Sources of Errors in Rainfall Measurements by Polarimetric Radar: Variability of Drop Size Distributions, Observational Noise, and Variation of Relationships between R and Polarimetric Parameters

Using a set of long-term disdrometric data and of actual radar measurements from the McGill S-band operational polarimetric radar, several sources of errors in rain measurement with polarimetric radar are explored in order to investigate their relative importance and the feasibility of a polarimetric technique for estimating R in the context of the McGill S-band operational radar that performs a full volume scan of 24 plan position indicators (PPIs) every 5 min. The sources of errors considered are the variability of drop size distributions (DSDs), observational noise, and systematic variation of the relationships between R and polarimetric parameters at different climate regimes. Additional polarimetric parameters dramatically reduce the effect of the DSD variability on rain estimates by radar. The effectiveness of various multiparameter relationships is investigated. The relationships from the literature that are derived from the DSD model and measured DSDs at a different climate regime differ from those derived from the disdrometric dataset herein. An application of these relationships to the Montreal dataset results in a bias (about 10%–20%) and the significant random error resulting from the DSD variability. These errors should be eliminated by using a relationship suitable for the local climate. Assuming a measurement noise as expected from a slow scanning polarimetric radar [ 1 rotation per minute (rpm)] and a 10-min smoothing, the R (Zh, ZDR) relationship outperforms the conventional R Zh because of the combined effect of the DSD variability and measurement errors. In addition, the marginal measurement noise that is required to have the same accuracy of R Zh and R (Zh, ZDR) algorithms is obtained as a function of temporal smoothing. The quantified measurement noise of the McGill S-band fast scanning operational radar ( 6 rpm) is significantly larger than that of a slow scanning radar, implying that a temporal averaging of ZDR of 1 h is needed to achieve some gain with R (Zh, ZDR).

[1]  P. Joe,et al.  Comparison of Raindrop Size Distribution Measurements by a Joss-Waldvogel Disdrometer, a PMS 2DG Spectrometer, and a POSS Doppler Radar , 1994 .

[2]  Witold F. Krajewski,et al.  Conditional Bias in Radar Rainfall Estimation. , 2000 .

[3]  Brian E. Sheppard,et al.  Measurement of Raindrop Size Distributions Using a Small Doppler Radar , 1990 .

[4]  Alexander V. Ryzhkov,et al.  Rainfall Estimation with a Polarimetric Prototype of WSR-88D , 2005 .

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

[6]  V. Chandrasekar,et al.  Error Structure of Multiparameter Radar and Surface Measurements of Rainfall Part II: X-Band Attenuation , 1988 .

[7]  Larry D. Travis,et al.  Light Scattering by Nonspherical Particles , 1998 .

[8]  Instrumental Uncertainties in Z–R Relationships and Raindrop Fall Velocities , 2003 .

[9]  Eugenio Gorgucci,et al.  Radar and Surface Measurement of Rainfall during CaPE: 26 July 1991 Case Study , 1995 .

[10]  D. Zrnic,et al.  Doppler Radar and Weather Observations , 1984 .

[11]  Alexander V. Ryzhkov,et al.  Considerations for Polarimetric Upgrades to Operational WSR-88D Radars , 2000 .

[12]  Julius Goldhirsh,et al.  Comparison of Simulated Rain Rates from Disdrometer Data Employing Polarimetric Radar Algorithms , 1989 .

[13]  R. Gunn,et al.  THE TERMINAL VELOCITY OF FALL FOR WATER DROPLETS IN STAGNANT AIR , 1949 .

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

[15]  A. W. Green,et al.  An Approximation for the Shapes of Large Raindrops , 1975 .

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

[17]  Isztar Zawadzki,et al.  The Effect of Mean and Differential Attenuation on the Precision and Accuracy of the Estimates of Reflectivity and Differential Reflectivity , 2003 .

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

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

[20]  D. Zrnic,et al.  Sensitivity Analysis of Polarimetric Variables at a 5-cm Wavelength in Rain , 2000 .

[21]  J. S. Marshall,et al.  Interpretation of the Fluctuating Echo from Randomly Distributed Scatterers. Part I , 1953 .

[22]  V. Chandrasekar,et al.  Classification of Hydrometeors Based on Polarimetric Radar Measurements: Development of Fuzzy Logic and Neuro-Fuzzy Systems, and In Situ Verification , 2000 .

[23]  Statistical Tools for Drop Size Distributions: Moments and Generalized Gamma , 2001 .

[24]  Anthony J. Illingworth,et al.  The Need to Represent Raindrop Size Spectra as Normalized Gamma Distributions for the Interpretation of Polarization Radar Observations , 2002 .

[25]  Karen Andsager,et al.  Laboratory Measurements of Axis Ratios for Large Raindrops , 1999 .

[26]  P. T. Willis,et al.  Functional fits to some observed drop size distributions and parameterization of rain , 1984 .

[27]  Eugenio Gorgucci,et al.  Estimation of Raindrop Size Distribution Parameters from Polarimetric Radar Measurements , 2002 .

[28]  V. Chandrasekar,et al.  Comments on “The Need to Represent Raindrop Size Spectra as Normalized Gamma Distributions for the Interpretation of Polarization Radar Observations” , 2003 .

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

[30]  Alexander V. Ryzhkov,et al.  Cloud Microphysics Retrieval Using S-Band Dual-Polarization Radar Measurements , 1999 .

[31]  Eugenio Gorgucci,et al.  Practical Aspects of Radar Rainfall Estimation Using Specific Differential Propagation Phase , 2000 .

[32]  A. R. Jameson An Alternative Approach to Estimating Rainfall Rate by Radar Using Propagation Differential Phase Shift , 1994 .

[33]  I. Zawadzki,et al.  An Experimental Study of Small-Scale Variability of Radar Reflectivity Using Disdrometer Observations , 2004 .

[34]  H. R. Pruppacher,et al.  A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air , 1970 .

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

[36]  V. N. Bringi,et al.  Potential Use of Radar Differential Reflectivity Measurements at Orthogonal Polarizations for Measuring Precipitation , 1976 .

[37]  P. R. Bevington,et al.  Data Reduction and Error Analysis for the Physical Sciences , 1969 .

[38]  H. Direskeneli,et al.  Disdrometer Measurements during an Intense Rainfall Event in Central Illinois: Implications for Differential Reflectivity Radar Observations , 1986 .

[39]  Remko Uijlenhoet,et al.  A general approach to double moment normalization of drop size distributions , 2004 .

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

[41]  V. Chandrasekar,et al.  An Examination of Propagation Effects in Rainfall on Radar Measurements at Microwave Frequencies , 1990 .

[42]  M. Sachidananda,et al.  Rain Rate Estimates from Differential Polarization Measurements , 1987 .

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

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

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

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

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

[48]  Isztar Zawadzki,et al.  Radar calibration by gage, disdrometer, and polarimetry: Theoretical limit caused by the variability of drop size distribution and application to fast scanning operational radar data , 2006 .

[49]  Peter T. May,et al.  Sensitivity of 5-cm Wavelength Polarimetric Radar Variables to Raindrop Axial Ratio and Drop Size Distribution , 2001 .

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

[51]  Eugenio Gorgucci,et al.  Optimization of multiparameter radar estimates of rainfall , 1993 .

[52]  Alexander V. Ryzhkov,et al.  Comparison of Dual-Polarization Radar Estimators of Rain , 1995 .

[53]  Gyu Won Lee,et al.  Variability of Drop Size Distributions: Noise and Noise Filtering in Disdrometric Data , 2005 .