Scaling of raindrop size distributions and classification of radar reflectivity–rain rate relations in intense Mediterranean precipitation

In radar hydrology the relationship between the reflectivity factor (Z) and the rainfall intensity (R) is generally assumed to follow a power law of which the parameters change both in space and time and depend on the drop size distribution (DSD). Based on disdrometer data, this study tries to improve our understanding of the temporal variability of the power-law relationship between Z and R using a scaling-law formalism for the raindrop size distribution proposed in previous contributions. In particular, this study focuses on the inter-event variability of Z-R coefficients and associated DSD-parameters and their relationship to the type of precipitation. This is crucial for developing improved quantitative precipitation estimation algorithms for extreme, flash flood triggering rainfall. Within the DSD scaling-law framework a new normalized parameter estimation method is presented, which calculates significantly faster than the original method and leads to bulk event estimates of the DSD-parameters and associated Z-R coefficients. Based on a 2.5-year disdrometer dataset collected in the Cevennes-Vivarais region in the south of France, comprising a total of 70 events, it is shown that the quality of the resulting Z-R relationships obtained by the new method compares well to two standard least-squares fitting techniques. A major benefit of the new implementation, as compared to such purely statistical methods, is that it also provides information concerning the properties of the DSD. For each of the 70 events this study also estimates the convective activity based on a threshold technique. Results show that convective events generally tend to have smaller Z-R exponents, which is assumed to result from an increased amount of drop interaction. For stratiform events, a much larger range in exponents is obtained, which is thought to depend on differences in meteorological origin (snow vs. ice). For the types of precipitation events observed in the Cevennes region, for a given value of the exponent, the prefactor of the Z-R relation tends to be larger for the more convective type of events. This emphasizes the different meteorological origin of the heavy rainfall observed in the south of France as compared to other regions of the world.

[1]  P. M. Austin,et al.  Relation between Measured Radar Reflectivity and Surface Rainfall , 1987 .

[2]  F. Marks,et al.  Partitioning tropical oceanic convective and stratiform rains by draft strength , 2000 .

[3]  D. Blanchard,et al.  Experiments on the Generation of Raindrop-Size Distributions by Drop Breakup , 1970 .

[4]  Matthias Steiner,et al.  Climatological Characterization of Three-Dimensional Storm Structure from Operational Radar and Rain Gauge Data , 1995 .

[5]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[6]  W. Schmid,et al.  Raindrop Size Distributions and the Radar Bright Band , 1996 .

[7]  Matthias Steiner,et al.  Reflectivity, Rain Rate, and Kinetic Energy Flux Relationships Based on Raindrop Spectra , 2000 .

[8]  K. Beard.  Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft , 1976 .

[9]  Edwin Campos,et al.  Instrumental Uncertainties in Z–R Relations , 2000 .

[10]  Paul L. Smith.  Raindrop Size Distributions: Exponential or Gamma—Does the Difference Matter? , 2003 .

[11]  J. M. Porrà,et al.  Experimental evidence of a general description for raindrop size distribution properties , 1998 .

[12]  Robert A. Black,et al.  The Concept of “Normalized” Distribution to Describe Raindrop Spectra: A Tool for Cloud Physics and Cloud Remote Sensing , 2001 .

[13]  Soroosh Sorooshian,et al.  Estimating Rainfall Intensities from Weather Radar Data: The Scale-Dependency Problem , 2003 .

[14]  Hervé Andrieu,et al.  Identification of Vertical Profiles of Radar Reflectivity for Hydrological Applications Using an Inverse Method. Part II: Formulation. , 1995 .

[15]  Matthias Steiner,et al.  Variability of Raindrop Size Distributions in a Squall Line and Implications for Radar Rainfall Estimation , 2003 .

[16]  G. Feingold,et al.  The Lognormal Fit to Raindrop Spectra from Frontal Convective Clouds in Israel , 1986 .

[17]  Louis J. Battan,et al.  Radar Observation of the Atmosphere , 1973 .

[18]  R. C. Srivastava,et al.  Evolution of Raindrop Size Distribution by Coalescence, Breakup, and Evaporation: Theory and Observations , 1995 .

[19]  Paul L. Smith,et al.  A Study of Sampling-Variability Effects in Raindrop Size Observations , 1993 .

[20]  R. Houze,et al.  Three-Dimensional Kinematic and Microphysical Evolution of Florida Cumulonimbus. Part II: Frequency Distributions of Vertical Velocity, Reflectivity, and Differential Reflectivity , 1995 .

[21]  R. Houze,et al.  Microphysics of the Rapid Development of Heavy Convective Precipitation , 2001 .

[22]  Brice Boudevillain,et al.  Radar rainfall estimation in the context of post-event analysis of flash-flood events , 2009 .

[23]  J. Marshall,et al.  THE DISTRIBUTION OF RAINDROPS WITH SIZE , 1948 .

[24]  Remko Uijlenhoet,et al.  Measurement and parameterization of rainfall microstructure , 2006 .

[25]  Matthias Steiner,et al.  A Microphysical Interpretation of Radar Reflectivity–Rain Rate Relationships , 2004 .

[26]  Isztar Zawadzki,et al.  Variability of Drop Size Distributions: Time-Scale Dependence of the Variability and Its Effects on Rain Estimation , 2005 .

[27]  J. M. Porrà,et al.  A general formulation for raindrop size distribution , 1994 .

[28]  H. Andrieu,et al.  The Catastrophic Flash-Flood Event of 8–9 September 2002 in the Gard Region, France: A First Case Study for the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory , 2005 .

[29]  Carlton W. Ulbrich,et al.  Path- and Area-Integrated Rainfall Measurement by Microwave Attenuation in the 1–3 cm Band , 1977 .

[30]  Hervé Andrieu,et al.  Bollène-2002 Experiment: Radar Quantitative Precipitation Estimation in the Cévennes–Vivarais Region, France. , 2009 .

[31]  Witold F. Krajewski,et al.  Radar–Rain Gauge Comparisons under Observational Uncertainties , 1999 .

[32]  R. C. Srivastava,et al.  Snow Size Spectra and Radar Reflectivity , 1970 .

[33]  Witold F. Krajewski,et al.  A modeling study of rainfall rate-reflectivity relationships , 1993 .

[34]  C. Ulbrich,et al.  An observationally based conceptual model of warm oceanic convective rain in the tropics , 2000 .

[35]  A. R. Jameson,et al.  Spurious power‐law relations among rainfall and radar parameters , 2002 .

[36]  Alexis Berne,et al.  Temporal and spatial resolution of rainfall measurements required for urban hydrology , 2004 .

[37]  R. Stewart,et al.  Temporal evolution of drop spectra to collisional equilibrium in steady and pulsating rain , 1987 .

[38]  Remko Uijlenhoet,et al.  Analytical solutions to sampling effects in drop size distribution measurements during stationary rainfall , 2006 .

[39]  R. Houze,et al.  Three-Dimensional Kinematic and Microphysical Evolution of Florida Cumulonimbus. Part I: Spatial Distribution of Updrafts, Downdrafts, and Precipitation , 1995 .

[40]  M. Steiner,et al.  The Microphysical Structure of Extreme Precipitation as Inferred from Ground-Based Raindrop Spectra , 2003 .

[41]  Olivier P. Prat,et al.  Exploring the Transient Behavior of Z–R Relationships: Implications for Radar Rainfall Estimation , 2009 .

[42]  M. Kitchen,et al.  Representativeness errors in comparisons between radar and gauge measurements of rainfall , 1992 .

[43]  Carlton W. Ulbrich,et al.  Microphysics of Raindrop Size Spectra: Tropical Continental and Maritime Storms , 2007 .

[44]  D. Short,et al.  Evidence from Tropical Raindrop Spectra of the Origin of Rain from Stratiform versus Convective Clouds , 1996 .

[45]  K. Beard.  Terminal Velocity Adjustment for Cloud and Precipitation Drops Aloft , 1977 .

[46]  A. R. Jameson,et al.  When is Rain Steady , 2002 .

[47]  Warner L. Ecklund,et al.  Tropical rainfall associated with convective and stratiform clouds : Intercomparison of disdrometer and profiler measurements , 1999 .

[48]  Christopher R. Williams,et al.  Systematic variation of drop size and radar-rainfall relations , 1999 .

[49]  Remko Uijlenhoet,et al.  Raindrop size distributions and radar reflectivity–rain rate relationships for radar hydrology , 2001 .

[50]  C. Ulbrich.  Natural Variations in the Analytical Form of the Raindrop Size Distribution , 1983 .

[51]  Brice Boudevillain,et al.  Variability of rain drop size distribution and its effect on the Z-R relationship: A case study for intense Mediterranean rainfall , 2008 .

[52]  Luca G. Lanza,et al.  The WMO Field Intercomparison of Rain Intensity Gauges , 2009 .

[53]  J. S. Marshall,et al.  Advances in Radar Weather , 1955 .

[54]  M. Steiner,et al.  Scale Dependence of Radar-Rainfall Rates—An Assessment Based on Raindrop Spectra , 2004 .

[55]  R. C. Srivastava,et al.  Doppler Radar Observations of Drop-Size Distributions in a Thunderstorm , 1971 .

[56]  Dong-Jun Seo,et al.  The WSR-88D rainfall algorithm , 1998 .

[57]  Daniel Sempere-Torres,et al.  Identification of the bright band through the analysis of volumetric radar data , 2000 .

[58]  Sandra E. Yuter,et al.  Measurements of Raindrop Size Distributions over the Pacific Warm Pool and Implications for Z-R Relations , 1997 .

[59]  I. Zawadzki,et al.  Variation with altitude of the drop-size distribution in steady light rain , 1991 .

[60]  D. Churchill,et al.  Development and Structure of Winter Monsoon Cloud Clusters On 10 December 1978 , 1984 .

[61]  R. Uijlenhoet,et al.  Parameterization of rainfall microstructure for radar meteorology and hydrology , 1999 .

[62]  V. Chandrasekar,et al.  Simulation of Radar Reflectivity and Surface Measurements of Rainfall , 1987 .

[63]  Henri Sauvageot,et al.  The Shape of Averaged Drop Size Distributions , 1995 .

[64]  J. Joss,et al.  Shapes of Raindrop Size Distributions , 1978 .

[65]  Frédéric Fabry,et al.  Long-Term Radar Observations of the Melting Layer of Precipitation and Their Interpretation , 1995 .

[66]  D. Blanchard.  RAINDROP SIZE-DISTRIBUTION IN HAWAIIAN RAINS , 1953 .

[67]  A. Waldvogel,et al.  The N0 Jump of Raindrop Spectra , 1974 .