• Alfieri, L., P. Claps, and F. Laio, 2010: Time-dependent ZR relationships for estimating rainfall fields from radar measurements. Nat. Hazards Earth Syst. Sci., 10, 149158, https://doi.org/10.5194/nhess-10-149-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., and C. W. Ulbrich, 1977: Path- and area-integrated rainfall measurement by microwave attenuation in the 1–3 cm band. J. Appl. Meteor., 16, 13221331, https://doi.org/10.1175/1520-0450(1977)016<1322:PAAIRM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., and C. W. Ulbrich, 2006: Drop size spectra and integral remote sensing parameters in the transition from convective to stratiform rain. Geophys. Res. Lett., 33, L16803, https://doi.org/10.1029/2006GL026824.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., C. W. Ulbrich, F. D. Mark Jr., R. A. Black, E. Amitai, P. T. Willis, and C. E. Samsury, 2000: Partitioning tropical oceanic convective and stratiform rains by draft strength. J. Geophys. Res., 105, 22592267, https://doi.org/10.1029/1999JD901009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Auf der Maur, A. N., 2001: Statistical tools for drop size distributions: Moments and generalized gamma. J. Atmos. Sci., 58, 407418, https://doi.org/10.1175/1520-0469(2001)058<0407:STFDSD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Austin, P. M., 1987: Relation between measured radar reflectivity and surface rainfall. Mon. Wea. Rev., 115, 10531070, https://doi.org/10.1175/1520-0493(1987)115<1053:RBMRRA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Battan, L. J., 1973: Radar Observations of the Atmosphere. University of Chicago Press, 324 pp.

  • Bringi, V. N., C. R. Williams, M. Thurai, and P. T. May, 2009: Using dual-polarized radar and dual-frequency profiler for DSD characterization: A case study from Darwin, Australia. J. Atmos. Oceanic Technol., 26, 21072122, https://doi.org/10.1175/2009JTECHA1258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bukovčić, P., D. S. Zrnić, and G. Zhang, 2015: Convective–stratiform separation using video disdrometer observations in central Oklahoma—The Bayesian approach. Atmos. Res., 155, 176191, https://doi.org/10.1016/j.atmosres.2014.12.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Campos, E., and I. Zawadzki, 2000: Instrumental uncertainties in ZR relations. J. Appl. Meteor., 39, 10881102, https://doi.org/10.1175/1520-0450(2000)039<1088:IUIZRR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caracciolo, C., F. Prodi, A. Battaglia, and F. Porcu, 2006: Analysis of the moments and parameters of a gamma DSD to infer precipitation properties: A convective stratiform discrimination algorithm. Atmos. Res., 80, 165186, https://doi.org/10.1016/j.atmosres.2005.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ciach, G. J., and W. F. Krajewski, 1999: Radar–rain gauge comparison under observational uncertainties. J. Appl. Meteor., 38, 15191525, https://doi.org/10.1175/1520-0450(1999)038<1519:RRGCUO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Adderio, L. P., F. Porcù, and A. Tokay, 2018: Evolution of drop size distribution in natural rain. Atmos. Res., 200, 7076, https://doi.org/10.1016/j.atmosres.2017.10.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doelling, I. G., J. Joss, and J. Riedl, 1998: Systematic variations of ZR-relationships from drop size distributions measured in northern Germany during seven years. Atmos. Res., 47–48, 635649, https://doi.org/10.1016/S0169-8095(98)00043-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fujiwara, M., 1965: Raindrop-size distributions from individual storms. J. Atmos. Sci., 22, 585591, https://doi.org/10.1175/1520-0469(1965)022<0585:RSDFIS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gunn, R., and G. D. Kinzer, 1949: The terminal velocity of fall for water droplets in stagnant air. J. Meteor., 6, 243248, https://doi.org/10.1175/1520-0469(1949)006<0243:TTVOFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 1993: Cloud Dynamics. Academic Press, 573 pp.

  • Hu, Z., and R. C. Srivastava, 1995: Evolution of raindrop size distributions by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 17611783, https://doi.org/10.1175/1520-0469(1995)052<1761:EORSDB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Illingworth, A. J., and T. M. Blackman, 2002: The need to represent raindrop size spectra as normalized gamma distributions for the interpretation of polarization radar observations. J. Appl. Meteor., 41, 286297, https://doi.org/10.1175/1520-0450(2002)041<0286:TNTRRS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Joss, J., and A. Waldvogel, 1970: A method to improve the accuracy of radar-measured amounts of precipitation. 14th Radar Meteorology Conf., Tucson, AZ, Amer. Meteor. Soc., 237–238.

    • Search Google Scholar
    • Export Citation
  • Krajewski, W. F., and J. A. Smith, 1991: On the estimation of climatological ZR relationships. J. Appl. Meteor., 30, 14361445, https://doi.org/10.1175/1520-0450(1991)030<1436:OTEOCR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, G. W., and I. Zawadzki, 2005: Variability of drop size distributions: Time-scale dependence of the variability and its effects on rain estimation. J. Appl. Meteor., 44, 241255, https://doi.org/10.1175/JAM2183.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, G. W., I. Zawadzki, W. Szyrmer, D. Sempere-Torres, and R. Uijlenhoet, 2004: A general approach to double-moment normalization of drop size distributions. J. Appl. Meteor., 43, 264281, https://doi.org/10.1175/1520-0450(2004)043<0264:AGATDN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lengfeld, K., M. Clemens, H. Münster, and F. Ament, 2014: Performance of high-resolution X-band weather radar networks—The PATTERN example. Atmos. Meas. Tech., 7, 41514166, https://doi.org/10.5194/amt-7-4151-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165166, https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., W. Hitschfeld, and K. L. S. Gunn, 1955: Advances in radar weather. Advances in Geophysics, Vol. 2, Academic Press, 1–56, https://doi.org/10.1016/S0065-2687(08)60310-6.

    • Crossref
    • Export Citation
  • METEK, 2009: MRR Physical Basics (Version 5.2.0.1). METEK Meteorologische Messtechnik GmbH, 20 pp.

  • Penide, G., A. Protat, V. V. Kumar, and P. T. May, 2013: Comparison of two convective/stratiform precipitation classification techniques: Radar reflectivity texture versus drop size distribution-based approach. J. Atmos. Oceanic Technol., 30, 27882797, https://doi.org/10.1175/JTECH-D-13-00019.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, G., B. Fischer, and T. Andersson, 2002: Rain observations with a vertically looking Micro Rain Radar (MRR). Boreal Environ. Res., 7, 353362.

    • Search Google Scholar
    • Export Citation
  • Peters, G., B. Fischer, H. Münster, M. Clemens, and A. Wagner, 2005: Profiles of raindrop size distributions as retrieved by microrain radars. J. Appl. Meteor., 44, 19301949, https://doi.org/10.1175/JAM2316.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2016a: Small-scale variability of the raindrop size distribution and its effect on areal rainfall retrieval. J. Hydrometeor., 17, 20772104, https://doi.org/10.1175/JHM-D-15-0214.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2016b: Spatial interpolation of experimental raindrop size distribution spectra. Quart. J. Roy. Meteor. Soc., 142, 125137, https://doi.org/10.1002/qj.2801.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2017: Retrieval of the raindrop size distribution from polarimetric radar data using double-moment normalization. Atmos. Meas. Tech., 10, 25732594, https://doi.org/10.5194/amt-10-2573-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., and C. W. Ulbrich, 2003: Cloud microphysical properties, processes, and rainfall estimations opportunities. Cloud Systems, Hurricanes, and the Tropical Rainfall Measuring Mission (TRMM), Meteor. Monogr., No. 51, Amer. Meteor. Soc., 237–258, https://doi.org/10.1175/0065-9401(2003)030<0237:CMPPAR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., E. Amitai, and D. B. Wolf, 1995a: Classification of rain regimes by the three-dimensional properties of reflectivity fields. J. Appl. Meteor., 34, 198211, https://doi.org/10.1175/1520-0450(1995)034<0198:CORRBT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., E. Amitai, and D. B. Wolf, 1995b: Improved accuracy of radar WPMM estimated rainfall upon application of objective classification criteria. J. Appl. Meteor., 34, 212223, https://doi.org/10.1175/1520-0450-34.1.212.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sempere-Torres, D., R. Sánches-Diezma, I. Zawadzki, and J. D. Creutin, 2000: Identification of stratiform and convective areas using radar data with application to the improvement of DSD analysis and ZR relations. Phys. Chem. Earth, 25, 985990, https://doi.org/10.1016/S1464-1909(00)00138-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Short, D. A., T. Kozu, and K. Nakamura, 1990: Rainrate and raindrop size distribution observations in Darwin, Australia. Proc. URSI Commision F Open Symp. on Regional Factors in Predicting Radiowave Attenuation Due to Rain, Rio de Janeiro, Brazil, International Union of Radio Science Commission, 35–40.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., and W. F. Krajewski, 1993: A modeling study of rainfall rate–reflectivity relationships. Water Resour. Res., 29, 25052514, https://doi.org/10.1029/93WR00962.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and R. A. Houze Jr., 1997: Sensitivity of the estimated monthly convective rain fraction to the choice of ZR relation. J. Appl. Meteor., 36, 452462, https://doi.org/10.1175/1520-0450(1997)036<0452:SOTEMC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 1998: Convective versus stratiform rainfall: An ice-microphysical and kinematic conceptual model. Atmos. Res., 47–48, 317326, https://doi.org/10.1016/S0169-8095(97)00086-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 2000: Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra. J. Appl. Meteor., 39, 19231940, https://doi.org/10.1175/1520-0450(2000)039<1923:RRRAKE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 2004: Scale dependence of radar-rainfall rates – An assessment based on raindrop spectra. J. Hydrometeor., 5, 11711180, https://doi.org/10.1175/JHM-383.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., R. A. Houze Jr., and S. E. Yuter, 1995: Climatological characterization of three-dimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor., 34, 19782007, https://doi.org/10.1175/1520-0450(1995)034<1978:CCOTDS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., J. A. Smith, and R. Uijlenhoet, 2004: A microphysical interpretation of radar reflectivity–rain rate relationships. J. Atmos. Sci., 61, 11141131, https://doi.org/10.1175/1520-0469(2004)061<1114:AMIORR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stout, G. E., and E. A. Mueller, 1968: Survey of relationships between rainfall rate and radar reflectivity in the measurement of precipitation. J. Appl. Meteor., 7, 465474, https://doi.org/10.1175/1520-0450(1968)007<0465:SORBRR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud, J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The concept of “normalized” distributions to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor., 40, 11181140, https://doi.org/10.1175/1520-0450(2001)040<1118:TCONDT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., and V. N. Bringi, 2018: Application of the generalized gamma model to represent the full rain drop size distribution. J. Appl. Meteor. Climatol., 57, 11971210, https://doi.org/10.1175/jamc-d-17-0235.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., V. N. Bringi, and P. T. May, 2010: CPOL radar-derived drop size distribution statistics of stratiform and convective rain for two regimes in Darwin, Australia. J. Atmos. Oceanic Technol., 27, 932942, https://doi.org/10.1175/2010JTECHA1349.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., P. N. Gatlin, and V. N. Bringi, 2016: Separating stratiform and convective rain types based on the drop size distribution characteristics using 2D video disdrometer data. Atmos. Res., 169, 416423, https://doi.org/10.1016/j.atmosres.2015.04.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., and D. A. Short, 1996: Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective clouds. J. Appl. Meteor., 35, 355371, https://doi.org/10.1175/1520-0450(1996)035<0355:EFTRSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., and P. G. Bashor, 2010: An experimental study of small-scale variability of raindrop size distributions. J. Appl. Meteor. Climatol., 49, 23482365, https://doi.org/10.1175/2010JAMC2269.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., D. A. Short, C. R. Williams, W. L. Ecklund, and K. S. Gage, 1999: Tropical rainfall associated with convective and stratiform clouds: Intercomparison of disdrometer and profiler measurements. J. Appl. Meteor., 38, 302320, https://doi.org/10.1175/1520-0450(1999)038<0302:TRAWCA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., L. P. D’Adderio, F. Porcù, D. B. Wolff, and W. A. Petersen, 2017: A field study of footprint-scale variability of raindrop size distribution. J. Hydrometeor., 18, 31653179, https://doi.org/10.1175/JHM-D-17-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Uijlenhoet, R., 2001: Raindrop size distributions and radar reflectivity–rain rate relationships of radar hydrology. Hydrol. Earth Syst. Sci., 5, 615627, https://doi.org/10.5194/hess-5-615-2001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the drop size distribution. J. Climate Appl. Meteor., 22, 17641775, https://doi.org/10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 1984: Assessment of the contribution of differential polarization to improve rainfall measurements. Radio Sci., 19, 4957, https://doi.org/10.1029/RS019i001p00049.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 1998: Rainfall microphysics and radar properties: Analysis methods for drop size spectra. J. Appl. Meteor., 37, 912923, https://doi.org/10.1175/1520-0450(1998)037<0912:RMARPA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 2002: On the separation of tropical convective and stratiform rains. J. Appl. Meteor., 41, 188195, https://doi.org/10.1175/1520-0450(2002)041<0188:OTSOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1974: The N0 jump of raindrop spectra. J. Atmos. Sci., 31, 10671078, https://doi.org/10.1175/1520-0469(1974)031<1067:TJORS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1975: Tropfenspektren, Niederschlagstyp und ZR Beziehungen (Drop spectra, precipitation types, and Z–R relations). Meteor. Z., 28, 3336.

    • Search Google Scholar
    • Export Citation
  • Yuter, S. E., and R. A. Houze Jr., 1997: Measurements of raindrop size distributions over the Pacific warm pool and implications for ZR relations. J. Appl. Meteor., 36, 847867, https://doi.org/10.1175/1520-0450(1997)036<0847:MORSDO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., 1984: Factors effecting the precision of radar measurements of rain. 22nd Conf. on Radar Meteorology, Zurich, Switzerland, Amer. Meteor. Soc., 251–256.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Time series of DSD N(D) and mass-weighted mean drop diameter Dm for periods of predominantly stratiform (1245–1330 UTC) and convective (1615–1700 UTC) precipitation at WST station on 19 Jul 2015. Gray colors indicate invalid spectra as defined in section 4a.

  • View in gallery

    Relationship between rain rate R and mass-weighted mean drop diameter Dm and the stratiform/convective classification after method 1 at WST station on 19 Jul 2015.

  • View in gallery

    Frequency distribution of factor α of the ZR relationship after Eq. (8) and the stratiform/convective classification after method 2 at WST station on 19 Jul 2015.

  • View in gallery

    Relationship between rain rate R and radar reflectivity Z and stratiform/convective classification after methods 1 and 2 at WST station on 19 Jul 2015. For reference the Marshall–Palmer ZR relationship is also shown.

  • View in gallery

    2D-histogram of radar reflectivity Z and rain rate R (color coded) at WST station for the testing period (April–September 2014) and ZR relationships adjusted to the respective data of the training period (April–September 2013).

  • View in gallery

    As in Fig. 5, but for (left) stratiform and (right) convective precipitation after (a),(b) method 1 and (c),(d) method 2 separately. Gray areas indicate the domain of the full testing dataset.

  • View in gallery

    Absolute differences between total accumulations of estimated rain rate RZ and DSD-based rain rate RDSD dependent on the ZR relationship and MRR station for the testing period (April–September 2014). Annotated numbers denote the respective relative differences (%).

  • View in gallery

    As in Fig. 7, but for WST station and dependent on rainfall intensity classes “light” (0.1 ≤ R < 1 mm h−1), “medium” (1 ≤ R < 10 mm h−1), and “heavy” (10 ≤ R < 200 mm h−1). Relative differences refer to the total rainfall accumulation.

  • View in gallery

    Distribution of difference between estimated rain rate RZ and DSD-based rain rate RDSD dependent on ZR relationship and rainfall intensity class at WST station for the testing period (April–September 2014). Gray lines and X symbols mark the median and arithmetic mean, and boxes and whiskers represent the interquartile range and the 5% and 95% quantiles, respectively.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 28 28 28
PDF Downloads 24 24 24

Stratiform and Convective Radar Reflectivity–Rain Rate Relationships and Their Potential to Improve Radar Rainfall Estimates

View More View Less
  • 1 Meteorological Institute, University of Hamburg, Hamburg, Germany
Full access

Abstract

The variability of the raindrop size distribution (DSD) contributes to large parts of the uncertainty in radar-based quantitative rainfall estimates. The variety of microphysical processes acting on the formation of rainfall generally leads to significantly different relationships between radar reflectivity Z and rain rate R for stratiform and convective rainfall. High-resolution observation data from three Micro Rain Radars in northern Germany are analyzed to quantify the potential of dual ZR relationships to improve radar rainfall estimates under idealized rainfall type identification and separation. Stratiform and convective rainfall are separated with two methods, establishing thresholds for the rain rate-dependent mean drop size and the α coefficient of the power-law ZR relationship. The two types of dual ZR relationships are tested against a standard Marshall–Palmer relationship and a globally adjusted single relationship. The comparison of DSD-based and reflectivity-derived rain rates shows that the use of stratiform and convective ZR relationships reduces the estimation error of the 6-month accumulated rainfall between 30% and 50% relative to a single ZR relationship. Consistent results for neighboring locations are obtained at different rainfall intensity classes. The range of estimation errors narrows by between 20% and 40% for 10-s-integrated rain rates, dependent on rainfall intensity and separation method. The presented technique also considerably reduces the occurrence of extreme underestimations of the true rain rate for heavy rainfall, which is particularly relevant for operational applications and flooding predictions.

© 2019 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: Bastian Kirsch, bastian.kirsch@uni-hamburg.de

Abstract

The variability of the raindrop size distribution (DSD) contributes to large parts of the uncertainty in radar-based quantitative rainfall estimates. The variety of microphysical processes acting on the formation of rainfall generally leads to significantly different relationships between radar reflectivity Z and rain rate R for stratiform and convective rainfall. High-resolution observation data from three Micro Rain Radars in northern Germany are analyzed to quantify the potential of dual ZR relationships to improve radar rainfall estimates under idealized rainfall type identification and separation. Stratiform and convective rainfall are separated with two methods, establishing thresholds for the rain rate-dependent mean drop size and the α coefficient of the power-law ZR relationship. The two types of dual ZR relationships are tested against a standard Marshall–Palmer relationship and a globally adjusted single relationship. The comparison of DSD-based and reflectivity-derived rain rates shows that the use of stratiform and convective ZR relationships reduces the estimation error of the 6-month accumulated rainfall between 30% and 50% relative to a single ZR relationship. Consistent results for neighboring locations are obtained at different rainfall intensity classes. The range of estimation errors narrows by between 20% and 40% for 10-s-integrated rain rates, dependent on rainfall intensity and separation method. The presented technique also considerably reduces the occurrence of extreme underestimations of the true rain rate for heavy rainfall, which is particularly relevant for operational applications and flooding predictions.

© 2019 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: Bastian Kirsch, bastian.kirsch@uni-hamburg.de

1. Introduction

As the main source of water for terrestrial systems, rainfall is of central importance for hydrological processes. The weather radar technique is a commonly used tool for quantitative precipitation estimation (QPE) and to obtain real-time estimates of the spatial and temporal rainfall distribution. Because of the variety of microphysical processes that are involved in the formation and transformation of precipitation particles, the drop size distribution (DSD) generally underlies large variations in space and time (Tokay and Bashor 2010; Tokay et al. 2017). Therefore, also the relationships between its integral parameters are of purely statistical nature and exhibit a highly transient character. This fact is especially relevant for the conversion of a received radar reflectivity signal Z into a rain rate R if the current DSD and its spatial variability is unknown. Even with a priori knowledge of the correct ZR relationship and without taking into account the uncertainties of radar measurements itself (Zawadzki 1984), the error of the radar-based QPE due to rainfall microphysics is significant (e.g., Ulbrich and Atlas 1984). Lee and Zawadzki (2005) quantified the average error in the instantaneous QPE that originates from the variability of the DSD to 41%. For the use of daily adjusted ZR relationships this error only reduces to 32%, which shows that a major part of the QPE uncertainty leads back to the inter- and intrastorm variability of the DSD. Alfieri et al. (2010) found a typical time scale of 3–5 h as an optimal calibration window for continuously adjusted ZR relationships and a reduction in the RMSE of the QPE of up to 28% relative to a fixed optimized ZR relationship.

Since single ZR relationships are rarely able to represent the complex microphysical formation processes of precipitation in its entirety, the application of separate ZR relationships for different rainfall types is a suitable method to reduce the QPE uncertainty. Atlas and Ulbrich (2006) emphasized the need to characterize the physical and dynamic nature of rain storms in remote sensing applications and the value of corresponding separation schemes for more precise radar rainfall estimates. An early study by Joss and Waldvogel (1970) revealed that the use of three different ZR relationships for drizzle, widespread and thunderstorm rainfall reduces the standard deviation of daily rainfall amounts by roughly one-half. Since then, many other authors discussed the issue of multiple ZR relationships for radar applications (e.g., Austin 1987; Steiner et al. 1995; Steiner and Houze 1997; Yuter and Houze 1997).

The existence of distinct rainfall regimes with considerably different microphysical properties has been well known for a long time (Fujiwara 1965; Stout and Mueller 1968). Waldvogel (1974) discussed rapid changes of the DSD intercept parameter N0 within single rainfall events, which marks the transition from one mesoscale precipitation area to another. These differences in the microphysical character of rainfall are mostly associated with stratiform and convective precipitation and their different formation mechanisms. Stratiform rainfall is generally formed in widespread regions of weak vertical air motion, where precipitation particles grow by water vapor deposition and aggregation of ice particles, melt into relatively large raindrops and often produce a bright band in radar signals in case of a sufficiently low 0°C isotherm. Convective precipitation particles mostly originate from strong localized updrafts of cumulonimbus clouds, primarily grow by collection of cloud droplets (i.e., coalescence, accretion, and riming) and are limited in size because of the dominating collision–breakup processes (Houze 1993; Tokay and Short 1996; Steiner and Smith 1998). In extreme cases of very strong convection (often in tropical environments) these processes may ultimately lead to the development of equilibrium DSDs (Hu and Srivastava 1995; D’Adderio et al. 2018).

The definition of objective criteria for a systematic separation of stratiform and convective rainfall is a challenging task. Numerous efforts have been made to develop separation algorithms for various instrumental setups either based on the texture of radar reflectivity fields (Rosenfeld et al. 1995a,b; Steiner et al. 1995; Yuter and Houze 1997; Sempere-Torres et al. 2000), updraft strength (Atlas et al. 2000), and properties of the DSD (Tokay et al. 1999; Caracciolo et al. 2006; Bringi et al. 2009; Bukovčić et al. 2015; Thurai et al. 2016). Comparisons between texture-based and DSD-based methods for tropical rainfall (Thurai et al. 2010; Penide et al. 2013) showed that both approaches yield reasonable results with slightly larger uncertainties for the convective mode. Yuter and Houze (1997), Steiner and Houze (1997), and Atlas et al. (2000) pointed out that purely DSD-based classification schemes cannot be accurate because of the wide range of possible drop sizes for the stratiform mode and, therefore, separate ZR relationships for stratiform and convective precipitation are not justified. Ulbrich and Atlas (2002) further discussed this remark and concluded that the tendency of convective rainfall to contain smaller drops and exhibit smaller reflectivities than stratiform rainfall of the same rain rate makes the bulk of DSDs separable and still leads to significantly different ZR relationships. However, ZR relationships derived from local DSD measurements are only valid for small domains.

The distinction between the stratiform and convective rainfall regime provides a very simple and physically justified framework to describe the general character of microphysical processes acting on the formation of raindrops, which is also linked to the macrophysical properties of rainfall (Houze 1993; Tokay and Short 1996). Therefore, this concept allows to infer microphysical properties of observed rainfall events in radar applications without any or only local DSD information. In this study we analyze an extensive dataset of high-resolution rainfall observations to quantify the potential improvement in QPE that arises from the use of refined ZR relationships specific for stratiform and convective rainfall. The conclusions drawn from our results are valid under the assumptions that the introduced methods provide a perfect separation of the two rainfall types and that each rainfall observation is correctly classified as either stratiform or convective. The paper organizes as follows: Section 2 briefly revisits the theoretical background of drop size distributions and ZR relationships, and section 3 describes the experimental database. After the introduction of two methods for the separation of stratiform and convective rainfall in section 4, the different single and dual ZR relationships are applied to DSD measurements and evaluated regarding their ability to improve the QPE in section 5, followed by a summary and conclusions of the study in section 6.

2. Theoretical background

The number concentration N(D) (mm−1 m−3) generally describes a population of differently sized raindrops per drop size D and unit volume of air. Several parameterizations for N(D) of different complexity have been proposed in literature. Generalizing the simple exponential DSD model by Marshall and Palmer (1948), Ulbrich (1983) introduced the more flexible and widely used standard gamma distribution
N(D)=N0Dμexp(ΛD),
which depends on intercept parameter N0 (mm−1 m−3), slope parameter Λ (mm−1), and dimensionless shape parameter μ. More realistic representations of observed DSDs and especially the small- and large-drop ends of the drop spectrum are achieved by different single- and double-moment normalization schemes (e.g., Testud et al. 2001; Illingworth and Blackman 2002; Lee et al. 2004) and the generalized gamma distribution (e.g., Auf der Maur 2001; Thurai and Bringi 2018). Independent of the DSD shape and assuming spherical drops, rain rate R (mm h−1) and radar reflectivity Z (mm6 m−3) are defined as
R=6π1040N(D)D3υ(D)dD
and
Z=0N(D)D6dD.
Neglecting the influence of vertical wind and turbulence, the fall velocity υ approximately depends on drop size D in the form of
υ(D)=υ0Dp,
where the coefficients υ0 = 3.778 m s−1 mmp and p = 0.67 found by Atlas and Ulbrich (1977) realize a close fit to data of Gunn and Kinzer (1949) in the diameter range 0.5 < D < 5.0 mm.
Although Z and R are generally independent measures of the DSD, the vast majority of related studies show strong evidence for a statistical relationship between both quantities in the general form of a power law
Z=αRβ,
where the multiplicative factor α and the exponent β are empirical constants. Since each single DSD determines specific values of radar reflectivity and rain rate, the ZR relationship describes the transformation of the DSD for variations in rain intensity. Therefore, the combination of the parameters α and β represents characteristic microphysical processes like coalescence, collision, or breakup, which act on the formation of a raindrop population and their variation in space and time and lead to the generally transient nature of the DSD (Houze 1993; Tokay and Short 1996; Steiner and Smith 1998; Steiner et al. 2004). While, for example, Marshall et al. (1955) or Joss and Waldvogel (1970) established widely used standard relationships, which realize a good representation of average rainfall conditions, a vast number of ZR relationships for different climatic conditions and precipitation type are known in literature (e.g., Battan 1973; Ulbrich 1983; Smith and Krajewski 1993; Doelling et al. 1998). Apart from the dominating microphysical processes, the parameters of measurement-based ZR relationships are also heavily influenced by factors like instrumental limitations (Krajewski and Smith 1991; Campos and Zawadzki 2000), scale variability of rainfall (Steiner and Smith 2004), and the applied derivation method (Doelling et al. 1998; Ciach and Krajewski 1999; Steiner and Smith 2000).

3. Data description

This study analyzes DSD data from Meteorologische Messtechnik GmbH (METEK) Micro Rain Radar (MRR) measurements in northern Germany between 2013 and 2015. MRRs are vertically oriented frequency modulated–continuous wave (FM-CW) K-band (24.1 GHz) radars, which retrieve DSD profiles from the range frequency shift and Doppler shift of falling raindrops. While the first moment of each Doppler spectrum is used to obtain the fall velocity, the ratio between spectral reflectivity and single particle backscattering cross section according to Mie scattering determines the drop number concentration N(D). The instrument also performs an internal noise removal and attenuation correction procedure (Peters et al. 2002; METEK 2009). The MRRs in the used setup observe N(D) for 46 drop size classes and diameters D between 0.246 and 5.05 mm with 10-s integration time. One important advantage of the MRR over commonly used in situ instruments like disdrometers is the much larger sampling volume, which guarantees a higher representativeness of observed DSDs. The MRRs measure DSD profiles for 31 range gates with a vertical resolution of 35 m and a maximum range of 1035 m, whereas we examine the fifth range gate (140–175 m) throughout this study. We made this choice to minimize the influence of near-field uncertainties as well as attenuation errors from higher levels. One important assumption for the derivation of DSDs is that the measured rain drops fall in stagnant air. In reality, the drop fall velocity is altered by vertical wind motion and turbulence, which typically leads to a misinterpretation of the actual drop size by vertically pointing Doppler radars. Although the presence of intense updrafts or downdrafts may introduce significant errors to single DSD retrievals, the vast majority of measurements are only affected by marginal air motions. Moreover, the sensitivity to vertical wind is largest for rain rates >10 mm h−1. Therefore, this error does not have a considerable impact on long-term rainfall statistics (Peters et al. 2005).

The MRRs are located about 50 km northwest of Hamburg, Germany, at the stations Itzehoe (WST; 53.9306°N 09.4847°E), Oelixdorf (MST; 53.9219°N 09.5815°E), and Kellinghusen (OST; 53.9417°N 09.7170°E). The three stations lie between 6.4 and 15.3 km apart from each other. For each year the MRR measurements are calibrated against local rain gauge data by comparing hourly rainfall sums between April and September. To filter out radar noise and unphysical data, we consider only DSDs with rain rates in the range 0.1 ≤ R ≤ 200 mm h−1 and positive integral parameters as rainfall. Furthermore, we exclude days with a rainfall accumulation lower than 1 mm from the dataset.

For this study, we analyze a total of 12 months of MRR measurement data, taken from two warm seasons to minimize the influence of solid-phase precipitation. The first 6-month period (1 April–30 September 2013) serves as a training dataset for the adjustment of the ZR relationships, which we test for the corresponding data of the second 6-month period (1 April–30 September 2014). For each of the three MRR stations WST, MST, and OST the test dataset consists of at least 67 000 valid DSD measurements, which provides a good basis for representative rainfall statistics.

4. Separation of stratiform and convective rainfall

a. Methods

In this study, we perform the stratiform/convective classification using two simple threshold methods, which are based on different integral parameters of the DSD. Method 1 (M1) arises from the classification of Tokay and Short (1996), who identified a stratiform and convective regime in tropical oceanic precipitation that experiences drastic changes in N0 as described by Waldvogel (1974). Testud et al. (2001) reformulated the original separation criterion dependent on N0 and R in the new form
R=1.64Dm4.25.
In Eq. (6), N0 is replaced by the mass-weighted mean drop diameter Dm, which is defined as the ratio of the fourth to the third moment of the DSD,
Dm=0N(D)D4dD0N(D)D3dD.
One important advantage of Dm over the number-weighted mean drop diameter D0 is its reduced sensitivity to the instrument-dependent sampling of small rain drops (Steiner et al. 2004). Consistent with the conceptual model of the underlying microphysics described in section 1, we consider DSDs with Dm smaller than Eq. (6) for a given R as convective, all others as stratiform. The temporal evolution of the DSD for two periods of a single rainfall event in Fig. 1 clearly illustrates the systematic differences in mean drop size and distribution shape that are typically associated with stratiform and convective precipitation. The periods of different rainfall types then eventually appear as distinct modes in the DmR space (Fig. 2).
Method 2 (M2) relates to the already mentioned assumption that the parameters of the ZR relationship generally reflect the rainfall type. Steiner et al. (2004) analytically derived a theoretical model of distinct ZR modes, which are either purely controlled by variations in drop number, drop size, or a combination of both. For the mixed-controlled case, which is a more realistic representation of average rainfall than the first two extreme cases, α is determined from single DSDs via
α=Γ(7+μ)[1046πυ01Γ(4+p+μ)]7+μ4+p+μ×[Γ(1+μ)(4+μ)1+μDm1+μNT]3p4+p+μ,
where the drop number density NT describes the zeroth moment of the DSD and Γ is the complete gamma function Γ(n+1)=0exp(x)xndx. According to Doelling et al. (1998) and Steiner and Smith (2000), the largest part of the natural variability of the ZR relationship is confined to α, while the assumption of a constant β is roughly valid. Also the study of Waldvogel (1975) suggests that the ZR relationships for separate rainfall types mainly differ in α while an increase in β results from mixed-type rainfall. Therefore, α qualifies as a criterion to separate the stratiform and convective regime. The proportionality between α and Dm in Eq. (8) suggests that convective rainfall generally relates to smaller values of α than stratiform rainfall. For the present study we chose a threshold of α = 150 since it shows a reasonable ability to discriminate between both rainfall types for several rainfall events as demonstrated by the local minimum in the frequency distribution in Fig. 3. We perform the calculation of μ in Eq. (8) via the method of moments (Ulbrich and Atlas 1998), whereas we only consider values in the range −1 < μ ≤ 50 to avoid undefined and unphysically high or low solutions for α. Furthermore, in the analysis for method 1 we also neglect all valid spectra with μ falling outside this range to ensure comparability between both separation methods.
Fig. 1.
Fig. 1.

Time series of DSD N(D) and mass-weighted mean drop diameter Dm for periods of predominantly stratiform (1245–1330 UTC) and convective (1615–1700 UTC) precipitation at WST station on 19 Jul 2015. Gray colors indicate invalid spectra as defined in section 4a.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

Fig. 2.
Fig. 2.

Relationship between rain rate R and mass-weighted mean drop diameter Dm and the stratiform/convective classification after method 1 at WST station on 19 Jul 2015.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

Fig. 3.
Fig. 3.

Frequency distribution of factor α of the ZR relationship after Eq. (8) and the stratiform/convective classification after method 2 at WST station on 19 Jul 2015.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

Many studies investigating the characterization of rainfall types show that the large intrinsic variability of DSDs may lead to considerable variations of the ZR relationship between individual storms or different climatic conditions. Probably arising from this circumstance, there is no general consent about the magnitude of ZR parameters for different rainfall types. While, for example, Waldvogel (1975), Uijlenhoet (2001), and Caracciolo et al. (2006) reported smaller α values for widespread than for thunderstorm rainfall, Short et al. (1990) and Tokay and Short (1996) observed the opposite for stratiform and convective rainfall. Steiner and Houze (1997) and Rosenfeld and Ulbrich (2003) named the different dynamic and microphysical precipitation processes between midlatitude and tropical rainfall as the main reason for this discrepancy. Other possible explanations lie in instrumental limitations, the observation height of the DSD, or sampling issues.

b. Separation performance

The two simple DSD-based methods we present here show a reasonable ability to identify different rainfall types in single rainfall events. Figure 4 illustrates the distinct modes of the ZR relationship that are associated with the stratiform and convective periods of the case presented in section 4a. The classification of both separation methods indicate a very good agreement with the visible clusters in ZR space and among each other (94.9%), which supports the physical validity of the two methods. We obtain similar results when applying the separation schemes to the entire six-month test dataset. At the WST station, method 1 classifies 46.6% of the DSDs as stratiform and 53.4% as convective, while roughly reversed portions result from method 2 (51.3% and 48.7%). The majority of DSDs (83.9%) receives an identical classification by methods 1 and 2, which shows that both separation methods are in good agreement to each other also on a seasonal time scale.

Fig. 4.
Fig. 4.

Relationship between rain rate R and radar reflectivity Z and stratiform/convective classification after methods 1 and 2 at WST station on 19 Jul 2015. For reference the Marshall–Palmer ZR relationship is also shown.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

The systematical differences between methods 1 and 2 become obvious when applying them to different rainfall intensities. According to the typical strength of midlatitude precipitation, we define the intensity classes light (0.1 ≤ R < 1 mm h−1), medium (1 ≤ R < 10 mm h−1), and heavy (10 ≤ R < 200 mm h−1). In the case of the WST station, 55.7% of the measurement data accounts for light rainfall, 41.2% for medium rainfall, and only 3.1% for heavy rainfall. Method 1 is able to reproduce the expected properties of convective precipitation as its percentage is considerably higher for heavy precipitation (68.2%) than for light (54.2%) or medium (51.1%) precipitation. Furthermore, convective rainfall accounts for a larger percentage in total rainfall accumulation than its overall occurrence (60.5% as compared with 53.4%). We cannot make these observations for method 2, which produces the largest portion of convective DSDs for light rainfall (59.8%) rather than for medium (34.1%) or heavy rainfall (42.2%), and its total rainfall accumulation (41.1%) is even underrepresented compared to its occurrence (48.7%). We obtain similar results from the data of the other two stations. One possible explanation for this discrepancy between the two methods lies in the different strategy to separate stratiform and convective rainfall, which in the case of method 1 is empirically derived from observation data, whereas method 2 focuses on a more technical separation of distinct modes in ZR space.

5. Application of stratiform and convective Z–R relationships

After introducing two methods to separate stratiform and convective precipitation in DSD measurements and evaluating their performance, the next step of this work is to assess the potential value of this distinction for quantitative radar-based rainfall estimates. We approach this question by comparing the ability of different ZR relationships to reproduce the true, but in most cases unknown, DSD-based rain rate RDSD from the radar reflectivity ZDSD that a weather radar virtually measures. We calculate the estimated rain rate RZ for four types of ZR relationship: a standard Marshall–Palmer (M–P) relationship (Z = 200R1.6), a single relationship adjusted globally for all rainfall data, and the respective dual ZR relationships for stratiform (S) and convective (C) rainfall after methods 1 and 2.

a. Derivation of Z–R relationships

Except for the prescribed Marshall–Palmer case, we adjust the coefficients of the power-law ZR relationships to the data of the training period (April–September 2013). Following the suggestion of Steiner and Smith (2004), we derive α and β by minimizing the normalized root-mean-square difference (RMSD) between n instantaneous pairs of radar reflectivity and rain rate,
RMSD={1n2i=1n[Ri(Zi/α)1/βRi]2}1/2,
under the additional constraint that
α=(i=1nZi1/β/i=1nRi)β.
We then obtain the values of the two parameters iteratively by varying β with α given by Eq. (10). One important advantage over a conventional least squares–fit regression approach is that the coefficients based on this procedure ensure unbiased rainfall accumulations (Krajewski and Smith 1991; Steiner and Smith 2000). To quantify the uncertainty of the parameter estimation, we repeat the described procedure for 1000 bootstrap samples of the training dataset.

Figure 5 and Table 1 present the resulting ZR relationships for the WST station superimposing the data of the testing period (April–September 2014) and the uncertainty ranges of the derived parameters, respectively. The globally adjusted relationship as well as the Marshall–Palmer ZR relationship shows a good visual agreement with the histogram of the testing dataset. The still considerable differences in the magnitude of α and β (M–P: Z = 200R1.60; global: Z = 180R1.41) become increasingly prominent for rain rates greater than 1 mm h−1, where the adjusted relationship indicates higher rain rates for a given radar reflectivity. Independent of the separation method, the ZR relationships for stratiform (M1: Z = 306R1.50; M2: Z = 287R1.41) and convective precipitation (M1: Z = 79R1.50; M2: Z = 79R1.33) are significantly different from each other. As expected, the multiplicative factor α exhibits considerably smaller values for the convective case than for the stratiform case, whereas for both rain types α is of similar magnitude among the two separation methods. We cannot make such a clear distinction between the rain types for exponent β, which is in good agreement with the relatively low variability of β as discussed in other studies (e.g., Doelling et al. 1998; Steiner and Smith 2000). Instead, the generally larger exponents for method 1 relative to method 2 mark the systematic differences between the two separation methods. The illustration of the ZR data and relationships separately after rain type and separation method (Fig. 6) shows the already discussed increasing convective fraction for increasing rain intensities associated with method 1. This broadening of the data in ZR space is similar to the effect of mixed rainfall types described by Waldvogel (1975), which also leads to an increased β coefficient and subsequently to lower estimated rain rates for a given radar reflectivity by the corresponding ZR relationship. In addition, the exponents of the stratiform and convective ZR relationships of method 1 are larger than those reported by Tokay and Short (1996) (stratiform: Z = 367R1.30; convective: Z = 139R1.43), who provided the basis for this separation method. Apart from the larger microphysical variability of midlatitude rainfall than for tropical rainfall, this may be explained by the weakly pronounced secondary mode within the convective regime for rain rates smaller than 1 mm h−1. This mode originates from drizzle rainfall, which indicates a high sensitivity of the MRR to small raindrops.

Fig. 5.
Fig. 5.

2D-histogram of radar reflectivity Z and rain rate R (color coded) at WST station for the testing period (April–September 2014) and ZR relationships adjusted to the respective data of the training period (April–September 2013).

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

Table 1.

Coefficients α and β of the ZR relationships adjusted to the respective data of the training period (April–September 2013) at WST station and the corresponding uncertainty range given by the 1% and 99% quantile of 1000 bootstrap samples.

Table 1.
Fig. 6.
Fig. 6.

As in Fig. 5, but for (left) stratiform and (right) convective precipitation after (a),(b) method 1 and (c),(d) method 2 separately. Gray areas indicate the domain of the full testing dataset.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

b. Results and discussion

We assess the performance of the four types of ZR relationship in estimating the correct rain rate from a measured radar reflectivity by comparing the DSD-based rain rate RDSD with the derived rain rate RZ. As a first step, we evaluate the differences in total rainfall accumulations for the respective rain rates (Fig. 7). With respect to the 10-s integration time of the measured DSDs, we define the rainfall accumulation as
R=i=1nRi360h1.
Consistently for all MRR stations, the Marshall–Palmer ZR relationship leads to an underestimation of the DSD-based rainfall accumulation by between 6.3% and 17.4%, whereas a slightly lower overestimation results from the globally adjusted ZR relationship (5.5%–12.6%). For the stratiform/convective ZR relationships we also observe a positive but generally smaller difference between the estimated and true rainfall totals. At all three MRRs the two-part relationships based on method 1 realize a larger reduction of the error relative to the single adjusted relationship than do those based on method 2. In the case of method 1 the decrease in difference relative to the single ZR relationship ranges between 30% and 49% and still reaches up to 35% for method 2, which is a considerable improvement of the rainfall estimation. With respect to the derivation procedure for the coefficients α and β, which calibrates for unbiased rainfall accumulations, the general positive estimation bias for the three derived ZR relationship types indicates the interannual rainfall variability between the training and testing periods.
Fig. 7.
Fig. 7.

Absolute differences between total accumulations of estimated rain rate RZ and DSD-based rain rate RDSD dependent on the ZR relationship and MRR station for the testing period (April–September 2014). Annotated numbers denote the respective relative differences (%).

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

As part of a more thorough investigation, Fig. 8 shows the absolute and relative difference between the estimated and DSD-based rainfall accumulations separated after the rainfall intensity classes as defined in section 4b. This analysis reveals that at the WST station for all four types of ZR relationship light rainfall only accounts for a negligible portion of the accumulation error, although this intensity class contains more than half of the measurement data. The slight but consistent underestimation of the rainfall sum most likely leads back to the already discussed drizzle mode present in the dataset. In the case of the Marshall–Palmer relationship about 70% of the accumulation deficit relates to heavy rainfall, which may be the result of an inadequate calibration of the instrument but is mainly an indicator for the good representation of light and medium rainfall by this relationship. For the three other relationship types, medium precipitation causes the largest portion of the deviations from the true rainfall accumulation, which argues for a better representation of heavy rainfall by these relationships than in the Marshall–Palmer case. Nevertheless, the use of separate ZR relationships for stratiform and convective rainfall leads to a considerable improvement of the rainfall estimate compared to the single relationship. For the heavy rainfall we observe only marginal differences between the single and dual adjusted relationships, while the sign of the errors reflects the already discussed higher β coefficients for ZR relationships after method 2 in contrast to method 1.

Fig. 8.
Fig. 8.

As in Fig. 7, but for WST station and dependent on rainfall intensity classes “light” (0.1 ≤ R < 1 mm h−1), “medium” (1 ≤ R < 10 mm h−1), and “heavy” (10 ≤ R < 200 mm h−1). Relative differences refer to the total rainfall accumulation.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

The differences between the instantaneous rain rates RZ and RDSD (Fig. 9) give more detailed insights into the performance of the different ZR relationships. Considering the entire testing dataset at the WST station, 90% of the estimated rain-rate data deviate only marginally from the DSD-based values with differences not greater than 3 mm h−1 for all ZR relationships. As expected, we obtain similar results from this analysis applied on the three rainfall intensity classes separately, which even in the case of medium intensity yields errors mostly smaller than 4.7 mm h−1. The by far largest uncertainty for the estimation of instantaneous rain rates results from heavy rainfall, which produces positive differences of more than 20 mm h−1 and negative differences of almost 30 mm h−1 dependent on the ZR relationship. In the case of the Marshall–Palmer relationship the heavily skewed and biased RZRDSD distribution explains the large underestimation of the intensity-specific and also overall rainfall accumulation as shown in Figs. 7 and 8. The three adjusted types of ZR relationship lead to much less skewed and only slightly biased error distribution for the current rain rate and, therefore, to more precise representations of the rainfall sum. Another important aspect, which is especially relevant for operational and hydrological applications, is the increase of the 5% quantile for the stratiform/convective ZR relationships of between 7 and 17 mm h−1 relative to both single relationships, which illustrates a considerable reduction of extreme underestimations of the true rain rate. Also the quantile ranges Q75Q25 (i.e., the interquartile range) and Q95Q5 of the differences between estimated and DSD-based rain rate in Table 2 quantify the value of two-part ZR relationships for the QPE. For the overall dataset and throughout all rainfall intensities, the application of the stratiform/convective ZR relationship after method 1 leads to a narrowing of the central 50% and 90% of estimation errors by at least 29% and 35% relative to the single adjusted relationship, respectively. We obtain similar values for method 2 but only slightly lower improvements in the case of heavy rainfall.

Fig. 9.
Fig. 9.

Distribution of difference between estimated rain rate RZ and DSD-based rain rate RDSD dependent on ZR relationship and rainfall intensity class at WST station for the testing period (April–September 2014). Gray lines and X symbols mark the median and arithmetic mean, and boxes and whiskers represent the interquartile range and the 5% and 95% quantiles, respectively.

Citation: Journal of Applied Meteorology and Climatology 58, 10; 10.1175/JAMC-D-19-0077.1

Table 2.

Quantile ranges Q75Q25 and Q95Q5 of difference between estimated rain rate Rz and DSD-based rain rate RDSD dependent on ZR relationship and rainfall intensity class at WST station for the testing period (April–September 2014).

Table 2.

The aim of this study is to test the concept of rainfall type-dependent ZR relationships for the usage in QPE applications that estimate surface rainfall from conventional weather radar measurements aloft. Since the comparison of single and dual ZR relationships presented here is based on MRR-retrieved DSD measurements, the results underlie some technical and conceptual limitations. One important aspect is the transferability of precipitation measurements between vertically profiling K-band MRRs and operational weather radars using longer wavelengths. Lengfeld et al. (2014) showed that MRR and X-band radar observations are in very good agreement with each other (correlation coefficient of 0.95), although this may not be true for other weather radar systems. We also assume the MRR measurements to represent both the upper-air radar and ground-based rainfall observations. While the latter is a good assumption because of the chosen height level (140–175 m) and the large sampling volume relative to other DSD-observing instruments, the former cannot be fulfilled due to the limited range of the MRR profile alone. According to Peters et al. (2005) at least for rainfall of weak and medium intensity below the melting layer ZR relationships are transferable from ground- to upper-level MRR measurements, while a significant height dependence of the DSD is present for strong rain rates. Here we derive and evaluate the ZR relationships at the same height to separate the effect of dual relationships from the DSD height dependency. Nevertheless, the improvement in rainfall estimation by two-part relationships for different height levels (not shown) suggests that stratiform/convective separation also has a positive influence on the QPE in the case of vertically transferred ZR relationships. Although these technical and conceptual drawbacks of this study may limit its applicability, the presented findings do not lose relevance concerning the potential improvement of the QPE.

6. Summary and conclusions

The aim of this study is to quantify to what extent the use of two separate ZR relationships for stratiform and convective precipitation may aid to reduce the uncertainty of radar rainfall estimates. For this purpose, we apply two methods, which are designed to separate both rainfall types based on properties of the DSD, to DSD data measured at three MRR stations in northern Germany. Method 1 utilizes a criterion for the rain-rate-dependent mean drop size based on the work of Tokay and Short (1996), whereas method 2 uses a discriminator for coefficient α of the ZR relationship, which we obtain from the mean drop size, drop number density, and DSD shape according to Steiner et al. (2004). For the comparison between the DSD-based rain rate RDSD and the estimated radar reflectivity–derived rain rate RZ, we train four types of ZR relationship (Marshall–Palmer, globally adjusted, and stratiform/convective after methods 1 and 2) for a 6-month period in the warm season of 2013 and test them for the corresponding data of the following year. The analysis of roughly 70 000 10-s-integrated DSD measurements for each station shows an agreement of more than 84% for the stratiform/convective classification of both methods but still reveals systematical differences regarding the portions of total rainfall accumulation for each type, introduced by the respective separation criteria. The higher exponents β of the resulting ZR relationships for method 1 than for method 2 also picture these differences. With respect to the total rainfall accumulations, for method 1 the use of dual ZR relationships leads to a reduction of the estimation error by between 30% and 50% relative to a single adjusted ZR relationship, whereas we obtain slightly smaller improvements associated with method 2. The same is true for different rainfall intensity classes. Comparing the instantaneous rain rates, both separation methods emphasize the benefit of rainfall-type-dependent ZR relationships by a narrowing of the interquartile range and the Q95Q5 quantile range of the differences between estimated and DSD-based rain rate by between 20% and 40%, dependent on separation method and rainfall intensity class. The use of dual relative to single ZR relationships especially limits the occurrence of extreme underestimations of the actual rain rate for heavy rainfall.

The presented findings clearly emphasize the potential of stratiform and convective ZR relationships to reduce the uncertainty of the QPE for hydrological applications and flooding predictions. Although the basic idea of improving the representation of highly scattered data by two models instead of one is trivial, the distinction between stratiform and convective rainfall still is a simple and intuitive concept with a clear physical background. In contrast to the conclusion drawn by Steiner et al. (1995), Steiner and Houze (1997), and Yuter and Houze (1997), the present study provides justification for the use of dual ZR relationships for radar rainfall estimations. Especially the large database including a variety of synoptical situations and the different representations of stratiform and convective rainfall by the two applied separation methods underline the credibility of the discussed results. Nevertheless, the very limited representativeness of measured DSDs, which allow the correct identification of the current rainfall type with respect to the four-dimensional rain field, stays a problem for the implementation of dynamical ZR relationships into QPE algorithms. Future efforts should focus on the application of dual ZR relationships to entire radar reflectivity fields to improve the spatial rainfall estimation. Due to the typical lack of widespread information about microphysical rainfall properties, the DSD information obtained from local MRR measurements may be horizontally interpolated or extrapolated (Raupach and Berne 2016a,b) or used in combination with retrievals of polarimetric radar measurements (Bringi et al. 2009; Thurai et al. 2010; Penide et al. 2013; Raupach and Berne 2017) to apply an appropriate ZR relationship. Moreover, the influence of effects like wind drift and drop size sorting remain a problem for the conversion of radar observations made aloft into precise rainfall estimations at the surface.

Acknowledgments

We thank three anonymous reviewers for providing us with helpful comments in improving the quality of the paper. This study was partly supported by the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) under Germany’s Excellence Strategy—EXC 2037 “Climate, Climatic Change, and Society”—Project 390683824.

REFERENCES

  • Alfieri, L., P. Claps, and F. Laio, 2010: Time-dependent ZR relationships for estimating rainfall fields from radar measurements. Nat. Hazards Earth Syst. Sci., 10, 149158, https://doi.org/10.5194/nhess-10-149-2010.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., and C. W. Ulbrich, 1977: Path- and area-integrated rainfall measurement by microwave attenuation in the 1–3 cm band. J. Appl. Meteor., 16, 13221331, https://doi.org/10.1175/1520-0450(1977)016<1322:PAAIRM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., and C. W. Ulbrich, 2006: Drop size spectra and integral remote sensing parameters in the transition from convective to stratiform rain. Geophys. Res. Lett., 33, L16803, https://doi.org/10.1029/2006GL026824.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Atlas, D., C. W. Ulbrich, F. D. Mark Jr., R. A. Black, E. Amitai, P. T. Willis, and C. E. Samsury, 2000: Partitioning tropical oceanic convective and stratiform rains by draft strength. J. Geophys. Res., 105, 22592267, https://doi.org/10.1029/1999JD901009.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Auf der Maur, A. N., 2001: Statistical tools for drop size distributions: Moments and generalized gamma. J. Atmos. Sci., 58, 407418, https://doi.org/10.1175/1520-0469(2001)058<0407:STFDSD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Austin, P. M., 1987: Relation between measured radar reflectivity and surface rainfall. Mon. Wea. Rev., 115, 10531070, https://doi.org/10.1175/1520-0493(1987)115<1053:RBMRRA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Battan, L. J., 1973: Radar Observations of the Atmosphere. University of Chicago Press, 324 pp.

  • Bringi, V. N., C. R. Williams, M. Thurai, and P. T. May, 2009: Using dual-polarized radar and dual-frequency profiler for DSD characterization: A case study from Darwin, Australia. J. Atmos. Oceanic Technol., 26, 21072122, https://doi.org/10.1175/2009JTECHA1258.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bukovčić, P., D. S. Zrnić, and G. Zhang, 2015: Convective–stratiform separation using video disdrometer observations in central Oklahoma—The Bayesian approach. Atmos. Res., 155, 176191, https://doi.org/10.1016/j.atmosres.2014.12.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Campos, E., and I. Zawadzki, 2000: Instrumental uncertainties in ZR relations. J. Appl. Meteor., 39, 10881102, https://doi.org/10.1175/1520-0450(2000)039<1088:IUIZRR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Caracciolo, C., F. Prodi, A. Battaglia, and F. Porcu, 2006: Analysis of the moments and parameters of a gamma DSD to infer precipitation properties: A convective stratiform discrimination algorithm. Atmos. Res., 80, 165186, https://doi.org/10.1016/j.atmosres.2005.07.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ciach, G. J., and W. F. Krajewski, 1999: Radar–rain gauge comparison under observational uncertainties. J. Appl. Meteor., 38, 15191525, https://doi.org/10.1175/1520-0450(1999)038<1519:RRGCUO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • D’Adderio, L. P., F. Porcù, and A. Tokay, 2018: Evolution of drop size distribution in natural rain. Atmos. Res., 200, 7076, https://doi.org/10.1016/j.atmosres.2017.10.003.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doelling, I. G., J. Joss, and J. Riedl, 1998: Systematic variations of ZR-relationships from drop size distributions measured in northern Germany during seven years. Atmos. Res., 47–48, 635649, https://doi.org/10.1016/S0169-8095(98)00043-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fujiwara, M., 1965: Raindrop-size distributions from individual storms. J. Atmos. Sci., 22, 585591, https://doi.org/10.1175/1520-0469(1965)022<0585:RSDFIS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gunn, R., and G. D. Kinzer, 1949: The terminal velocity of fall for water droplets in stagnant air. J. Meteor., 6, 243248, https://doi.org/10.1175/1520-0469(1949)006<0243:TTVOFF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Houze, R. A., Jr., 1993: Cloud Dynamics. Academic Press, 573 pp.

  • Hu, Z., and R. C. Srivastava, 1995: Evolution of raindrop size distributions by coalescence, breakup, and evaporation: Theory and observations. J. Atmos. Sci., 52, 17611783, https://doi.org/10.1175/1520-0469(1995)052<1761:EORSDB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Illingworth, A. J., and T. M. Blackman, 2002: The need to represent raindrop size spectra as normalized gamma distributions for the interpretation of polarization radar observations. J. Appl. Meteor., 41, 286297, https://doi.org/10.1175/1520-0450(2002)041<0286:TNTRRS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Joss, J., and A. Waldvogel, 1970: A method to improve the accuracy of radar-measured amounts of precipitation. 14th Radar Meteorology Conf., Tucson, AZ, Amer. Meteor. Soc., 237–238.

    • Search Google Scholar
    • Export Citation
  • Krajewski, W. F., and J. A. Smith, 1991: On the estimation of climatological ZR relationships. J. Appl. Meteor., 30, 14361445, https://doi.org/10.1175/1520-0450(1991)030<1436:OTEOCR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, G. W., and I. Zawadzki, 2005: Variability of drop size distributions: Time-scale dependence of the variability and its effects on rain estimation. J. Appl. Meteor., 44, 241255, https://doi.org/10.1175/JAM2183.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lee, G. W., I. Zawadzki, W. Szyrmer, D. Sempere-Torres, and R. Uijlenhoet, 2004: A general approach to double-moment normalization of drop size distributions. J. Appl. Meteor., 43, 264281, https://doi.org/10.1175/1520-0450(2004)043<0264:AGATDN>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lengfeld, K., M. Clemens, H. Münster, and F. Ament, 2014: Performance of high-resolution X-band weather radar networks—The PATTERN example. Atmos. Meas. Tech., 7, 41514166, https://doi.org/10.5194/amt-7-4151-2014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165166, https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., W. Hitschfeld, and K. L. S. Gunn, 1955: Advances in radar weather. Advances in Geophysics, Vol. 2, Academic Press, 1–56, https://doi.org/10.1016/S0065-2687(08)60310-6.

    • Crossref
    • Export Citation
  • METEK, 2009: MRR Physical Basics (Version 5.2.0.1). METEK Meteorologische Messtechnik GmbH, 20 pp.

  • Penide, G., A. Protat, V. V. Kumar, and P. T. May, 2013: Comparison of two convective/stratiform precipitation classification techniques: Radar reflectivity texture versus drop size distribution-based approach. J. Atmos. Oceanic Technol., 30, 27882797, https://doi.org/10.1175/JTECH-D-13-00019.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peters, G., B. Fischer, and T. Andersson, 2002: Rain observations with a vertically looking Micro Rain Radar (MRR). Boreal Environ. Res., 7, 353362.

    • Search Google Scholar
    • Export Citation
  • Peters, G., B. Fischer, H. Münster, M. Clemens, and A. Wagner, 2005: Profiles of raindrop size distributions as retrieved by microrain radars. J. Appl. Meteor., 44, 19301949, https://doi.org/10.1175/JAM2316.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2016a: Small-scale variability of the raindrop size distribution and its effect on areal rainfall retrieval. J. Hydrometeor., 17, 20772104, https://doi.org/10.1175/JHM-D-15-0214.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2016b: Spatial interpolation of experimental raindrop size distribution spectra. Quart. J. Roy. Meteor. Soc., 142, 125137, https://doi.org/10.1002/qj.2801.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Raupach, T. H., and A. Berne, 2017: Retrieval of the raindrop size distribution from polarimetric radar data using double-moment normalization. Atmos. Meas. Tech., 10, 25732594, https://doi.org/10.5194/amt-10-2573-2017.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., and C. W. Ulbrich, 2003: Cloud microphysical properties, processes, and rainfall estimations opportunities. Cloud Systems, Hurricanes, and the Tropical Rainfall Measuring Mission (TRMM), Meteor. Monogr., No. 51, Amer. Meteor. Soc., 237–258, https://doi.org/10.1175/0065-9401(2003)030<0237:CMPPAR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., E. Amitai, and D. B. Wolf, 1995a: Classification of rain regimes by the three-dimensional properties of reflectivity fields. J. Appl. Meteor., 34, 198211, https://doi.org/10.1175/1520-0450(1995)034<0198:CORRBT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rosenfeld, D., E. Amitai, and D. B. Wolf, 1995b: Improved accuracy of radar WPMM estimated rainfall upon application of objective classification criteria. J. Appl. Meteor., 34, 212223, https://doi.org/10.1175/1520-0450-34.1.212.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sempere-Torres, D., R. Sánches-Diezma, I. Zawadzki, and J. D. Creutin, 2000: Identification of stratiform and convective areas using radar data with application to the improvement of DSD analysis and ZR relations. Phys. Chem. Earth, 25, 985990, https://doi.org/10.1016/S1464-1909(00)00138-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Short, D. A., T. Kozu, and K. Nakamura, 1990: Rainrate and raindrop size distribution observations in Darwin, Australia. Proc. URSI Commision F Open Symp. on Regional Factors in Predicting Radiowave Attenuation Due to Rain, Rio de Janeiro, Brazil, International Union of Radio Science Commission, 35–40.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., and W. F. Krajewski, 1993: A modeling study of rainfall rate–reflectivity relationships. Water Resour. Res., 29, 25052514, https://doi.org/10.1029/93WR00962.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and R. A. Houze Jr., 1997: Sensitivity of the estimated monthly convective rain fraction to the choice of ZR relation. J. Appl. Meteor., 36, 452462, https://doi.org/10.1175/1520-0450(1997)036<0452:SOTEMC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 1998: Convective versus stratiform rainfall: An ice-microphysical and kinematic conceptual model. Atmos. Res., 47–48, 317326, https://doi.org/10.1016/S0169-8095(97)00086-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 2000: Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra. J. Appl. Meteor., 39, 19231940, https://doi.org/10.1175/1520-0450(2000)039<1923:RRRAKE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., and J. A. Smith, 2004: Scale dependence of radar-rainfall rates – An assessment based on raindrop spectra. J. Hydrometeor., 5, 11711180, https://doi.org/10.1175/JHM-383.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., R. A. Houze Jr., and S. E. Yuter, 1995: Climatological characterization of three-dimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor., 34, 19782007, https://doi.org/10.1175/1520-0450(1995)034<1978:CCOTDS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Steiner, M., J. A. Smith, and R. Uijlenhoet, 2004: A microphysical interpretation of radar reflectivity–rain rate relationships. J. Atmos. Sci., 61, 11141131, https://doi.org/10.1175/1520-0469(2004)061<1114:AMIORR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stout, G. E., and E. A. Mueller, 1968: Survey of relationships between rainfall rate and radar reflectivity in the measurement of precipitation. J. Appl. Meteor., 7, 465474, https://doi.org/10.1175/1520-0450(1968)007<0465:SORBRR>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Testud, J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The concept of “normalized” distributions to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor., 40, 11181140, https://doi.org/10.1175/1520-0450(2001)040<1118:TCONDT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., and V. N. Bringi, 2018: Application of the generalized gamma model to represent the full rain drop size distribution. J. Appl. Meteor. Climatol., 57, 11971210, https://doi.org/10.1175/jamc-d-17-0235.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., V. N. Bringi, and P. T. May, 2010: CPOL radar-derived drop size distribution statistics of stratiform and convective rain for two regimes in Darwin, Australia. J. Atmos. Oceanic Technol., 27, 932942, https://doi.org/10.1175/2010JTECHA1349.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thurai, M., P. N. Gatlin, and V. N. Bringi, 2016: Separating stratiform and convective rain types based on the drop size distribution characteristics using 2D video disdrometer data. Atmos. Res., 169, 416423, https://doi.org/10.1016/j.atmosres.2015.04.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., and D. A. Short, 1996: Evidence from tropical raindrop spectra of the origin of rain from stratiform versus convective clouds. J. Appl. Meteor., 35, 355371, https://doi.org/10.1175/1520-0450(1996)035<0355:EFTRSO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., and P. G. Bashor, 2010: An experimental study of small-scale variability of raindrop size distributions. J. Appl. Meteor. Climatol., 49, 23482365, https://doi.org/10.1175/2010JAMC2269.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., D. A. Short, C. R. Williams, W. L. Ecklund, and K. S. Gage, 1999: Tropical rainfall associated with convective and stratiform clouds: Intercomparison of disdrometer and profiler measurements. J. Appl. Meteor., 38, 302320, https://doi.org/10.1175/1520-0450(1999)038<0302:TRAWCA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tokay, A., L. P. D’Adderio, F. Porcù, D. B. Wolff, and W. A. Petersen, 2017: A field study of footprint-scale variability of raindrop size distribution. J. Hydrometeor., 18, 31653179, https://doi.org/10.1175/JHM-D-17-0003.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Uijlenhoet, R., 2001: Raindrop size distributions and radar reflectivity–rain rate relationships of radar hydrology. Hydrol. Earth Syst. Sci., 5, 615627, https://doi.org/10.5194/hess-5-615-2001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the drop size distribution. J. Climate Appl. Meteor., 22, 17641775, https://doi.org/10.1175/1520-0450(1983)022<1764:NVITAF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 1984: Assessment of the contribution of differential polarization to improve rainfall measurements. Radio Sci., 19, 4957, https://doi.org/10.1029/RS019i001p00049.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 1998: Rainfall microphysics and radar properties: Analysis methods for drop size spectra. J. Appl. Meteor., 37, 912923, https://doi.org/10.1175/1520-0450(1998)037<0912:RMARPA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ulbrich, C. W., and D. Atlas, 2002: On the separation of tropical convective and stratiform rains. J. Appl. Meteor., 41, 188195, https://doi.org/10.1175/1520-0450(2002)041<0188:OTSOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1974: The N0 jump of raindrop spectra. J. Atmos. Sci., 31, 10671078, https://doi.org/10.1175/1520-0469(1974)031<1067:TJORS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waldvogel, A., 1975: Tropfenspektren, Niederschlagstyp und ZR Beziehungen (Drop spectra, precipitation types, and Z–R relations). Meteor. Z., 28, 3336.

    • Search Google Scholar
    • Export Citation
  • Yuter, S. E., and R. A. Houze Jr., 1997: Measurements of raindrop size distributions over the Pacific warm pool and implications for ZR relations. J. Appl. Meteor., 36, 847867, https://doi.org/10.1175/1520-0450(1997)036<0847:MORSDO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zawadzki, I., 1984: Factors effecting the precision of radar measurements of rain. 22nd Conf. on Radar Meteorology, Zurich, Switzerland, Amer. Meteor. Soc., 251–256.

    • Search Google Scholar
    • Export Citation
Save