to inaccurate estimates of KDP, while estimates of PIA lead to Z values associated with only a slight degradation of the average error for attenuation correction, ±1.5 dB.

To improve the DP method, Testud et al. (2000) introduced the ZPHI method that estimates A(r) in a path interval [rp;rq], where rq>rp. First, A(r) is expressed as a function of two known variables, z(r) and z(rq), and one unknown, A(rq). Then, A(rq) is obtained using z(rq) and the empirical relation ΔPIA = αΔΦDP, where ΔPIA = PIA(rq) − PIA(rp) and ΔΦDP = ΦDP(rq)ΦDP(rp). In this way, A(r) is estimated at Δr scales, reducing errors related to KDP(r). Although [rp;rq] can be freely selected; ΔΦDP could be inaccurate at short path intervals and/or be contaminated by δhv(rp) and δhv(rq). In addition, if z(r) includes localized observations of hail or mixtures of rain and hail in [rp;rq], then A(r) might be biased over the entire path interval.

Using a constant α may lead to limited approximations of A(r) and PIA(r) because α is sensitive to DSD, drop shape, and temperature variabilities (Jameson 1992). To take into account the sensitivity of α, Bringi et al. (2001) extended the ZPHI method to search for optimal α values at C-band frequencies, called the CZPHI method. An initial value for α is selected from a predefined interval [αmin;αmax], and A(r) is estimated according to the ZPHI method. The estimated A(r) is integrated over [rp;rq] to build a differential phase profile denoted as ΦDP(r,α). Repeating this procedure for the remaining values of α, the optimal α is the one that minimizes the error E (°) given by
E=i=pq|ΦDP(ri,α)ΦDP(ri)|,withi=p,,q.
Note that the optimization process requires the estimation of ΦDP, which implies the need for a proper way to filter noise and δhv components from ΨDP while maintaining its spatial variability. However, meeting such requirements is not straightforward; therefore, the reliability of an “optimal” α to estimate A and PIA depends on the performance of the chosen approach to estimate ΦDP. The inputs and outputs associated with the three presented attenuation correction methods are summarized in Fig. 1.

To determine PIA(r)DP, integrate the specific differential attenuation ADP(r) (dB km−1) that is given by ADP=γA. The DP and ZPHI methods assume γ to be constant, whereas the CZPHI technique searches for an optimal γ, addressing its sensitivity to DSD variability (i.e., rain type). However, such sensitivity of γ is less at X-band frequencies than at C- and S-band frequencies (Ryzhkov et al. 2014). In this work, ADP will be given by ADP = γA(CZPHI), where A(CZPHI) represents the specific attenuation determined by the CZPHI approach and γ is assumed a constant.

Representative values for α and γ at X-band frequencies can be given by the mean fit of simulated polarimetric relations using a large set of DSDs and different drop shapes and temperatures. For example, Kim et al. (2010) and Ryzhkov et al. (2014) demonstrated that α values vary in the interval [0.1; 0.6] dB (°)−1, and Otto and Russchenberg (2011) obtained an average value of 0.34 dB (°)−1 for α and for γ a value of 0.1618. Similar results were suggested by Testud et al. (2000), α=0.315 dB (°)−1; Kim et al. (2010), α=0.35 dB (°)−1; and Snyder et al. (2010) α=0.313 dB (°)−1; while Ryzhkov et al. (2014) estimated γ equal to 0.14 for tropical rain (i.e., low ZDR and high KDP) and 0.19 for continental rain (i.e., high ZDR and low KDP). It is important to note that other authors have suggested smaller average values for α. For example, Bringi and Chandrasekar (2001) simulated polarimetric variables in rain and indicated that α=0.23 dB (°)−1. Matrosov et al. (2014) avoided simulations by using observations resulting from collocated X- and S-band radars and found α in the range of 0.20–0.31 dB (°)−1. Thus, a representative value for α can vary depending on models and assumptions used to simulate polarimetric variables, on the type of observed storms and their geographical locations, and on the accuracy of measurements.

c. Estimation technique for δhv

A δhv approach is presented to identify and separate Mie scattering signatures from noise and random fluctuations embedded in ΨDP. A flowchart of the δhv algorithm is illustrated in Fig. 2. Three inputs are required: a 2D ΨDP field measured in rain, the corresponding KDP field obtained from the AHR approach, and the A field estimated by the CZPHI method. Given these inputs, the resulting δhv field is based on the following five steps:

  1. Design and apply a filter to smooth strong outliers from a ΨDP profile, taking Δr into account. Correct each smoothed ΨDP profile for system phase offset by subtracting the mean of ΨDP over the first 5% of measured gates.
  2. Obtain ΦDP by integrating profiles of A, if they are associated with a minimum error E, otherwise by integrating KDP profiles. Next, subtract ΦDP from ΨDP, profile by profile, as a first attempt to estimate the corresponding δhv field. The next steps are related to 2D processing.
  3. Remove unusual δhv values larger than 12° from the δhv field. According to Testud et al. (2000), Trömel et al. (2013), and Schneebeli et al. (2014), the simulated δhv values at X-band frequencies rarely reach 12°. The remaining noise in δhv is reduced by assuming that similar values of δhv are collocated with similar values of KDP as follows. Set Kmin as the minimum of KDP and Kmax as Kmin+ΔK, where ΔK (° km−1) is given by Eq. (4). Define S as a set of δhv samples, whose gates are collocated with KDP values in the interval [Kmin;Kmax]. Reject δhv samples from S that are outside the interval [δ¯hvυσδhv; δ¯hv+υσδhv], where δ¯hv and σδhv indicate the arithmetic mean and the standard deviation of the samples in S, respectively; υ is a predefined threshold in the interval [1;2] and a value of 1 is chosen. This process is iterated by shifting [Kmin;Kmax] toward high values in small steps such that Kmin = Kmax and Kmax = Kmin+ΔK until Kmax is equal to the maximum of KDP. To obtain sufficient samples in S, ΔK is given as
    ΔK={0.2Kmin2.5°km1,0.52.5°<Kmin<8°km1,1.0Kmin8°km1,
    because high KDP values are less frequent than small KDP values (e.g., see the KDP fields in Figs. 3, 8, and 11).
  4. Apply a 2D interpolation method to fill empty gaps on δhv caused by step 3. For this task, the inpainting (or image fill-in) algorithm (Bertalmio et al. 2003; Criminisi et al. 2004; Elad et al. 2005) is selected because it is one of the image processing algorithms commonly used to smoothly interpolate 2D images. The essential idea is to formulate a partial differential equation (PDE) for the “hole” (interior unknowns) and to use the perimeter of the hole to obtain boundary values. The solution for the interior unknowns involves the discretization of PDEs on the unknowns’ points into a system of linear equations. D’Errico (2006) implemented an inpainting code for 2D arrays that is freely available and used for this step. The code offers multiple methods to formulate a PDE, and the method referred to as the spring method is selected because it provides a reasonable compromise between accuracy and computational time.
  5. (optional) To better distinguish storm cells from their background (i.e., for radar displaying purposes), it is recommended to replace areas of δhv that are linked to |KDP| < 0.4° km−1 (i.e., weak rain echoes) by a representative value. This value is chosen as the mean of δhv samples constrained by |KDP| < 0.4° km−1 and |δhv|<σ¯δhv, where σ¯δhv indicates the mean of σδhv samples obtained in a similar manner as in step 3 but using δhv after step 4. The value of 0.4° km−1 is found to match the 30-dBZ level used in this work for storm cell identification.
Fig. 2.
Fig. 2.

A flowchart for the estimation of δhv. It consists of five steps, where steps 1 and 2 are processed in 1D (i.e., along a PPI radial), while steps 3–5 are processed in 2D (i.e., a complete PPI).

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

Fig. 3.
Fig. 3.

Observations by IDRA radar at elevation angle of 0.5° in the NL at 1216 UTC 18 Jun 2011, event E1. Fields of (a) differential phase ΨDP, (b) z, (c) KDP(C) from the conventional approach, and (d) KDP(AHR) from the AHR approach. In (b)–(d), attenuation-corrected 30-dBZ levels are indicated by black contour lines; in (c) and (d), −1° km−1 levels are indicated by magenta contour lines. The red rings are at 5-km increments.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

3. Evaluation of KDP processing by the ZPHI method

a. Datasettings and preprocessing

The polarimetric X-band International Research Center for Telecommunications and Radar (IRCTR) Drizzle Radar (IDRA; Figueras i Ventura 2009) is located at the Cabauw Experimental Site for Atmospheric Research (CESAR) observatory in the Netherlands (NL) at a height of 213 m from ground level (Leijnse et al. 2010). Its operational range and range resolution are equal to 15.3 and 0.03 km, respectively, while the antenna rotates over 360° in 1 min. Four storm events, E1–E4, that occurred in the Netherlands during the year 2011 will be used for demonstration and analysis purposes. A description of these events is summarized in Table 1.

Table 1.

Description of four storm events E1–E4 observed in the Netherlands.

Table 1.

To remove areas that include particles other than rain and/or areas with low signal-to-noise ratio (SNR), measurements of linear depolarization ratio LDR (dB) are used, such that range gates with LDR larger than −18 dB are discarded from ΨDP, z, and zdr fields. Further preprocessing includes suppressing isolated segments of a ΨDP profile smaller than 0.25 km and rejecting a ΨDP profile if the percentage of gates with measurements is less than 5%. Because a ΨDP profile could be noisy at ranges behind strong reflectivity echoes associated with low SNR and fully attenuated signals, its range extent needs to be determined. The ending range of a ΨDP profile is determined based on σ¯P, which represents the average of multiple σP samples by running a five-gate window along the ΨDP profile. If σ¯P is less than 1.5°, then the ending range is given by the last measured gate in the downrange direction. Otherwise, the ending range is set by the middle gate of the second consecutive window whose σP values are less than σ¯P, starting at the last measured gate and moving toward the radar. The ending range is used to limit the corresponding extent of z and zdr profiles. After this, σ¯P is calculated again to estimate KDP by the conventional technique.

b. Comparison between KDP and A

Next, KDP(C) and KDP(AHR) will be compared against A(ZPHI) using the empirical relation A = αKDP, where α is 0.34 dB (°)−1, as suggested by Otto and Russchenberg (2011). In this scheme, A(ZPHI) is used as a reference to evaluate both KDP techniques and their impact on Z.

To estimate KDP(C), a finite impulse response (FIR) filter is used such that the order of the filter is 36 and the cutoff range scale is 1 km, including a Hann window. The required threshold τ is set to 1.5σ¯P. Such a filter design is found suitable for Δr= 0.03 km. For the estimation of KDP(AHR), values of L on the order of 3 km are associated with theoretical values of σK< 0.5° km−1 for Δr = 0.03 km (Reinoso-Rondinel et al. 2018) and therefore [Lmin;Lmax] is predefined as [2;5] km. The z and zdr inputs are corrected for attenuation and differential attenuation, respectively, according to the DP method, in which a linear regression fit of 1 km is applied to ΨDP profiles. To estimate σZDR a five-gate window is run along a given ZDR profile. For the calculation of A(ZPHI), ΔΦDP is derived from ΦDP(C) instead of ΦDP(AHR) to evaluate KDP(AHR) in an independent manner. A path interval [rp;rq] is defined by the first and last data points, in the downrange direction, of a ΦDP(C) profile. In cases where ΔΦDP< 0° as a result of a reduced SNR profile, the estimation of A(ZPHI) is avoided.

Results from the storm event E1 at 1216 UTC are shown in Fig. 3. The ΨDP field shows a rapid increment in range on the north side of the storm, whereas ΨDP rarely increases on the south side. Note that the ΨDP field is not adjusted for phase offset. The attenuated z field represents a relatively small cell of a nonuniform structure in close proximity to the radar. The 30-dBZ contour is obtained from the attenuation-corrected Z using the ZPHI method [i.e., after calculating A(ZPHI) as explained previously]. Comparing KDP(C) and KDP(AHR), the KDP(AHR) field is able to maintain the spatial variability of the storm down to range resolution scale, eliminating areas of KDP smaller than −1° km−1, which are present in KDP(C). However, the coverage of the KDP(AHR) field is smaller than that of KDP(C). This is because in the AHR approach, it is not always possible to obtain ΔΨDP samples with negligible Δδhv; that is, M=0 in Eq. (2). Note that isolated KDP segments smaller than 2 km were removed from both KDP fields in order to avoid estimates of KDP that could be associated with noisy areas and/or low accuracy.

The scatterplots KDP(C)–A(ZPHI) and KDP(AHR)–A(ZPHI) resulting from the same event, E1, are compared in Fig. 4. In Fig. 4a, it can be seen that the KDP(AHR)–A(ZPHI) scatterplot (14 783 data points) is more consistent than that of KDP(C)–A(ZPHI) (15 490 data points) with respect to the empirical relation A = 0.34KDP. In a quantified comparison, the correlation coefficient ρKA between KDP(C) and A(ZPHI) is equal to 0.65, whereas for KDP(AHR) and A(ZPHI) it is 0.96. Their corresponding standard deviations σKA with respect to the empirical relation are 1.20 and 0.41° km−1, respectively. To compare the impact of both KDP techniques on the DP method, z values are corrected for attenuation using the DP and ZPHI correction methods, and are denoted as Z(DP, C), Z(DP, AHR), and Z(ZPHI, C); see Fig. 1. The scatterplots Z(DP, C)–Z(ZPHI, C) and Z(DP, AHR)–Z(ZPHI, C) are compared in Fig. 4b such that Z(ZPHI, C) estimates are used as reference. It is observed that for relatively high values of Z(ZPHI, C), Z(DP, C) values are slightly overcorrected, which agrees with Gorgucci and Chandrasekar (2005) and Snyder et al. (2010). In contrast, Z(DP,AHR) values are found significantly consistent with Z(ZPHI, C) estimates. The mean biases associated with Z(DP,C) and Z(DP, AHR) are equal to 0.95 and −0.21 dB, respectively, for Z(ZPHI, C) ≥35 dBZ. The errors quantified by ρKA, σKA, and bias Z are summarized in Table 2. The remaining events, E2–E4, at 1450, 1955, and 0558 UTC, respectively, were also analyzed in a similar manner and the corresponding quantified errors are indicated in Table 2.

Fig. 4.
Fig. 4.

(a) The KDP(C)–A(ZPHI) scatterplot resulting from event E1 at 1216 UTC is indicated by red dots, and the KDP(AHR)–A(ZPHI) scatterplot is indicated by green dots. In addition, the empirical relation KDP = (1/α)A is indicated by the black line, where α = 0.34 dB (°)−1. (b) As in (a), but for Z(DP, C)–Z(ZPHI) and Z(DP, AHR)–Z(ZPHI) scatterplots. Also, the relation Z(DP) = Z(ZPHI) is indicated by the black line. The biases are computed for Z(ZPHI) ≥ 35 dBZ.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

Table 2.

Comparison results between KDP(C) estimates and KDP(AHR) using as a reference values of A(ZPHI) resulting from the ZPHI method for four storm events. Data points in each event are given: event E1 (~14 000), E2 (~13 000), E3 (~40 000), and E4 (~30 000).

Table 2.

From the previous analysis, the following can be highlighted. The values of KDP(AHR) and A(ZPHI), determined by two independent methods, show a strong agreement to the empirical relation A=αKDP, leading to equivalent Z(DP,AHR) and Z(ZPHI,C) results. In the contrary, the agreement between KDP(C) and A(ZPHI) is less evident, and although KDP(C) barely includes substantial errors on attenuation-corrected Z(DP,C), it can significantly impact estimates of A by the DP method. Similar findings at X-band frequencies were reported by Gorgucci and Chandrasekar (2005) but using simulated data.

4. Impact of KDP processing on the CZPHI method

In this section, the ability to estimate ΦDP by both KDP approaches is studied and their impact on the performance of finding optimal α values for the estimation of A and the correction of Z by the CZPHI method is measured. For analysis purposes, the minimum E obtained from Eq. (3) is expressed as E = ei, with i = p,,q, where ei represents the minimum error at range ri. As such, the arithmetic mean and standard deviation of ei, e¯min (°) and σemin (°), respectively, will be used as quality measures.

At X-band frequencies, [αmin;αmax] is predefined as [0.1;0.6] dB (°)−1 with steps of 0.02 dB (°)−1, as suggested by Park et al. (2005b) and Ryzhkov et al. (2014). For a correct optimization process, it is recommended that rqrp should be at least 3 km and that ΔΦDP be larger than 10°. In addition, if the ΦDP(C) profile is used in Eq. (3), then the percentage of gates with KDP> 0° km−1 should be at least 50%, whereas if the ΦDP(AHR) profile is used, the percentage of gates with KDP> 0.5° km−1 and NSE < 20% should be larger than 80%. The percentage threshold for ΦDP(C) is less than for ΦDP(AHR) because the conventional method rarely avoids negative KDP values. If these conditions are met, α is selected by minimizing E, considering only range gates that satisfy the stated conditions; otherwise α is equal to 0.34 dB (°)−1.

a. Event E1: Single cell

1) Optimization analysis

Results involved in the optimization process along azimuth 288.1° for storm event E1 at 1216 UTC are shown in Figs. 5a–c. In Fig. 5a, it is seen that the minimum E when ΦDP(C) is used is much larger than when ΦDP(AHR) is used and their corresponding optimal values for α are αΦDP(C) = 0.24 and αΦDP(AHR) = 0.34 dB (°)−1. The reason why the two α values are different can be explained by observing the measured ΨDP and the estimated ΦDP(C) and ΦDP(AHR) profiles shown in Figs. 5b and 5c, respectively. First, note that ΨDP might include (i) a δhv bump in the range [3.5;5.5] km and (ii) oscillations in the range [6.5;8.5] km. Second, the δhv bump is more noticeable in ΦDP(C) than in ΦDP(AHR). In consequence, the matching between ΦDP(C) and ΦDP(CZPHI) shown in Fig. 5b is not as good as the one observed in Fig. 5c. Note that ΦDP(CZPHI) represents ΦDP(ri,α) in Eq. (3). The extent of the ΦDP(AHR) profile is less than that of ΦDP(C) because M in Eq. (2) appears to be 0 at the beginning and ending ranges of ΨDP. However, this limited extent of ΦDP(AHR) avoids the oscillations seen at the ending ranges of ΨDP.

Fig. 5.
Fig. 5.

(a) Errors obtained from Eq. (3): EΦDP(C) (red) and EΦDP(AHR) (green) in the azimuth 288.1°, as a function of α [αmin;αmax]. (b) Profiles of ΨDP, ΦDP(C), and ΦDP(CZPHI) are shown as a function of range. In addition, upper and lower ΦDP(CZPHI) bounds (dashed lines) corresponding to αmin and αmax, respectively. (c) As in (b), but using ΦDP(AHR) rather than ΦDP(C). (d) Stemplots of selected αΦDP(C) (red) and αΦDP(AHR) (green) as a function of azimuth.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

The selected αΦDP(C) and αΦDP(AHR) values as a function of azimuth for the same storm are depicted in Fig. 5d. Values for α that are related to a minimum E (i.e., optimal α values) are encircled by black edges, while those that are nonrelated to a minimum E are represented without edges. Note that optimal αΦDP(AHR) values are close to 0.34 dB (°)−1, whereas those related to ΦDP(C) are mostly smaller than 0.34 dB (°)−1 and sometime equal to αmin. An optimal α that equals αmin or αmax could be associated with an inadequate matching between the input ΦDP and the obtained ΦDP(CZPHI), which can lead to incorrect α. The resulting e¯min values associated with ΦDP(C) and ΦDP(AHR) are 2.16° and 0.20°, respectively, and their corresponding σemin values are 0.75° and 0.08°. These results come from the azimuthal sector [280°;310°], which covers approximately the north side of the storm shown in Fig. 3. Outside this sector, the constant α was selected, associated with either ΦDP(C) or ΦDP(AHR), because the stated conditions were not met.

2) Performance analysis

The impact of the optimal selection of αΦDP(C) and αΦDP(AHR) on the estimation of A(CZPHI) is measured using KDP(AHR) as a reference because of 1) the consistency between KDP(AHR) and A(ZPHI) demonstrated in section 3b and 2) the fact that the presented data were collected from one radar. Hence, the following analysis is based on internal polarimetry consistency.

The scatterplots A(CZPHI, C)–KDP(AHR) and A(CZPHI, AHR)–KDP(AHR) resulting from event E1 are shown in Fig. 6a. Observe that multiple A(CZPHI, C) estimates are smaller than those from A(CZPHI, AHR) as a consequence of selecting “small optimal” αΦDP(C) values. The correlation coefficient ρAK from A(CZPHI, C)–KDP(AHR) is equal to 0.78, while from A(CZPHI, AHR)–KDP(AHR) it is 0.98. Their corresponding standard deviations σAK with respect to A = αKDP are 0.28 and 0.05 dB km−1, respectively, where α values are given by αΦDP(AHR). In Fig. 6b, attenuation-corrected Z(CZPHI, C) and Z(CZPHI, AHR) are compared against Z(DP, AHR), where Z(DP, AHR) is obtained from KDP(AHR) and αΦDP(AHR). Their root-mean-square errors (RMSE) are equal to 1.67 and 0.10 dB, respectively, for Z(DP, AHR) ≥ 35 dBZ. This means that the attenuation-correctioned CZPHI method can lead to lower performance than the ZPHI method, comparing Fig. 6b with Fig. 4b. In this analysis, the RMSE was used instead of the mean bias to take into account the standard deviation of Z(CZPHI) estimates associated with the variability of α. The quantified errors used to evaluate the CZPHI method are summarized in Table 3.

Fig. 6.
Fig. 6.

(a) The A(CZPHI, C)–KDP(AHR) and A(CZPHI, AHR)–KDP(AHR) scatterplots resulting from event E1 at 1216 UTC are represented by the red and green dots, respectively. (b) As in (a), but for Z(CZPHI, C)–Z(DP, AHR) and Z(CZPHI, AHR)–Z(DP, AHR) scatterplots. In addition, the relation Z(CZPHI) = Z(DP) is indicated by the black line.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

Table 3.

Comparison results between A(CZPHI, C) and A(CZPHI, AHR) using KDP(AHR) as a reference for four storm events.

Table 3.

A similar analysis of A(CZPHI) is performed using KDP(C) as a reference instead of KDP(AHR) and the results are summarized next. The correlation coefficient between A(CZPHI, C) and KDP(C) is equal to 0.59 and smaller than those shown in Fig. 6a. This is because of the limited accuracy associated with KDP(C). The resulting RMSE between Z(CZPHI, C) and Z(DP, C) is equal to 0.82 and smaller than the case when Z(DP, AHR) is used as a reference. This is because Z(CZPHI, C) and Z(DP, C) are obtained from the same αΦDP(C) values, leading to similar attenuation correction results. Nonetheless, even if Z(DP, C) is set as a reference, their resulting RMSE is still larger than the one from Z(CZPHI, AHR)–Z(DP, AHR).

Attenuated z and zdr and attenuation-corrected Z(CZPHI, AHR) and ZDR fields from event E1 are displayed in Fig. 7. The Z(CZPHI, AHR) field restored attenuated z areas with PIA values up to 14 dB mostly on the north side of the storm cell, which is associated with rapid increments of ΨDP (see Fig. 3). A similar situation is observed by comparing the fields of zdr and ZDR, where enhanced areas of ZDR correspond to oblate raindrops. From the ZDR field, it seems that its lower bound is between −2 and −1 dB, which could be due to radar miscalibration rather than prolate-shaped particles, and therefore Z and ZDR fields may not represent calibrated measurements. Furthermore, the radial pattern presented in the zdr and ZDR fields may be associated with an azimuthal modulation as result of a metallic fence near the radar causing PBB effects (Giangrande and Ryzhkov 2005). Although such error sources may cause uncertainties on Z and ZDR, they do not seem to affect estimates of KDP and A by neither of the discussed methods and they do not influence the results of the presented analysis.

Fig. 7.
Fig. 7.

Event E1 at 1216 UTC. Fields of (a) z, (b) zdr, (c) Z(CZPHI,AHR), and (d) ZDR are illustrated. The black contours represent the 30-dBZ level.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

b. Event E2: Mini-supercell

The performance of the CZPHI method from event E2 at 1450 UTC is analyzed in a similar manner as for event E1 and the quantified errors are summarized in Table 3. The results show again that the CZPHI method performs better when α is given by αΦDP(AHR) instead of αΦDP(C). Nonetheless, event E2 shows specific signatures associated with the spatial distribution of raindrop size that can be used to illustrate the ability of selecting proper α values using the outcome of both KDP approaches.

The resulting Z(CZPHI, AHR) and ZDR fields at 1450 UTC, associated with PIA (PIADP) values up to 10 dB (1.6 dB), are shown in Fig. 8. In the Z(CZPHI, AHR) field, a significant gradient can be seen along the inflow edge of the storm (arrow 1), as well as a narrow echo appendage (arrow 2). An echo appendage typically curves in the presence of a mesocyclone process; however, this feature was not seen during the considered period. The ZDR field shows an area of significantly enhanced values along the inflow edge (arrow 3). This feature, commonly seen in supercell storms, is referred to as the ZDR arc signature as a result of possible size sorting processes (Kumjian and Ryzhkov 2008). The fields of KDP(C) and KDP(AHR) are also illustrated in Fig. 8. It is seen that the KDP(AHR) field retains the spatial variability of the storm better than the KDP(C) field while reducing negative KDP estimates. Note that both KDP fields show enhanced values along the inflow edge of the storm with values as high as 12° km−1 collocated with the ZDR arc. Estimates of KDP over the echo appendage, in both KDP fields, are not possible because of its narrow width of less than 1 km.

Fig. 8.
Fig. 8.

Event E2 at 1450 UTC. Fields of (a) Z(CZPHI, AHR), (b) ZDR, (c) KDP(C), and (d) KDP(AHR) are shown. The black contours indicate the 30-dBZ level, and the magenta contours in (c) show the −1° km−1 level. In addition, the Z gradient along the inflow edge, the Z narrow appendage, and the ZDR arc signatures are indicated by arrows 1–3, respectively. The low-level inflow in (a) is represented by the three arrows.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

The selected values for αΦDP(C) and αΦDP(AHR) are given in Fig. 9 as a function of azimuth. Observe that the optimization of α using ΦDP(C) was possible only in three azimuthal profiles of the mini-supercell. This is because in multiple azimuthal profiles, the percentage of gates per profile with KDP(C) > 0° km−1 is less than 50%, which led to the selection of the constant α, avoiding suboptimal α values. This means that in those profiles, A is given by the ZPHI method, leading to a reasonable correlation ρAK as shown in Table 3. On the other hand, the optimization of α using ΦDP(AHR) occurred in multiple azimuthal profiles, resulting in values mostly larger than 0.34 dB (°)−1 in contrast to those resulting from ΦDP(C). According to Ryzhkov and Zrnić (1995) and Carey et al. (2000), such large values are expected in areas of big raindrops, which is consistent with the ZDR arc signature.

Fig. 9.
Fig. 9.

Event E2 at 1450 UTC. Selected values for α using ΦDP(C) and ΦDP(AHR) are given by the stemplots in red and green, respectively, as a function of azimuth.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

c. Event E3: Tornadic cell

This event was associated with a bow apex feature along the leading edge of the storm. According to Funk et al. (1999), cyclonic circulations can occur along or near the leading bow apex, which can produce tornadoes of F0–F3 intensity. For a detailed observation of event E3, only the southeast side of the Z(CZPHI, AHR), ZDR, KDP(C), and KDP(AHR) fields at 1955 UTC are shown in Fig. 10. The Z field shows a strong gradient along the leading edge (arrow 4), indicating a region of strong convergence and low-level inflow (white arrows). A bow apex attribute resulting possibly from a descending rear inflow jet (Weisman and Trapp 2003) is also noticeable (arrow 5). This feature seems to be associated with a rotation pattern in the form of a hook or weak-echo hole (Bluestein et al. 2007) (extended arrow 6) that caused wind and tornado damage as indicated in Table 1. It is also observed that the core of the weak-echo hole, whose inner diameter is approximately 0.75 km, is related to bounded weak ZDR and KDP values, located in the center of the white circles. It can be observed that KDP(AHR) preserves the storm structure better than KDP(C) because the AHR approach avoids a segmented KDP texture and negative KDP values, which are observed in the KDP(C) field. Maximum values of PIA and PIADP reached 18 and 3 dB, respectively, while fully attenuated areas (south side) occurred behind strong rain echoes associated with KDP values on the order of 10° km−1.

Fig. 10.
Fig. 10.

Event E3 at 1955 UTC. Fields of (a) Z(CZPHI, AHR), (b) ZDR, (c) KDP(C), and (d) KDP(AHR) are indicated. Various levels are shown: 40 dBZ (black contours), 1° km−1 (red contours), and −1° km−1 (magenta contours). The Z gradient along the inflow edge (arrow 4), the bow apex (arrow 5), and the weak-echo hole (arrow 6) are given in (a). The low-level inflow (white arrows) and the rotation pattern associated with the echo-weak hole (white circles) are also shown.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

The resulting values of αΦDP(C) and αΦDP(AHR) as a function of the azimuthal sector [0°; 360°], not shown here, indicate that for most azimuthal profiles, α values are associated with a minimum error E, except in the azimuthal sector of [40°; 120°], where estimates of A were determined by the ZPHI method. This sector was related to light and uniform rain profiles, where ΔΦDP values are smaller than 10°. Optimal values of αΦDP(AHR) are predominantly found between 0.34 and 0.50 dB (°)−1. The absence of α> 0.50 dB (°)−1, in contrast to event E2, may indicate the lack of big drops present at this time. Selected values of αΦDP(C) are frequently smaller than or equal to 0.34 dB (°)−1 but in a few profiles they are equal to 0.1 or 0.6 dB (°)−1, possibly as a result of an inadequate optimization process. The resulting e¯min and σemin, together with ρAK, σAK, and RMSE are given in Table 3, showing that ΦDP(AHR) profiles lead to more reliable values of α and better estimates of A and Z.

d. Event E4: Irregular-shaped cell

In contrast to events E1–E3, E4 is mainly related to light rain with a few spots of moderate rain and it is not associated with any known reflectivity signatures. In addition, multiple radial paths with reflectivity echoes larger than 30 dBZ are mostly smaller than 5 km, in which PIA reached values of 2.5 dB, and only in few profiles it increased to 14 dB. The fields of Z(CZPHI, AHR), ZDR, KDP(C), and KDP(AHR) at 0558 UTC are shown in Fig. 11. Comparing the fields of Z and KDP, the KDP(AHR) field maintains the spatial structure of the storm better than KDP(C). It can be seen that the magnitudes of KDP(C) and KDP(AHR) are frequently smaller than 4° km−1, implying a slow incremental behavior of estimated ΦDP profiles. As such, only the azimuthal sectors [75°; 150°] (east side) and [250°; 280°] (west side) were associated with ΔΦDP> 10°. In both sectors, the optimization process was characterized by an inadequate performance because, in multiple azimuthal profiles, repetitive values equal to 0.1 dB (°)−1 were selected and the associated errors were larger than those found in E1–E3. In the remaining profiles, values of αΦDP(C) were smaller than 0.34 dB (°)−1, while values of αΦDP(AHR) were comparable to 0.34 dB (°)−1, indicating the absence of raindrops of considerable size. The results associated with the selection of α using ΦDP(C) and ΦDP(AHR) are indicated in Table 3, showing a decreased performance of the CZPHI method compared to the results of E1–E3.

Fig. 11.
Fig. 11.

As in Fig. 8, but for E4 at 0558 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

5. Evaluation of δhv estimates

For each storm event, the preprocessed ΨDP (section 3a), the obtained KDP(AHR) fields, and A(CZPHI, AHR) fields were set as inputs to the δhv algorithm for its evaluation. As part of the δhv approach (step 1), a low-pass FIR filter specified by a 32-filter order and 1-km cutoff range scale was applied to the ΨDP field.

The estimated δhv fields resulting from storm events E1–E4 at 1216, 1450, 1955, and 0558 UTC, respectively, are shown in Fig. 12. In all events, it can be seen that the areas of δhv that are given by a uniform value correspond to the areas of Z smaller than the 30-dBZ level, which defines the shape of the described storm cells. Moreover, a spatial correlation between the δhv fields and their corresponding ZDR fields is observed, which confirms the correlation nature between δhv and ZDR (e.g., compare Figs. 12a and 7d). Such a spatial correlation is not exclusive to δhv and ZDR because a similar correlation is also observed between the fields of δhv, Z, and KDP, exemplifying the self-consistency relation (Scarchilli et al. 1996) between ZDR, Z, and KDP in a comparable manner.

Fig. 12.
Fig. 12.

The resulting fields of δhv from E1 to E4 at (a) 1216, (b) 1450, (c) 1955, and (d) 0558 UTC. The white contours indicate the 30-dBZ level, whereas the black contours in (c) represent the 40-dBZ level.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

The ability of the algorithm to capture the spatial variability of δhv is substantial. For example, in Fig. 12a, significant δhv values are more visible on the north side than on the south side of the storm cell, indicating the presence of Mie scattering. Another example of the spatial variability and consistency aspects of δhv is derived from E2, where increased δhv values (δhv> 7°), shown in Fig. 12b, are collocated with increased Z, ZDR, and KDP values shown in Fig. 8. This scenario suggests the presence of DSDs related to big raindrops, which is consistent with the ZDR arc shown in Fig. 8 and the large values for α given in Fig. 9.

In event E3, estimates of δhv were achieved only in the azimuthal sector [10°; 128°], see Fig. 12c, where it was possible to correct ΨDP profiles for system phase offset at beginning ranges (step 1). Outside this sector, ΨDP measurements were associated with a rapid increase as a result of heavy rain, not shown here, causing difficulties when removing the phase offset. Nonetheless, the δhv field shows features that are consistent with the structure of the tornadic storm, illustrated by Fig. 10, that is bounded by weak values in the center of the weak-echo hole, increased values on the south side of the apex feature, and uniform values in areas of light rain. In contrast to E3, the ΨDP field from event E4 was associated with light rain at the beginning ranges, allowing for phase-offset correction over the entire azimuthal scan. The estimated δhv field shown in Fig. 12d is characterized by values in the range 2°–5°, indicating that this event, in contrast to E1–E3, is dominated by small and medium raindrop sizes.

During the estimation of δhv, a percentage of δhv samples were removed (step 3) and replaced by interpolated values (step 4). Moreover, the areas of δhv collocated with |KDP(AHR)|< 0.4° km−1 (i.e., areas of light rain) were replaced by a uniform value (step 5). The percentages I (%) of δhv resulting from interpolation in E1–E4 are 25.12%, 27.48%, 29.42%, and 27.06%, respectively, while the uniform values U (°) are 0.59°, 0.65°, 0.87°, and 0.13°, respectively, and they are summarized in Table 4.

Table 4.

Comparison results between δhv estimates from steps 1 and 2 (S12) and steps 1–4 (S14) of the δhv algorithm for four storm events. Also, the results from step 4 (S4) and step 5 (S5) are summarized. For E3, ~20 000 data points were considered because of the limited sector of the δhv field.

Table 4.

To evaluate the improvements expected from adding steps 3 and 4 to the calculation of δhv given by steps 1 and 2 [i.e., similar to the calculation derived from Eq. (1)], the results obtained from steps 1 and 2 denoted as δhv(S12) and the results obtained from steps 1–4 indicated as δhv(S14) will be compared. This comparison could be performed using ZDR measurements because δhv and ZDR show a similar sensitivity to raindrop size. However, the presented measurements of ZDR are affected by an azimuthal modulation pattern and radar miscalibration, limiting the use of ZDR. Instead, an empirical relation in rain at 9.41 GHz between δhv and KDP demonstrated by Schneebeli et al. (2014) is used to conduct further assessments on δhv. In their work, range profiles of stochastically simulated DSDs were obtained such that their DSD properties, in terms of spatial and temporal structures (i.e., small-scale variability), match the properties of DSDs measured by a network of ground-based disdrometers. Although measured DSDs could have been used instead of simulated DSDs, the simulation of representative DSDs allows for obtaining a sufficient set and a wide range of KDP and δhv values, which is rarely the case for measured DSDs. The scattering amplitudes were given by T matrix calculations in which three different but commonly used models for drop shape were considered, while equivolumetric spherical drop diameters were given by [0.1;7.0] mm. In addition, three temperatures of 27°, 17°, and 7°C were included. From their simulated δhvKDP scatterplot (not shown here), two empirical linear fits were given as
L1:δhv=2.37KDP+0.0540°KDP2.5°km1
and
L2:δhv=0.14KDP+5.52.5°<KDP15°km1.

The resulting δhv(S12)–KDP and δhv(S14)–KDP scatterplots from event E1 are presented in Fig. 13, where KDP is given by KDP(AHR). In addition, the δ¯hv and δ¯hv±σδhv curves, derived from δhv(S14) as a function of KDP, are also shown. Both statistical curves were obtained in a similar manner as in step 3. The strong agreement between the δ¯hv curve and linear fits L1 and L2 shows an indirect validation of the presented method to estimate 2D δhv in rain. The spread of estimated δhv(S14)–KDP scatterplot is found to be comparable to the spread of the simulated δhvKDP scatterplot. Using both remarks, it can be said that the estimation of δhv associated with δhv(S14) is capable of reducing the outliers seen in δhv(S12), illustrating improvements from steps 3 and 4. These outliers could be due to random oscillations of ΨDP profiles or a decreasing behavior of ΨDP with range. To quantify the consistency of the scatterplots, the mean absolute error (MAE; °) between the δ¯hv magnitudes and the empirical linear fits is used as a quality measure. The resulting MAE values related to δhv(S12) and δhv(S14) are equal to 0.74° and 0.37°, respectively. Moreover, the arithmetic mean of the σδhv samples [mean standard deviation (MSD; °)], derived from δhv(S12) is equal to 1.66°, whereas for δhv(S14) it is reduced to 1.10°. Similar analyses were conducted for events E2–E4 and the quantified errors are summarized in Table 4.

Fig. 13.
Fig. 13.

Event E1 at 1216 UTC. The δhvKDP(AHR) scatterplots resulting from steps 1 and 2 (blue) and steps 1–4 (green) of the δhv algorithm. The thick black line represents δ¯hv (i.e., mean values of δhv estimates as a function of KDP), while the thin lines represent δ¯hv±σδhv. The gray straight lines indicate two linear relations, L1 and L2, derived from scattering simulations in rain.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

6. Assessment on A and δhv

a. Performance of the CZPHI method

To further evaluate the CZPHI method, the same quality measures introduced in section 4 and the storm events E1–E4 are used but during time periods, as given in Table 1. For a representative and concise evaluation, only the results from event E2 will be discussed in detail. During the first 20 min, this event consisted of an ordinary storm cell of a small size, ~50 km2. When this cell was exiting the “view” of the radar, around 1420 UTC, another storm cell entered the scope of the radar. This storm manifested the characteristics of a mini-supercell during the period 1430–1500 UTC and that of a decaying storm after 1500 UTC. The quality measures resulting from event E2 are shown in Fig. 14.

Fig. 14.
Fig. 14.

Time series of quality measures from the CZPHI method for event E2. (a) Mean values e¯min (solid lines) related to ΦDP(C) (red) and ΦDP(AHR) (green). The corresponding variabilities e¯min±σemin (dashed lines). (b) ρAK (solid lines) and σAK (dashed lines) related to ΦDP(C) (red) and ΦDP(AHR) (green). (c) RMSE of Z associated with ΦDP(C) (red) and ΦDP(AHR) (green).

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

Figure 14a illustrates the time series of the mean and standard deviation of the errors related to the optimization of the parameter α. From these results, it can be inferred that the degree of similarity between the ΦDP(CZPHI) and ΦDP profiles is much higher when ΦDP is given by ΦDP(AHR) instead of ΦDP(C), leading to a more reliable selection of αΦDP(AHR). In the period 1415–1430 UTC, the optimization of α did not occur because the storm scenario was given by weak rain echoes and rain paths of less than 3 km, which are not sufficient to meet the established conditions. The increments of e¯min and σemin during 1500–1510 UTC correspond to a temporal reduction of the storm cell in size and intensity, associated with the decaying phase of the storm.

The impact of the optimization of α on the estimation of A is quantified by comparing A(CZPHI, C) and A(CZPHI, AHR) against KDP(AHR) using their degree of correlation ρAK and dispersion σAK. The time series in Fig. 14b show values of ρAK very close to 1 when A is given by A(CZPHI, AHR) instead of A(CZPHI, C). The two ρAK time series are sometimes comparable because A and KDP estimates could remain linear even if the selected values for α are suboptimal, provided that the α values are alike. In contrast, the results of σAK appear to be more sensitive to the choice of α because σAK evaluates the spread of the difference between A(CZPHI) and A(DP, AHR) estimates. The decreasing behavior of ρAK during the period 1420–1430 UTC corresponds to inaccurate A(ZPHI, C) values resulting from noisy estimates of ΔΦDP over small paths of light rain. In Fig. 14c, the time series of RMSE illustrate the impact of A(CZPHI) on attenuation-corrected Z. It can be said that between A(CZPHI, C) and A(CZPHI, AHR), the estimates of A(CZPHI, C) can impact negatively on the accuracy of Z. Furthermore, the RMSE magnitudes for both cases tend to increase from a scenario given by an ordinary cell, before 1420 UTC, to a complex mini-supercell, after 1420 UTC. This tendency is due to the spatial structure of the storm cells that can pose a more or less challenging task to capture the sensitivity of α to DSD and drop size variabilities. Such a challenging level can be depicted from the e¯min±σemin time series, as they exhibit a noticeable spread after 1420 UTC, indicating the difficulty in minimizing the error E. The discontinuity of RMSE observed around 1420 UTC is because of the lack of Z samples ≥ 35 dBZ to compute RMSE. The quality measures resulting from the events E1, E3, and E4 presented similar results to those calculated from event E2. For example, in events E1–E4, e¯min related to ΦDP(AHR) and ΦDP(C) were found on the order of 0°–0.5° and 1°–2.5°, respectively, except in event E4, where it increased to 1° for the case of ΦDP(AHR). In addition, RMSE values derived from Z(CZPHI, C) were found in the range of 1–2 dB, while for Z(CZPHI, AHR) they were seen between 0 and 0.5 dB.

To analyze the distribution of the optimal values for α associated with a minimum E, the histograms of αΦDP(C) and αΦDP(AHR) resulting from the optimization process during the same time periods of E1–E4 are shown in Fig. 15. Each histogram consists of 11 bins whose centers are separated by 0.05 dB (°)−1, while the sum of the bin heights is equal to 1. In events E1–E3, a frequent selection of αΦDP(C) equal to 0.1 dB (°)−1 is observed, as a result of a recurrent mismatch between the measured ΨDP and estimated ΦDP, while for the case of αΦDP(AHR) such selection is only occasionally seen. The selection of α in the vicinity of 0.34 dB (°)−1 is more evident in the case of αΦDP(AHR) than in the case of αΦDP(C). This remark agrees with the empirical value of α that is obtained from simulations and fitting procedures. Nonetheless, the histogram of αΦDP(AHR) from E2 also shows a reasonable contribution from α larger than the empirical one. The reason for such a contribution is because of the increased size of raindrops associated with the mini-supercell structure as shown in Figs. 8 and 9 and an inadequate optimization process during the decaying period. In event E4, a repetitive selection of α equal to 0.1 and 0.6 dB (°)−1 is noted, indicating an unstable behavior of the optimization process, which agrees with the increasing behavior of the e¯min and e¯min±σemin times series but is not shown here.

Fig. 15.
Fig. 15.

(a) Histograms of optimal αΦDP(C) (red) and αΦDP(AHR) (green) for event E1. (b)–(d) As in (a), but for E2–E4, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

b. Performance of the δhv algorithm

To further assess the δhv algorithm, the results related to steps 1 and 2 and steps 1–4 are compared using the time periods of events E1–E4 and the quality measures MAE, MSD, and I. Recall that MAE and MSD were calculated using the empirical relation between δhv and KDP. The time series resulting from all events are shown in Fig. 16. In general, it is observed that the results associated with δhv(S14) yield more satisfying results than those from δhv(S12). However, the amount of improvement changes according to the evolution of the storms.

Fig. 16.
Fig. 16.

(a) Time series of quality measures from the δhv algorithm for event E1. Left y axis: MAE + 5° resulting from steps 1 and 2 (solid blue) and from steps 1–4 (solid green). The black line indicates the 5° shift. MSD from steps 1 and 2 (dashed blue) and from steps 1–4 (dashed green). Right y axis: I resulting from step 4 (magenta). (b)–(d) As in (a), but for E2–E4, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 35, 12; 10.1175/JTECH-D-17-0219.1

In terms of MAE, the improvement observed from δhv(S14) with respect to δhv(S12) is more visible during periods of light rain echoes over small paths, which complicates the estimation of ΦDP from noisy ΨDP. For example, in Fig. 16a, the storm scenario of E1 during 1205–1215 UTC was dominated by segmented profiles of ΨDP, values of KDP in the range from −2° to 3° km−1, and a temporal increase of e¯min. A similar scenario occurred during the last 20 min of event E2, Fig. 16b, that corresponds to the decaying phase of the mini-supercell storm and to the increased values of e¯min. Note that in all events, the MAE time series resulting from δhv(S14) show a different range in which they fluctuate. For instance, the resulting time series from events E1 and E3 are on the order of 0°–1°, while for events E2 and E4 they are on the order of 0°–2° and 1°–2°, respectively. Thus, for E1 and E3, MAE values may indicate a favorable and persistent agreement, on average, with the empirical relations. For E2 and E4, the slightly increased values of MAE reflect the challenge of estimating δhv, because of the strong variability of drop size, and the noisy measurements of ΨDP, respectively. Such a range of fluctuations in E2 and E4 may be linked to the accuracy of selecting optimal α values because the selection of suboptimal αΦDP(AHR) values were depicted more frequently than for E1 and E3; see Fig. 15. Further, the fluctuations of MAE in all events can be connected to some extent with a misrepresentation of the empirical δhvKDP fit relations. The discontinuities seen in E2–E4 are associated with episodes of moderate to heavy rain located adjacent to or on top of the radar, leading to a difficult scenario to remove the offset of the ΨDP profiles (step 1 of the δhv method) or, sometimes, to a significant increase of the noise floor.

In contrast to MAE, MSD time series depict an evident improvement obtained from δhv(S14) in relation to δhv(S12). Note that in all events, the MSD time series for the case of δhv(S14) oscillate for the range of 1°–2°, contrary to those observed for the range of 1°–4° for δhv(S12), and show a uniform dispersion level and stable performance. The stability of the MSD values can be interpreted as a satisfactory performance of the steps 3 and 4 of the δhv approach in which δhv values outside the ±1σδhv extent are filtered and replaced by interpolated values. The time series of I resulting from the estimation of δhv(S14) represent, in a percentage manner, the number of occasions that δhv(S12) estimates were replaced by interpolated values. It can be seen that the percentage of δhv samples being interpolated increases from E1 toward E4: E1 (10%–20%), E2 and E3 (10%–30%), and E4 (20%–40%). Such tendency is consistent with the challenging level, presented by each event, of estimating accurate ΦDP either from A(CZPHI, AHR) or directly from KDP(AHR). Note that in this analysis, the impact of estimating ΦDP from A(CZPHI, C) or KDP(C) on the estimation of δhv was not taken into account, instead the analysis focused on measuring the benefits of including steps 3 and 4, which is the mitigation of erroneous δhv samples derived from steps 1 and 2.

7. Summary and conclusions

In weather radar polarimetry at X-band frequencies, the differential phase ΨDP consists of two components: the propagation differential phase ΦDP and the backscatter differential phase δhv. The use of ΦDP-based variables such as the specific differential phase KDP and the specific attenuation A has improved radar measurements affected by, for example, attenuation, miscalibration, and partial beam blockage. Another variable of interest is δhv because of its sensitivity to the dominant size of raindrops, similarly to ZDR. However, the accuracy of KDP, A, and δhv strongly depends on the ability to separate ΦDP and δhv from noisy ΨDP measurements, especially over short rain paths. This work has explored the impact of estimating ΦDP profiles on the estimation of A and thereby on the attenuation correction of Z using the extended version of the ZPHI method, the CZPHI method. Special attention was given to the optimization of the parameter α that relates KDP and A in rain. Also, a technique to improve the calculation of δhv in rain has been proposed, with an emphasis on storm cells observed over short range paths. For such purposes, the conventional range-filtering method and the adaptive high-resolution (AHR) approach were implemented to estimate KDP, denoted as KDP(C) and KDP(AHR), respectively. Additionally, the ZPHI method (with a constant α) and the CZPHI technique (with a variable α) were adapted at X-band frequencies to estimate A, denoted as A(ZPHI) and A(CZPHI), respectively. Moreover, the results obtained from the AHR and CZPHI methods were included in the estimation of δhv together with an interpolation process.

In the analysis associated with a constant α, KDP(AHR) and A(ZPHI) magnitudes show a strong consistency, leading to a correlation coefficient of ~0.96 for moderate to heavy rain and of ~0.92 for light rain. In contrast, KDP(C) and A(ZPHI) present a low agreement; nonetheless, KDP(C) and KDP(AHR) lead to similar errors on the attenuation correction of Z, with a slight degradation related to KDP(C). This means that the reduced performance of KDP(C) does not severely affect the correction of Z, but it can negatively impact the estimation of A. These findings confirm the conclusions of similar studies that when KDP (or ΦDP) is not properly estimated, the performance of the DP (i.e., A=αKDP) and ZPHI methods for attenuation correction purposes are similar, with a lower performance of the DP method in estimating A (Gorgucci and Chandrasekar 2005).

In the study related to a variable α, the CZPHI method was tested using ΦDP profiles that are given by ΦDP(C) and ΦDP(AHR). A comparative analysis indicates that in the optimization of α, ΦDP(AHR) profiles lead to minimum errors smaller than those related to ΦDP(C) profiles, and therefore the α values associated with ΦDP(AHR) appear to better represent the variability of DSD in the observed storms. The impact of the selected values of α on the estimation of A was measured in terms of ρAK and σAK, showing an improved performance of the CZPHI method when α is associated with ΦDP(AHR) instead of ΦDP(C). A similar conclusion is given about the impact of A(CZPHI) on the correction of Z but measured in terms of the RMSE. For this analysis, KDP(AHR) was used as a reference because of the strong relation seen between KDP(AHR) and A(ZPHI) and the fact that data were obtained from one radar (i.e., without independent measurements at the same time of the storm events). Nonetheless, such a methodology allows a volume-to-volume comparison between estimates of A and KDP obtained from independent approaches. On the one hand, the time series analysis illustrates the degradation of the CZPHI method when the selection of α is connected to ΦDP(C). This agrees with previous studies in which the performance of the CZPHI technique for attenuation correction purposes can decrease compared to the ZPHI approach (Snyder et al. 2010). On the other hand, ΦDP(AHR) seems to improve the optimal selection of α because the errors related to the optimization process are on the order of 0°–0.5°, in contrast to 1°–2.5° for ΦDP(C). Moreover, the histograms of αΦDP(AHR) confirm, in most of the cases, that the selection of α is consistent with empirical values of α. However, in scenarios dominated by light rain, the optimization can lead to the selection of erroneous α values. Nonetheless, the presented analysis shows the potential of combining the AHR and CZPHI approaches for a better estimation of A and correction of Z in rain recurring to the optimization of the parameter α over short range paths.

The proposed δhv algorithm, which considers the reconstruction of ΦDP by the AHR and the CZPHI approaches, provides 2D δhv fields that depict the spatial variability of raindrop size and exhibit a spatial distribution similar to the one of ZDR. Given that Z and KDP also depend to some extent on the size of raindrops, the estimated δhv fields also show a spatial correlation with the fields of attenuation-corrected Z and KDP(AHR), mainly in areas of KDP> 0.4° km−1. The results of the time series analyses, which correspond to the evolution of the presented storms, show a significant agreement between estimated δhvKDP(AHR) scatterplots and experimental linear fits in rain, with a mean absolute error (MAE) and a mean standard deviation (MSD) on the order of 0°–2° and 1°–2°, respectively. In addition, the time series of MAE and MSD depicted that the proposed algorithm outperformed the approach of estimating δhv, that is, by the difference between ΨDP and ΦDP [i.e., similar to Eq. (1)]. Such improvement is mainly because of the filtering and interpolation steps considered during the estimation of δhv by the proposed algorithm. The percentage of δhv samples resulting from these two steps range from 10% to 40%. This range corresponds to the amount of noise and/or fluctuations inherent to ΨDP and the accuracy of reconstructing ΦDP. The suggested δhv method is highly sensitive to any possible mismatch between ΨDP and ΦDP at beginning ranges. For example, δhv cannot be accurately estimated when the slope of ΨDP increases rapidly at beginning ranges (i.e., when a storm is on top of or adjacent to a radar). Nonetheless, the presented δhv algorithm is able to depict areas of moderate to large raindrops (i.e., Mie scattering signatures) at high spatial resolution.

Even though it was shown that the presented work can provide improved estimates of α, A, and δhv in rain using data from an X-band radar with calibration limitations, further development of the proposed techniques is required to achieve the ambitions of real-time operations. This effort may require an automatic algorithm to separate rain particles from other hydrometeors, tuning of the frequency-dependent coefficients in the relations between polarimetric variables, and sensitivity analysis to temperature conditions. It may also require quality control to examine the impact of long-range observations and complex terrain—related to nonuniform beam filling, beam blockage, and phase folding—on the measurements of ΨDP, Z, and ZDR, which can lead to a reduced performance of the discussed methods. Therefore, before applying the presented techniques, it is important to (i) identify error sources that can affect the quality of measured polarimetric variables (Gourley et al. 2006) and (ii) discriminate rain from other hydrometeors (Lim et al. 2013). In situations where Z and ZDR data are corrupted and/or in areas other than rain, it is recommended to use the conventional approach to estimate ΦDP, the ZPHI method to estimate A, and the proposed algorithm to estimate δhv but excluding steps 3–5. Regarding the implementation of the presented algorithms, the AHR approach is basically a mean average estimator with an adaptive but simple characteristic of the selection of the pathlengths to obtain derivatives of ΨDP. The CZPHI method requires a ΨDP extent of at least 3 km as well as a set of predefined conditions to avoid suboptimal results. The δhv algorithm mainly adds two more steps (filtering and interpolation) to the direct estimation of δhv, which do not require any costly computational processing.

A careful ΨDP processing is vital to unleash the full potential of polarimetric weather radars, especially at X-band frequencies. This work shows an alternative to processing ΨDP profiles in rain and thereby allows an improved selection of α related to the CZPHI method and enhanced estimation of δhv in difficult scenarios characterized by small ΔΦDP magnitudes (~10°–50°) and short path intervals (~5–10 km). This alternative could be beneficial when a long path needs to be segmented because of detected areas of hail along a beam. Although the results of α, Z, and δhv could be further assessed using external data from, for example, a network of disdrometers, microwave links, or collocated S- and X-band radars to consolidate the findings of this work, it is foreseen that in the context of ΨDP processing, such as the one presented in this work, users can benefit from better observations of ΨDP-based variables in convective storm cells.

Acknowledgments

Gratitudes to 4TUDatacentrum for its support of maintaining IDRA data, an open access dataset (Russchenberg et al. 2010). Also, the authors thank Dr. Jacopo Grazioli and Dr. Yadong Wang for their constructive discussion. This work was supported by RainGain through INTERREG IV B.

REFERENCES

  • Bertalmio,M.,L. Vese,G. Spario, andS. Osher,2003:Simultaneous structure and texture image inpainting.IEEE Trans. Image Process.,12,882889, https://doi.org/10.1109/TIP.2003.815261.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bluestein,H.,M. French,R. Tanamachi,S. Frasier,K. Hardwick,F. Junyent, andA. Pazmany,2007:Close-range observations of tornadoes in supercells made with a dual-polarization, X-band, mobile Doppler radar.Mon. Wea. Rev.,135,15221543, https://doi.org/10.1175/MWR3349.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi,V. N., andV. Chandrasekar,2001: Polarimetric Doppler Weather Radar Principles and Applications. Cambridge University Press, 636 pp.

    • Crossref
    • Export Citation
  • Bringi,V. N.,V. Chandrasekar,N. Balakrishman, andD. Zrnić,1990:An examination of propagation effects in rainfall on radar measurements at microwave frequencies.J. Atmos. Oceanic Technol.,7,829840, https://doi.org/10.1175/1520-0426(1990)007<0829:AEOPEI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bringi,V. N.,T. Kennan, andV. Chandrasekar,2001:Correcting C-band reflectivity and differential reflectivity data for rain attenuation: A self-consistent method with constraints.IEEE Trans. Geosci. Remote Sens.,39,19061915, https://doi.org/10.1109/36.951081.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carey,L.,S. Rutledge,D. Ahijevych, andT. Keenan,2000:Correcting propagation effects in C-band polarimetric radar observations of tropical convection using differential propagation phase.J. Appl. Meteor.,39,14051433, https://doi.org/10.1175/1520-0450(2000)039<1405:CPEICB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chandrasekar,V.,H. Chen, andB. Philips,2018:Principles of high-resolution radar network for hazard mitigation and disaster management in an urban environment.J. Meteor. Soc. Japan,96A,119139, https://doi.org/10.2151/jmsj.2018-015.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Criminisi,A.,P. Perez, andK. Toyama,2004:Region filling and object removal by exemplar-based image inpainting.IEEE Trans. Image Process.,13,12001212, https://doi.org/10.1109/TIP.2004.833105.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Errico,J.,2006: Data interpolation by image inpaiting. Version 1.1.0.0, MATLAB Central File Exchange, http://www.mathworks.com/matlabcentral/fileexchange/4551.

  • Diederich,M.,A. Ryzhkov,C. Simmer,P. Zhang, andS. Trömel,2015:Use of specific attenuation for rainfall measurement at X-band radar wavelengths. Part I: Radar calibration and partial beam blockage estimation.J. Hydrometeor.,16,487502, https://doi.org/10.1175/JHM-D-14-0066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doviak,R. J., andD. S. Zrnić,1993: Doppler Radar and Weather Observations. 2nd ed. Academic, 562 pp.

  • Doviak,R. J.,V. Bringi,A. Ryshkov,A. Zahrai, andD. Zrnic,2000:Considerations for polarimetric upgrades to operational WSR-88D radars.J. Atmos. Oceanic Technol.,17,257278, https://doi.org/10.1175/1520-0426(2000)017<0257:CFPUTO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Elad,M.,J. Starck,P. Querre, andD. Donoho,2005:Simultaneous cartoon and texture image inpainting using morphological component analysis.Appl. Comput. Harmonic Anal.,19,340358, https://doi.org/10.1016/j.acha.2005.03.005.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Figueras i Ventura,J.,2009: Design of a high resolution X-band Doppler polarimetric radar. Ph.D. thesis, Delft University of Technology, 162 pp.

  • Funk,T. W.,K. E. Darmofal,J. D. Kirkpatrick,V. L. Dewald,R. W. Przybylinski,G. K. Schmocker, andY.-J. Lin,1999:Storm reflectivity and mesocyclone evolution associated with the 15 April 1994 squall line over Kentucky and southern Indiana.Wea. Forecasting,14,976993, https://doi.org/10.1175/1520-0434(1999)014<0976:SRAMEA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giangrande,S. E., andA. V. Ryzhkov,2005:Calibration of dual-polarization radar in the presence of partial beam blockage.J. Atmos. Oceanic Technol.,22,11561166, https://doi.org/10.1175/JTECH1766.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giangrande,S. E.,R. McGraw, andL. Lei,2013:An application of linear programming to polarimetric radar differential phase processing.J. Atmos. Oceanic Technol.,30,17161729, https://doi.org/10.1175/JTECH-D-12-00147.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci,E., andV. Chandrasekar,2005:Evaluation of attenuation correction methodology for dual-polarization radars: Application to X-band systems.J. Atmos. Oceanic Technol.,22,11951206, https://doi.org/10.1175/JTECH1763.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorgucci,E.,V. Chandrasekar, andL. Baldini,2006:Correction of X-band radar observations for propagation effects based on the self-consistency principle.J. Atmos. Oceanic Technol.,23,16681681, https://doi.org/10.1175/JTECH1950.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gourley,J. J.,P. Tabary, andJ. P. D. Chatelet,2006:Data quality of the Meteo-France C-band polarimetric radar.J. Atmos. Oceanic Technol.,23,13401356, https://doi.org/10.1175/JTECH1912.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Grazioli,J.,M. Schneebeli, andA. Berne,2014:Accuracy of phase-based algorithm for the estimation of the specific differential phase shift using simulated polarimetric weather radar data.IEEE Geosci. Remote Sens. Lett.,11,763767, https://doi.org/10.1109/LGRS.2013.2278620.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang,H.,G. Zhang,K. Zhao, andS. E. Giangrande,2017:A hybrid method to estimate specific differential phase and rainfall with linear programming and physics constraints.IEEE Trans. Geosci. Remote Sens.,55,96111, https://doi.org/10.1109/TGRS.2016.2596295.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hubbert,J., andV. N. Bringi,1995:An iterative filtering technique for the analysis of copolar differential phase and dual-frequency radar measurements.J. Atmos. Oceanic Technol.,12,643648, https://doi.org/10.1175/1520-0426(1995)012<0643:AIFTFT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jameson,A. R.,1992:The effect of temperature on attenuation correction schemes in rain using polarization propagation differential phase shift.J. Appl. Meteor.,31,11061118, https://doi.org/10.1175/1520-0450(1992)031<1106:TEOTOA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kim,D.-S.,M. Maki, andD.-I. Lee,2010:Retrieval of three-dimensional raindrop size distribution using X-band polarimetric radar data.J. Atmos. Oceanic Technol.,27,12651285, https://doi.org/10.1175/2010JTECHA1407.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kumjian,M. R., andA. V. Ryzhkov,2008:Polarimetric signatures in supercell thunderstorms.J. Appl. Meteor. Climatol.,47,19401961, https://doi.org/10.1175/2007JAMC1874.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leijnse,H., andCoauthors,2010:Precipitation measurement at CESAR, the Netherlands.J. Hydrometeor.,11,13221329, https://doi.org/10.1175/2010JHM1245.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim,S., andV. Chandrasekar,2016:A robust attenuation correction system for reflectivity and differential reflectivity in weather radars.IEEE Trans. Geosci. Remote Sens.,54,17271737, https://doi.org/10.1109/TGRS.2015.2487984.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lim,S.,R. Cifelli,V. Chandrasekar, andS. Y. Matrosov,2013:Precipitation classification and quantification using X-band dual-polarization weather radar: Application in the hydrometeorology testbed.J. Atmos. Oceanic Technol.,30,21082120, https://doi.org/10.1175/JTECH-D-12-00123.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,K. Clark,B. Martner, andA. Tokay,2002:X-band polarimetric radar measurements of rainfall.J. Appl. Meteor.,41,941952, https://doi.org/10.1175/1520-0450(2002)041<0941:XBPRMO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,D. E. Kingsmill,B. E. Martner, andF. M. Ralph,2005:The utility of X-band polarimetric radar for quantitative estimates of rainfall parameters.J. Hydrometeor.,6,248262, https://doi.org/10.1175/JHM424.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Matrosov,S. Y.,P. C. Kennedy, andR. Cifelli,2014:Experimentally based estimates of relations between X-band radar signal attenuation characteristics and differential phase in rain.J. Atmos. Oceanic Technol.,31,24422450, https://doi.org/10.1175/JTECH-D-13-00231.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLaughlin,D., andCoauthors,2009:Short-wavelength technology and the potential for distributed networks of small radar systems.Bull. Amer. Meteor. Soc.,90,17971817, https://doi.org/10.1175/2009BAMS2507.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Otto,T., andH. W. J. Russchenberg,2010: Estimation of the raindrop-size distribution at X-band using specific differential phase and differential backscatter phase. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology (ERAD 2010), Sibiu, Romania, Meteor Romania, 6 pp., https://www.erad2010.com/pdf/oral/thursday/xband/07_ERAD2010_0109.pdf.

  • Otto,T., andH. W. J. Russchenberg,2011:Estimation of specific differential phase and differential backscatter phase from polarimetric weather radar measurements of rain.IEEE Geosci. Remote Sens. Lett.,8,988992, https://doi.org/10.1109/LGRS.2011.2145354.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park,S.-G.,V. N. Bringi,V. Chandrasekar,M. Maki, andK. Iwanami,2005a:Correction of radar reflectivity and differential reflectivity for rain attenuation at X band. Part I: Theoretical and empirical basis.J. Atmos. Oceanic Technol.,22,16211632, https://doi.org/10.1175/JTECH1803.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Park,S.-G.,M. Maki,K. Iwanami,V. N. Bringi, andV. Chandrasekar,2005b:Correction of radar reflectivity and differential reflectivity for rain attenuation at X band. Part II: Evaluation and application.J. Atmos. Oceanic Technol.,22,16331655, https://doi.org/10.1175/JTECH1804.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reinoso-Rondinel,R.,C. Unal, andH. Russchenberg,2018:Adaptive and high-resolution estimation of specific differential phase for polarimetric X-band weather radars.J. Atmos. Oceanic Technol.,35,555573, https://doi.org/10.1175/JTECH-D-17-0105.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Russchenberg,H.,T. Otto,R. Reinoso-Rondinel,C. Unal, andJ. Yin,2010: IDRA weather radar measurements—All data. 4TU Centre for Research Data, Delft University of Technology. Subset used: IDRA processed data with standard range, accessed 12 October 2012, https://doi.org/10.4121/uuid:5f3bcaa2-a456-4a66-a67b-1eec928cae6d.

    • Crossref
    • Export Citation
  • Ryzhkov,A., andD. S. Zrnić,1995:Precipitation and attenuation measurements at 10-cm wavelength.J. Appl. Meteor.,34,21212134, https://doi.org/10.1175/1520-0450(1995)034<2120:PAAMAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ryzhkov,A., andD. S. Zrnić,2005: Radar polarimetry at S, C, and X bands: Comparative analysis and operational implications. 32nd Conf. on Radar Meteor., Albuquerque, NM, Amer. Meteor. Soc., 9R3, https://ams.confex.com/ams/32Rad11Meso/webprogram/Paper95684.html.

  • Ryzhkov,A.,M. Diederich,P. Zhang, andC. Simmer,2014:Potential utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage, and radar networking.J. Atmos. Oceanic Technol.,31,599619, https://doi.org/10.1175/JTECH-D-13-00038.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli,G.,E. Gorgucci,V. Chandrasekar, andT. A. Seliga,1993:Rainfall estimation using polarimetric techniques at C-band frequencies.J. Appl. Meteor.,32,11501160, https://doi.org/10.1175/1520-0450(1993)032<1150:REUPTA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scarchilli,G.,E. Gorgucci,V. Chandrasekar, andA. Dobaie,1996:Self-consistency of polarization diversity measurement of rainfall.IEEE Trans. Geosci. Remote Sens.,34,2226, https://doi.org/10.1109/36.481887.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneebeli,M., andA. Berne,2012:An extended Kalman filter framework for polarimetric X-band weather radar data processing.J. Atmos. Oceanic Technol.,29,711730, https://doi.org/10.1175/JTECH-D-10-05053.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneebeli,M.,J. Grazioli, andA. Berne,2014:Improved estimation of the specific differential phase shift using a compilation of Kalman filter ensembles.IEEE Trans. Geosci. Remote Sens.,52,51375149, https://doi.org/10.1109/TGRS.2013.2287017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Snyder,J.,H. Bluestein, andG. Zhang,2010:Attenuation correction and hydrometeor classification of high-resolution, X-band, dual-polarized mobile radar measurements in severe convective storms.J. Atmos. Oceanic Technol.,27,19792001, https://doi.org/10.1175/2010JTECHA1356.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud,J.,E. L. Bouar,E. Obligis, andM. Ali-Mehenni,2000:The rain profiling algorithm applied to polarimetric weather radar.J. Atmos. Oceanic Technol.,17,332356, https://doi.org/10.1175/1520-0426(2000)017<0332:TRPAAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Trömel,S.,M. R. Kumjian,A. V. Ryzhkov,C. Simmer, andM. Diederich,2013:Backscatter differential phase—Estimation and variability.J. Appl. Meteor. Climatol.,52,25292548, https://doi.org/10.1175/JAMC-D-13-0124.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang,Y., andV. Chandrasekar,2009:Algorithm for estimation of the specific differential phase.J. Atmos. Oceanic Technol.,26,25652578, https://doi.org/10.1175/2009JTECHA1358.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang,Y.,P. Zhang,A. V. Ryzhkov,J. Zhang, andP.-L. Chang,2014:Utilization of specific attenuation for tropical rainfall estimation in complex terrain.J. Hydrometeor.,15,22502266, https://doi.org/10.1175/JHM-D-14-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Weisman,M., andR. Trapp,2003:Low-level mesovortices within squall lines and bow echoes. Part I: Overview and dependence on environment shear.Mon. Wea. Rev.,131,27792803, https://doi.org/10.1175/1520-0493(2003)131<2779:LMWSLA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save