# APPLICATIONS OF THE DIFFERENTIAL REFLECTIVITY RADAR TECHNIQUE: FOCUS ON ESTIMATION OF RAINFALL PARAMETERS AND MICROWAVE ATTENUATION PREDICTION

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University Microfilms International APPLICATIONS OF THE DIFFERENTIAL REFLECTIVITY RADAR TECHNIQUE: FOCUS ON ESTIMATION OF RAINFALL PARAMETERS AND MICROWAVE ATTENUATION PREDICTION DISSERTATION Presented in Partial Fulfillment of. the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Haldun Direskeneli, B.S., M.S. The Ohio State University 1987 Dissertation Committee: Approved by Richard N. Boyd Walter E. Mitchell, Jr. David L. Moffatt Advisor (J • Department of Electrical Engineering To My Family ii ABSTRACT This study explores the application of the differential reflectivity radar method to estimate rainfall parameters by comparing radar-derived estimates with ground-based disdrometer and raingage measurements. The derivation of the empirical relationships linking the rainfall parameters rainfall rate (R), water content (M) and median volume diameter (Dq ) to the radar observables horizontal reflectivity factor (Zjj) and/or differential reflectivity are described based on simulations employing disdrometer measurements made during a 1982 field experiment in central Illinois. Three case studies are described utilizing these relationships to compare radar estimates with ground-based measurements. For the Ohio State Precipitation Experiments (OSPE, 1982) a systematic approach to select the appropriate radar volume to be compared with the disdrometer is described including a cross correlation analysis between the (Z^ Z_jj) pairs obtained from the radar measurements and disdrometer-derived values. The empirical (Zjj, Zj^) relationship for R resulted in 9% and 24% for' the normalized bias and standard error, respectively, compared to 31% and 36% for the best conventional single parameter Z-R relationship. The MAYPOLE '83 experiment involved the transformation of dis drometer measurements to the radar altitudes to account for drop size iii sorting due to different fall velocities within a narrow radar beamwidth and resulted in a very good agreement between the radar- and disdrometer-derived parameters. MAYPOLE '84 comparisons involved high raingage rainfall rates (R > 120 mm h ^ max estimates. which were compared with the radar r After fall time and wind transport of raindrops were accounted for, errors of 7% for the bias and 30% for the standard error were obtained, considerably better than the results using Z-R relationships. The work also examines application of the method to predict C-band reflectivity profiles from S-band measurements and compares the results with actual C-band measurements. This test includes the estimation of C-band specific attenuation and reflectivity factor from S-band (Zjj Z_„) measurements. Potential applications of the Z^^ method to scavenging of aerosols and estimation of vertical air velocities are also considered, based on simulations derived from a disdrometer data base. iv ACKNOWLEDGMENTS I wish to express my appreciation and thanks to my advisor, Dr. Thomas A. Seliga. His guidance, suggestions and assistance are deeply appreciated. I also extend my appreciation to Dr. Kftltegin Aydin for his numerous invaluable suggestions throughout the course of this work. Additional gratitude is extended to Dr. Viswanathan N. Bringi of Colorado State University, Mr. Richard E. Carbone, Dr. Paul Herzegh, Dr. Jeff Keeler and Ms. Cindy Mueller of the National Center for Atmospheric Research for their assistance during the MAYPOLE field projects and to Dr. Eugene A. Mueller of the Illinois State Water Survey for his help during the Ohio State Precipitation Experiments field project. I wish to thank the College of Engineering at The Pennsylvania State University for providing me the support and opportunity to reside at Penn State to complete my research. I extend my thanks to The Ohio State University for providing tuition support for one year while in residence at Penn State. Appreciation is extended to the staff of the Communications and Space Sciences Laboratory for their assistance during my stay at Penn State. v Finally, special thanks to Ms. Barbara Webb for her time and efforts, particularly during the final stages of this work. Ms. Helen Clark's patience and competence in typing the dissertation have been especially helpful. This research was supported by the Atmospheric Research Section, National Science Foundation, the Air Force Office of Scientific Research, the Army Research Office, and the National Aeronautics and Space Administration under NSF Grant ATM-80033767, and by the Army Research Office through the University Corporation for Atmospheric Research under subcontract NCAR S3025. vi TABLE OF CONTENTS A B S T R A C T ........................................................ iii ACKNOWLEDGEMENTS ................................................ v V I T A ............................................................ xi LIST OF T A B L E S ................................................. xiv LIST OF FIGURES................................................... xviii LIST OF SYMBOLS.................................................... xxix CHAPTER 1. INTRODUCTION............................................ 1.1 1.2 1.3 2. 1 General Nature of the Problem.................... Previous Related Studies ........................ Research Objectives and Approach ................ 1 4 8 DIFFERENTIAL REFLECTIVITY RADAR METHOD AND EXPERIMENTAL FACTORS................................... 11 2.1 Differential Reflectivity Method ................ 11 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 11 14 16 16 2.1.6 2.1.7 2.2 Radar Observables ......................... Rainfall Parameters ...................... Specific Attenuation...................... Drop Size Distribution.................... Single Parameter Estimationof Rainfall Parameters............................... Differential Reflectivity Radar Technique . Statistical Considerations................ 18 19 23 Experimental Facilities.......................... 28 2.2.1 28 Radars..................................... 2.2.1.1 2.2.1.2 2.2.1.3 CHILL Radar (OSPE)................ CP-2 and CP-4 Radars (MAYPOLE •83, ' 8 4 ) ....................... Antenna Performance.............. vii 28 29 29 2.2.2 Ground Facilities 2.2.2.1 2.2.2.2 3. Disdrometer ..................... Portable Automated Mesonet(PAM) . 30 31 DISDROMETER-BASED RAINFALL SIMULATIONS................. 32 Disdrometer Measurements ........................ Relationships between RainfallParameters and Radar Observables............................... 32 3.2.1 3.2.2 Rainfall Rate and Water C o n t e n t .......... Median Volume Diameter.................... 35 42 Error Computations ............................... 46 3.3.1 48 3.1 3.2 3.3 3.3.2 4. 30 Simulated Comparisons of Rainfall Parameters............................... Choice of Relationships.................. DIFFERENTIAL REFLECTIVITY RADAR MEASUREMENTS OF RAINFALL................................................ 4.1 OSPE Case Study................................... 4.1.1 4.1.2 4.1.3 Cell Selection............................. Swath S e l e c t i o n .......................... Radar-Disdrometer Comparisons ............ 4.1.3.1 4.1.3.2 4.1.3.3 4.1.3.4 60 61 65 77 91 95 97 98 R e m a r k s ................................... 100 Radar-Disdrometer Comparisons: 4 June 1983 MAYPOLE '83 Experiment ......................... 101 4.2.1 4.2.2 4.2.3 4.2.4 4.3 48 Rainfall Rate..................... Liquid Water Content ............ Median Volume Diameter .......... Reflectivity Factor and Differ ential Reflectivity............ 4.1.4 4.2 35 Radar and Disdrometer Measurements........ Transformation of Disdrometer Time Records to Radar Altitudes....................... Disdrometer-Radar Comparisons ............ R e m a r k s ................................... Radar-Raingage Comparisons: 15 June 1984 MAYPOLE Experiment ............................. 4.3.1 4.3.2 4.3.3 4.3.4 Raingage Measurements .................... Radar Measurements........................ Raingage-Radar Comparisons................ R e m a r k s ................................... viii 99 102 108 Ill 129 129 130 131 137 143 5. PREDICTION AND COMPARISONS OF C-BAND REFLECTIVITY PROFILES FROM S-BAND MEASUREMENTS ............... 5.1 5.2 Introduction..................................... Simultaneous Operation of CP-4 (5.45 cm) and CP-2 (10.7 cm) Radars........................... C-Band Specific Attenuation and Reflectivity Factor from S-Band Measurements................. Prediction Procedure . ........................ S-Band Predictions and C-Band Measurements . . . . Summary........................................... 160 173 176 182 OTHER APPLICATIONS...................................... 186 6.1 186 5.3 5.4 5.5 5.6 6. Aerosol Scavenging Rates ........................ 6.2 145 147 Scavenging Rates........................... Simulations ............................... 189 193 Vertical Air Velocities.......................... 199 6.1.1 6.1.2 6.2.1 6.2.2 6.2.3 6.2.4 7. 145 Previous Studies........................... Doppler Velocity Components ............... Model Computations......................... Proposed Experiment ....................... 201 203 206 209 SUMMARY AND CONCLUSIONS ................................ 213 7.1 7.2 213 215 Review of the Problem............................ Simulated and Experimental Results .............. 7.2.1 7.2.2 Disdrometer Simulations ................... Case Studies............................... 215 216 7.2.2.1 7.2.2.2 216 7.2.2.3 7.2.3 7.2.4 7.3 OSPE Disdrometer Comparisons . . . MAYPOLE '83 Disdrometer Comparisons..................... MAYPOLE '84 Raingage Comparisons . 217 218 C-Band P r o f i l e s ........................... Other Applications......................... 218 219 Recommendations for Future Research.............. 220 7.3.1 7.3.2 7.3.3 7.3.4 Rainfall Studies........................... Hydrology, Flash Flood Forecasting and Weather Modification..................... Prediction of (Z„, Z_.„) Profiles at Attenuating Wavelengths ................. Cloud Physics, Scavenging, Earth Energy and Radiation Budget..................... ix 220 221 221 222 APPENDIX Radar Specifications LIST OF REFER E N C E S ............................................ x 224 228 VITA 13 September 1955.................Born - Cihanbeyli, Turkey 1978 , ........................... B.S., Electrical Engineering Middle East Technical University, Ankara, Turkey 1978 ............................. Graduate Teaching Associate, Physics, Middle East Technical University 1979-1981......................... Graduate Research/Teaching Associate, Atmospheric Sciences Program and Electrical Engineering Department, The Ohio State University, Columbus, Ohio 1981 ............................. M.S., Electrical Engineering, The Ohio State University 1981-1985......................... Graduate Research Associate, Atmospheric Sciences Program, The Ohio State University 1985-1987. ... ................. Research Assistant, Communications and Space Sciences Laboratory, The Pennsylvania State University, University Park, Pennsylvania PUBLICATIONS Direskeneli, H . , 1981: Effective Propagation Characteristics in Random Medium Using Multiple Scattering Medium. Atmos. Sci. Prog. Rep. No. AS-S-113, The Ohio State University, Columbus. Direskeneli, H . , T. A. Seliga, and K. Aydin, 1983: Differential Reflectivity (Zq r ) Measurements of Rainfall Compared with Ground Based Disdrometer Measurements. Preprints 21st Conf. Radar Meteor., Edmonton, Alberta, Canada, AMS, A75-A78. xi Seliga, T. A., K. Aydin, and H. Direskeneli, 1983: Disdrometer Measurements During a Unique Rainfall Event in Central Illinois and Their Implication for Differential Reflectivity Radar Observations. Preprints 21st Conf Radar Meteor., Edmonton, Alberta, Canada, AMS, 467-474. Seliga, T. A., K. Aydin, and H. Direskeneli, 1983: Possible Evidence for Strong Vertical Electric Fields in Thunderstorms from Differential Reflectivity Measurements. Preprints 21st Conf. Radar Meteor., Edmonton, Alberta, Canada, AMS, 500-502. Seliga, T. A., K. Aydin, and H. Direskeneli, 1984: Comparison of Disdrometer-Derived Rainfall and Radar Parameters During MAYPOLE '83. Preprints 22nd Conf. Radar Meteor., Zurich, Switzerland, AMS, 358-363. Seliga, T. A., K. Aydin, and H. Direskeneli, 1986: Disdrometer Measurements During an Intense Rainfall Even in Central Illinois: Implications for Differential Reflectivity Radar Observations. J. Climate and Appl. Meteor., 25(6), 835-846. Direskeneli, H . , K. Aydin, and T. A. Seliga, 1986:Radar Estimation of Rainfall Rate Using Reflectivity Factor and Differential Reflectivity Measurements Obtained During MAYPOLE '84: Comparison with Ground-Based Raingages. Preprints 23rd Conf. Radar Meteor., Snowmass, Co., AMS, 116-120. Aydin, K., T. A. Seliga, and H. Direskeneli, 1987: Rainfall Parameters Derived from Dual Polarization Radar Measurements Compared with a Ground-Based Disdrometer in Central Illinois. 1987 International Geoscience and Remote Sensing Symposium (IGARSS '87). IEEE/URSI, Ann Arbor, Michigan. Direskeneli, H., T. A. Seliga, and K. Aydin, 1987: Prediction of C-Band Reflectivity Profiles in Rainfall Using S-Band Dual Linear Polarization Measurements and Comparisons with Simultaneous C-Band Measurements. 1987 International Geoscience and Remote Sensing Symposium (IGARSS '87). IEEE/URSI, Ann Arbor, Michigan. Aydin, K., H. Direskeneli, and T. A. Seliga, 1987: Dual Polarization Radar Estimation of Rainfall Parameters Compared with GroundBased Disdrometer Measurements: 29 October 1982, Central Illinois Experiment. Accepted for publication in IEEE Trans. Geosc. Remote Sensing. FIELDS OF STUDY Major Field: Electrical Engineering Studies in Electromagnetic Theory: L. Peters, Jr., C. A. Levis Studies in Communications: Moffatt Professors R. G. Koujoumjian, Professors C. E. Warren, D. L. xii Fields of Study (continued) Studies in Atmospheric Sciences: Arnfield, M. R. Foster Studies in Mathematics: Studies in Statistics: Professors T. A. Seliga, A. J. Professors H. D. Colson, S. Drobot Professor J. C. Hsu xiii LIST OF TABLES PAGE TABLE 3.1. 3.2. 3.3. Estimated fractional standard deviations (FSD) of rainfall rate (R), horizontal reflectivity factor (Zfl) and differential reflectivity (Zq r ) in thunderstorms at R = 1, 10_and 100 mm h-^-. Here ZR is in mm6m“3 and Zd r = Z^/Zy where Zy is the vertical reflectivity factor ....................... 36 (R/Zfl)- and (M/Zr J-Zd r relationships derived from' regression analyses. The estimated constants for these power law relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for [log (R/Zr ) and log Z q r ] and [log (M/Zr) and log Z q r ] are also listed. R is the rainfall rate, M water content, Z r reflectivity factor and Z r r differential reflectivity ........ AO (R/Zh)“ and (M/Zh)-Do relationships derived from regression analyses. The estimated constants for these power law relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for [log (R/Zh) and log Do] and [log (M/Zr) and log Do] are also listed. R is the rainfall rate, M water content, Dq median volume diameters and Z r reflectivity f a c t o r .............. A1 Zj)R(dB)-Do(mra) relationships derived from regression analyses. The estimated constants for these relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for the linear (Z r r and Do) and power law (log Z DR and log D q ) relationships are also listed. Results were obtained from data in the ranges 0.2 < Zp^ < 2.6 and 0.7 < D q < 3.0. Zj>r is the differential reflectivity and D q median volume d i a m e t e r ........................................... A5 xiv Rainfall rate errors for the heavy rainfall event of October 6, 1982 in central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 through 3-2A). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2 and Eqs. (3-5, 7, 9, 25, 26, 27) are used in obtaining rainfall rates from the simulated radar measurements. The disdrometerderived rainfall rates are treated as reference values ............................................ Water content errors for the heavy rainfall event of October 6, 1982 in central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relation ships given in Table 3.2 and Eqs. (3-6, 8, 10, 28, 29) are used in obtaining water contents from the simulated radar measurements. The disdrometerderived water contents are treated as reference values ............................................ Median volume diameter errors for the heavy rain fall event of October 6, 1982 in central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24). Differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.4 and Eqs. (3-17, 18) are used in obtaining median volume diameters from the simulated radar measurements. The disdrometerderived median volume diameters are treated as reference values ................................. Rainfall rate errors for two independent rainfall events that occurred on June 8 and 13, 1982 near Boulder, Colorado, in terms on NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of rain drop size distributions, and the relationships given in Table 3.2, and Eqs. (3-5, 7, 9, 25-27) are used in obtaining rainfall rates from the simulated radar measurements. The disdrometerderived rainfall rates are treated as reference values ............................................ Water content errors for two independent rainfall events that occurred on June 8 and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2 and Eqs. (3-6, 8, 10, 29) are used in obtaining water contents from the simulated radar measurements. The disdrometerderived water contents are treated as reference values ............................................ Median volume diameter errors for two independent rainfall events that occurred on June 8 and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 through 3-24). Reflec tivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions and the relationships given in Table 3.4 and Eqs. (3-17 through 3-18) are used in obtaining median volume diameters from the simulated radar measurements. The disdrometerderived median volume diameters are treated as reference values ................................. Cell D4 radar-disdrometer comparisons of rainfall rate, water content, median volume diameter, reflectivity factor and differential reflectivity for the 29 October 1982 rainfall event. Rg, Rgfj, Rg , Mp, M q employ radar observed (ZR , ZDR) whereas RZR» RMS* rMP» rJW and mD0 use ZH only. Doe and D q q are estimated from ZpR . Disdrometer values are the reference values for all entries ......... Swath radar-disdrometer comparisons as in Table 4.2, except the results are for the swath averages of cells (B4, C4, D4, E4) shown in Fig. 5.2. Rg^ and Rgjflj employ (ZH » ZDR) for rainfall rate estimation with different averaging considerations (see Section 4.1.3). ZR is the reflectivity factor and ZpR differential reflectivity................. Statistical summary of radar- and disdrometerderived parameters including mean values (x), standard deviations (s), correlation coefficients ( ), and the slope (A) and the intercept (B) of the linear regression coefficients. The super scripts D and R for ZR , ZpR and Dq and the subscripts D and R for R refer to disdrometerand radar-derived values, respectively, where Zg is the reflectivity factor, ZpR is the differential reflectivity. R is the rainfall rate, D q is the median volume diameter ........................... 5.1. Description of radar measurements................... 148 5.2. Disdrometer-derived specific attenuation empirical formulas for 5.45 cm specific attenuation - 10.7 cm reflectivity factor and differential reflec tivity relationships ............................... 167 Disdrometer-derived reflectivity factorempirical formulas for 5.45 cm reflectivity factor - 10.7 cm reflectivity factor and differential reflectivity relationships....................................... 172 Empirical formulas to estimate precipitation scavenging rates A from both (Zjj, Z^r) and (R, D q ). Relationships were derived from multiple regression analyses using disdrometer data and for different aerosol radii. Correlation coefficients (p) for the regression relation relating the logarithms of the parameters are also shown. R is the rainfall rate, D q is the median value diameter, Zjj is the reflectivity factor, Zj)R is the differential reflectivity ....................................... 191 Empirical formulas to estimate precipitation scavenging rates A from both ZH and R. Relation ships were derived from regression analyses using disdrometer data and for different aerosol radii. Correlation coefficients (p) for the regression relationship relating the logarithms of the parameters are also shown. R is the rainfall rate and ZH is the reflectivity factor................... 192 Constants of the <vt>- Z DR relationship derived from a linear regression analysis of the relation ship expressed in base 10 logarithms. Correspond ing 95% confidence limits and correlation coefficients (p) are also given, is the reflectivity weighted fall velocity and Z^R is the differential reflectivity........................... 208 5.3 6.1. 6.2. 6.3. xvii LIST OF FIGURES FIGURE 2.1. 2.2. 2.3. 2.4. 2.5. 3.1(a). 3.1(b). PAGE Raindrop distortion model: an oblate spheroid is the body of revolution formed when an ellipse is rotated about its minor axis................................... 15 Rain parameter diagram for exponential drop size distribution model. Radar reflectivity factor versus rainfall rate with isopleths of median volume diameter Dq and parameter N q . Data points represent estimates inferred from radar measurements (Seliga et al., 1981), and MP signifies the Marshall-Palmer Z-R relationship........................................ 20 Raindrop canting angle (a), (a) in the plane of incidence with an angle of incidence(9), and (b) per pendicular to the plane of incidence 22 Variation in Z d r with canting angle a (a) in the plane of incidence, and (b) perpendicular to the plane of incidence. Zero canting angle (a = 0) results in maximum Z jjr where Z jjr is the differential reflectivity (Al-Khatib et al., 1979)............................... 24 Standard deviation (dB) of the square law estimator as a function of sample size m and cross-correlation coefficient p (Bringi and Seliga, 1980) .............. 27 Time records of R and M during the 6 October 1982 rainfall event in central Illinois. Solid lines are actual disdrometer measurements representing 2 min running average of 30 s recordings. Crosses are the simulated radar estimates of R and M computed for Eq. (3-5) using disdrometer-derived (Z jj, Z q r ). Zero time indicates values averaged over 1513:30-1515:30. R is the rainfall rate, M water content, Z h reflec tivity factor and Z q r differential reflectivity . . . . 33 Time record of Do during the 6 October 1982 rainfall event in central Illinois. Solid lines are actual disdrometer measurements representing 2 min running averages of 30 s recordings. Crosses are simulated radar estimates of D q computed from Eq. (3-15) using the disdrometer-derived Z q r . D o is the median volume diameter and Z ^ differential reflectivity............ 34 xviii 3.2. 3.3. 3.A. 3.5. 3.6. 3.7. 3.8. 3.9. 4.1. 4.2. Scatter plot of R/Z h versus Z q r for the data set shown in Fig. 3.1(a). The fitted curve corresponds to Eq. (3-5). R is the rainfall rate, Zg reflectivity factor and Z q r differential reflectivity............... 37 Scatter plot of M/Zu versus Z q r for the data set shown in Fig. 3.1(b). The fitted curve corresponds to Eq. (3-6). M is the water content, Zjj reflectivity factor and Z q r differential reflectivity.............. 37 Scatter plot of R/Zj, versus D q . The fitted curve corresponds to the 2-section relationship given in Table 3.3. R is the rainfall rate, Zg reflectivity factor and D q median volume diameter................... 38 Scatter plot of M/Z™ versus D q . The fitted curve corresponds to the 2-section relationship given in Table 3.3. M is the water content, ZH reflectivity and D q median volume diameter ......................... 38 Scatter plot of D q versus Zq ,> on (a) logarithmic and (b) linear scales obtained from the data set shown in Fig. 3.1. The fitted curve corresponds to Eq. (3-15). D q is the median volume diameter and ZH differential reflectivity............................................ 44 Scatter plot of Re derived from the empirical relationship given in Eq. (3-6) versus disdrometerderived where R is the rainfall rate.................. 49 Scatter plot of Me derived from the empirical relationship given in Eq. (3-6) versus disdrometerderived where M is the water content................... 49 Scatter plot of D q £ derived from the empirical relationship given in Eq. (3-15) versus disdrometerderived where D q is the median volume diameter . . . 50 The relative locations of the CHILL radar and the disdrometer for the 29 October 1982 rainfall event in central Illinois. Z# contours of a rain cell obtained from three different PPI scans are also shown which were used to estimate storm speed and direction. The times indicate beginning of the scans. Zjj is the reflectivity factor ................................... 64 The spatial cell network used in the cross-correlation analysis of the radar versus disdrometer data for the central Illinois rainfall event (see Section 4.1). Columns 1-7 are along the storm track, whereas rows (A-E) are along the radar rays at the indicated azimuth angles. The numbers in each cell correspond to the first of the six range gates to be averaged. Disdrometer is located at the center of cell A4 . . . . 66 xi x A.A. A.A(c). A.5. A.6. A.7. A.8(a). Cross-correlation coefficients for (a) ZH and (b ) time series data obtained from radar and disdrometer measurements shown for optimum delay times for radar measurements. Z h is the reflectivity factor and ZpR differential reflectivity ............................. 69 Cell DA scatter plots of (a) Rg derived from the radar (ZR , Z DR) using Eq. (3-5) versus disdrometerderived Rp ana (b) Mg derived from the radar (ZR , ZDR) using Eq. (3-6) versus disdrometer-derived Mg. R is the rainfall rate, M water content, ZH reflectivity factor and Z DR differential reflectivity............... 71 Cell DA scatter plot of Dgg derived from the radar ^DR' using Eq, (3-15) versus disdrometer-derived D o d » where D q is the median volume diameter................. 72 Cell DA scatter plots of radar measured (a) Z h and (b) Z d r versus their corresponding values derived from disdrometer measurements. Zh is the reflectivity factor and ZDR is the differential reflectivity . . . . 73 Horizontal distance X traveled by raindrops of different sizes during their fall to the ground versus terminal velocity v t of the raindrops. Results are shown for different boundary layer depths and for raindrops originating from upper, mid and lower beam heights h. The horizontal extent of the radar swath and the disdrometer drop diameter corresponding to the Vf. axis are also superimposed................... 77 Time of impact on the disdrometer of the raindrops originating from lower, mid and upper beam heights, h plotted for raindrops with different terminal velocities, v t and disdrometer drop diameters. The direction of the disdrometer time sample with respect to radar sampling time and the percentage of disdrometer sample observed by radar for different v t are also shown. .................... 79 Time records of R and M during the 29 October 1982 rainfall event in central Illinois. The solid lines represent 2.5 min running averages of 30 s disdrometer samples with zero time corresponding to values averaged over 0018-0020:30. The points indicate radar estimates derived from (Zh » ZpR) using Eqs. (3-5) and (3-6) delayed by 2 min. R is the rainfall rate, M water content, Z h reflectivity factor and Zj)R differential reflectivity......................... 80 xx A.8(b). A.9. A.10. A.10. A.11. A.12. A.13. Time record of Do during the 29 October 1982 rainfall event in central Illinois. The solid lines represent 2.5 min running averages of 30-s disdrometer samples with the zero time corresponding to values averaged over the time interval 0018-0020:30. The points indicate radar estimates derived from (ZR , ZpR ) using Eq. (3-15) delayed by 2 min. D q is the median volume diameter, ZR reflectivity factor and ZpR differential reflectivity............................................ 81 Time records of ZR and ZpR for the rainfall event shown in Fig. A.8. The points are obtained from the radar measurements and the solid lines are the disdrometer-derived values. ZR is the reflectivity factor and ZpR differential reflectivity............... 82 Swath scatter plots of (a) Rg derived from the empirical relationship of Eq. (3-5) and (b) R q derived from the gamma model relationship of Eq. (3-9) using radar (ZR , ZpR) versus Rp obtained from the disdrometer [see next page for (c) and (d)]. R is the rainfall rate, ZR reflectivity factor and ZpR differential reflectivity ............................. 83 Swath scatter plots of (c) R z r derived from the empirical Z-R relationship of Eq. (A-6) and (d) RMS derived from the Mueller-Sims (1966) relationship of Eq. (A-5) using radar Z h versus Rp obtained from the disdrometer [see previous page for (a) and (b)]. R is the rainfall rate and Z R reflectivity factor . . . 87 Swath scatter plots of (a) M g derived from the empirical relationship of Eq. (3-6) and (b) M derived from the gamma model relationship of Eq. (3-10) using radar (Zp» Z p R) versus M d obtained from the disdrometer. M is the water content, Z R reflec tivity factor and Z ^ differential reflectivity . . . . 85 Swath scatter plots of (a) D q g derived from the gamma model relationship of Eq. (3-18) and (b) D q e derived from the empirical relationship of Eq. (3-15) using radar ZpR versus D o d obtained from the disdrometer. D q is the median volume diameter and Z DR is the differential reflectivity................... 86 Swath scatter plots of radar measured (a) Zp and (b) Z p R versus their corresponding values derived from the disdrometer measurements. Z R is the reflectivity factor and Z p R is the differential reflectivity............................................ 87 xxi A.1A. A.15. A.16. A.17. Relative locations of the CP-2 radar and the disdrometer during the A June 1983 rainfall event in Boulder, Colorado. The trajectory of the rain drops, the location of the radar volumes used for different elevation angles and the radar rays and the range gates used for averaging are also shown . . . 106 Time records of the computed radar observables (a) Zh and (b) Zq R corresponding to the disdrometer measurements for the A June 1983 event in Boulder, Colorado. Also shown are (c) R and (d) Dq measured by the disdrometer for the same event. Zj$ is the reflectivity factor, Zjj differential reflectivity, R rainfall rate and D q median volume diameter ........ 107 Vertical distributions of raindrops with different terminal velocities and their corresponding disdrometer size categories at 15 s intervals to determine the raindrops contributing to the radar sampling volumes at the six elevation angles. Pairs of drop size distributions averaged to obtain 30 s disdrometer samples and the radar beamwidth at different elevation angles are also indicated ........ 110 Time records of the transformed rainfall parameters (a) ZH , (b) ZDR, (c) R and (d) D q derived from the disdrometer measurements corresponding to 1° radar elevation angle. ZR is the reflectivity factor, ZD£ differential reflectivity, R rainfall rate and D q median volume diameter ............................... A.18. A.19. A.20. 112 Time records of the transformed rainfall parameters (a) Z jj, (b) Z DR, (c) R and (d) D q derived from the disdrometer measurements corresponding to 2° radar elevation angle. ZR is the reflectivity factor, Z q R differential reflectivity, R rainfall rate and D q median volume diameter ............................... 113 Time records of the transformed rainfall parameters (a) Zh» (b) ZdO> (c ) R and (d) D q derived from the disdrometer measurements corresponding to 3° radar elevation angle. Zu is the reflectivity factor, ZDR differential reflectivity, R rainfall rate and D^ median volume diameter ............................. 114 Time records of the transformed rainfall parameters (a) ZH , (b) ZDR, (c) R and (d) D q derived from the disdrometer measurements corresponding to A° radar elevation angle. Z jj is the reflectivity factor, Zpjj differential reflectivity, R rainfall rate and D q median volume diameter ............................. 115 xxii A.21. Time records of the transformed rainfall parameters (a) ZR , (b) ZDR, (c) R and (d) D q derived from the disdrometer measurements corresponding to 5° radar elevation angle. ZR is the reflectivity factor, ZDR differential reflectivity, R rainfall rate and D median volume diameter ............................. 116 Time records of the transformed rainfall parameters (a) Z , (b) Z , (c) R and (d) D q derived from the disdrometer measurements corresponding to 6 radar elevation angle. Z R is the reflectivity factor, Z p R differential reflectivity, R rainfall rate and D q median volume diameter ............................. 117 Scatter plots of radar-observed (a) Z ^ a n d (b) Z§R versus their corresponding value Z R and ZD,, obtained from the results shown in Figs. A. 17A.23(a) and A.17-A.23(b), respectively. ZR is the reflectivity factor and Z DR is the differential reflectivity............................................ 118 Scatter plots of radar-derived rainfall rates computed from (a) the empirical (ZR , ZDR> relationship and (b) Marshall-Palmer relationship versus disdrometerderived rainfall rates shown in Figs. A.17-A.23(c). ZH is the reflectivity factor and ZDR differential reflectivity............................................ 119 Scatter plot of D q derived from the radar measure ments of ZDR versus disdrometer-derived values shown in Figs. A.17-A.23(d) where D q is the median volume diameter................................................ 120 The relative locations of the CP-2 radar and the two PAM stations during the 15 June 198A rainfall event in Boulder, Colorado................................... 126 Constant altitude (2.A km MSL) PPI's of (a) ZR and (b) Z n_ generated from the value scan between 1705:3b-1707:31 MDT during the 15 June 198A event. Z is the reflectivity factor and ZR differential reflectivity.......................................... 128 A.27(c). Constant altitude (2.A km MSL) PPI of R generated from the volume scan between 1705:36-1707:31 MDT during the 15 June 198A event where R is the rainfall r a t e ........................................ 129 A.22. A.23. A.2A. A.25. A.26. A.27. A.28. Constant altitude (2.A km MSL) PPI's of (a) Z R and (b) ZDR generated from the volume scan between 1716:A0-1718:31 MDT during the 15 June 198A event . . xxiii 132 A.28(c). A.29. A.30. A.31. A.32. A.33. A.3A. 5.1. Constant altitude (2.A km MSL) PPI of R(mm h ) generated from the volume scan between 1716:AO1718: 31 MDT during the 15 June event where R is the rainfall r a t e ....................................... 133 RHI's of (a) Z jj and (b) ZDR generated from the volume scan between 1705:36-1707:31 MDT during the 15 June 198A event which shows a North-South vertical cross-section of (ZR , Z..R ) passing through the PAM 15 site located 27.8 km east of CP-2. Zh . is the reflectivity factor and ZDR differential reflectivity.............. 13A Time record of R obtained from PAM 15 raingage measurements. Also shown are the radar estimates R~ d r derived from the empirical relationship using (ZR , Zj)R) and (a) Rjyjp derived from the MarshallPalmer relationship and (b) Rj derived from the Jones (1956) relationship of Eq. (A-8). Zero time corresponds to 1700 MDT. R is the rainfall rate, ZR is the reflectivity factor and ZpR is the differential reflectivity ........................... 138 Time record of R obtained from PAM 11 raingage measurements. Also shown are the radar estimates R Zd r derived from the empirical relationship using (ZR , ZDR) and (a) R^p derived from the MarshallPalmer relationship and (b) Rj derived from the Jones (1956) relationship of Eq. (A-8). Zero time corresponds to 1700 MDT. R is the rainfall rate, Z ji is the reflectivity factor and ZpR is the differential reflectivity ...................... 139 Scatter plot of R z d r derived from the empirical relationship using (Z^, ZDR) versus R obtained from the measurements of both PAM 11 and 15 raingages. R is the rainfall rate...................... 1A1 Scatter plot of Rj^p derived from the MarshallPalmer relationship versus R obtained from the PAM 11 and 15 raingages where R is the rainfall rate.................................................. 1A2 Scatter plot of Rj derived from the Jones (1956) relationship of Eq. (A-8) versus R obtained from the PAM 11 and 15 raingages where R is the rain fall r a t e ............................................ 1A2 Demonstrating the applicability of using CAPPI's for deriving CP-A reflectivity fields affected by attenuation along ray paths....................... 150 xx iv 5.2(a). 5.2. 5.3. 5.4. 5.5. 5.6. 5.7. 5.8. Constant altitude (3.0 km MSL) PPI of Zu ^q generated from the CP-2 volume scan between 1418*.52-1422:02 during the 30 June 1984 event. Z jj^ q *-s the S-band reflectivity factor ................................. 152 Constantaltitude (3.0 km MSL) PPI's of (b) ZpR and (c) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event. ZDR is the differential reflectivity and R is the rainfall rate............................... 153 Constant altitude (3.0 km MSL) PPI of Zjj5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event. ZR 5 is the C-band reflectivity factor ................................. 154 RHI's of (a) Z jjiq generated from the CP-2 volume scan between 1418:52-1422:02 and (b) Zjj5 generated from the CP-4 volume scan between 1418:33-]421:12 during the 30 June 1984 event showing an East-West vertical cross-section of (Zr ^q , Zr j ) at y = 20 km. Zrio end Z R 5 are the S-band ana the C-band reflectivity factors,respectively.................... 155 RHI's of (a) ZDR and (b) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event showing an East-West vertical cross-section of (R, ZDR) at y = 20 km. Zpp is the differential reflectivity and R is the rainfall rate.................................................. 156 RHI's of (a) Z r i q generated from the CP-2 volume scan between 1418:52-1422:02 and (b) Z R 5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event showing an East-West vertical cross-section of (Zjjio* ^h 5) at y = 22 km. Zflio and Z R 5 are the S-band and the C-band reflectivity factors, respectively.................. 158 RHI's of (a) ZDR and (b) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event showing an East-West vertical cross-section of (R, ZDR) at y = 22 km. Z DR is the differential reflectivity and R is the rainfall r a t e ....................................... 159 Scatter plot of ZR versus ZDR obtained from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event. The solid line is the rainfall boundary defined by Aydin et al. (1986). Both negative and large values of Z jjR at low Z jj are thought to be due to ground clutter. ZR is the reflectivity factor and Z DR differential reflec tivity................................................ 161 xxv Variation of (a) A h s /Zh IO and (b) Ah 5/Zv 10 versus ZDR for disdrometer-derived distributions (see next page for (c) and (d)]. AH^ is the C-band specific attenuation at horizontal polarization and ZR i q , Z v i o (S-band) horizontal and vertical reflectivity factors, respectively. ZDR is the differential reflectivity........................................ Variation of (c) and (d) Ayg/Zyjn versus ZDR ^or disdrometer-derived distribution [see previous page for (a) and (b)J. A V 5 is the C-band specific attenuation at vertical polarization and ZH10* ZV10 S-band horizontal and vertical reflec tivity factors, respectively. Zj)R is the differential reflectivity . . . ................... Variation of predicted A^5 / Z v e r s u s Znp for the disdrometer-derived distributions where A£5 is derived from the empirical relationship given in Table 5.2 in the form of Eq. (5-1). Aj*c is the predicted C-band specific attenuation at vertical polarization, S-band horizontal reflectivity factor and ZDR differential reflectivity.......... Errors between the actual and the predicted values of the attenuation (AR 5 /AR 5 ) versus Zdr for disdrometer derived distributions. a ]|5 is derived from the empirical relationship given in Table 5.2 in the form of Eq. (5-1). A R 5 is the C-band specific attenuation and Z q R differential reflectivity. ................................. . . Variation of (a) Z ^ / Z ^ g an<i (b) ZH5^ZV10 versus ZDR for disdrometer-derived distributions [see next page for (c) and (d)]. Z-^5 t^ie C-band horizontal reflectivity factor and ZR i q » Zyio S-band horizontal and vertical reflectivity factors, respectively. ZDR is the differential reflec tivity. . ........ ............................... Variation of (c) Z ^ / Z ^ o anc* (<*) ZV5^ZH10 versus Z DR for disdrometer-derived distributions [see previous page for (a) and (b)]. Z ^ is the C-band vertical reflectivity factor and Z r i q , Zy^g S-band horizontal and vertical reflectivity factors, respectively. ZDR is the differential reflec tivity.............................................. xxv i 5.13. 5.14. 5.15. 5.16. 5.17. 5.18. 5.19. 5.20. 6.1. Variation of predicted Zr j /Zh IO versus Zd r for the disdrometer-derived distributions where Z^j isderived from the empirical relationship given in Table 5.3 in the form of Eq. (5-2). Zg^ is the predicted C-band horizontal reflectivity factor, Zh i o S-band horizontal reflectivity factor. Zd r is the differential reflectivity..................... 171 Predicted CP-4 reflectivity values derived from CP-2 (Zr i o » Zd r ) measurements. The azimuth angles and the gate spacing used in the prediction scheme for rays along paths originating from CP-4 are also indicated. Azimuth angles are measured CCW from north. Zr i o the S-band reflectivity factor and Z d r differential reflectivity............ 175 The predicted C-band CP-4 reflectivity factor contours (Fig. 5.14) superimposed as an overlay on the actual CP-4 measurements (Fig. 5.3) for the 15 June 1984 e v e n t . ................................. 178 Spatial variation of reflectivity factors at S-band measured by CP-2 compared with the pre dicted and the measured reflectivity factors at C-band along the CP-4 rays with azimuth angles (a) 35° and (b) 40° CCW from north................... 180 Spatial variation of reflectivity factors at S-band measureed by CP-2 and the simulated reflectivity factors at C-band along the same ray originating from CP-2 at an azimuth angle of 38.2° CCW from north. C-band reflectivity values without accounting for attenuation ( Z ^ ) are also shown . . . 181 Scatter plot of the predicted and measured reflectivity factors for the CP-4 radar at C-band for the ray with the azimuth angle 35° CCW from n o r t h ................................................ 183 Scatter plot of the predicted and measured reflectivity factors for the CP-4 radar at C-band for the ray with the azimuth angle 40° CCW from north ..................................... 183 Scatter plot of the predicted and actual reflec tivity factors for the CP-4 radar at C-band for even rays with the aximuth angles between 3 0 0 -45 ° CCW from n o t h ........................................ 184 Computed scavenging rate A and rainfall rate R scatter plot for aerosols of radius 0.2 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982..................... 194 xxvii 6.2(a). 6.2(b). 6.2(c). 6.2(d). 6.3. 6.A. 6.5. Computed and simulated time history of A for aerosols of radius 0.2 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate . . . . 195 Computed and simulated time history of A for aerosols of radius 0.5 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. .. 196 Computed and simulated time history of A for aerosols of radius 1.0 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. .. 197 Computed and simulated time history of A for aerosols of radius 2.0 corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. .. 198 Computed scavenging rates Ashowing their variability with aerosol size in the range 0.2 - 2 ym ym 200 . Reflectivity weighted fall velocity dependence on derived from disdrometer simulations ........ 207 Reflectivity weighted fall velocity dependence on Zfj derived from disdrometer simulations, including empirical <vt> - Z relationships due to Rogers (1964), Sakhan and Srivastava (1971), Joss and Waldvogel (1970) and this work, indicated as R, SR, JVJ and D, respectivelyv where Z is the reflectivity factor ................................. 210 xxviii LIST OF SYMBOLS Description Symbol Unit A Specific attenuation a Semi-minor axis of a raindrop AAD Average absolute difference AD Average difference ^H5 C-band specific attenuation at horizontal polarization (dB km ^5 C-band specific attenuation at vertical polarization (dB km b Semi-major axis of a raindrop CAPPI Constant altitude plan position indicator CCW Counter-clockwise CW Clockwise CST Central standard time D, De Equivolume diameter (mm) Median volume diameter (mm) D max Maximum equivolume diameter (mm) dB Decibels dBZ Decibels of the reflectivity factor DSD Drop size distribution E Scavenging efficiency f Radar frequency FSD Fractional standard deviation D0 (dB km (mm) (mm) -1 (mm (Hz) xx ix -3 m ) GOES Geostationary Operational Environmental Satellite H Horizontal polarization ISWS Illinois State Water Survey |k |2 Refractivity factor at S- and C-bands (=0.93) K Direction of propagation M Liquid water content M Complex index of refraction for water m Parameter of the gamma model DSD MAYPOLE MAY POLarization Experiment MDT Mountain daylight time MSL Mean sea level NB Normalized bias NCAR National Center for Atmospheric Research N(D) Raindrop size distribution N m Parameter of the gamma model DSD No Parameter of the exponential model DSD NSED Normalized standard error of the difference OSPE Ohio State Precipitation Experiment P, Pr Total average backscattered power PAM Portable automated mesonet PPI Plan position indicator R Target range R Rainfall rate r Axial ratio (a/b) RHI Range height indicator SB Sample bias S(v) Doppler velocity spectrum (W m ^ s) Sn (v) Normalized Doppler velocity spectrum (m-1 s) u, Horizontal wind velocity (m s_1) v Doppler velocity (m s-1) <v> Reflectivity weighted Doppler velocity (m s-1) v Terminal velocity (m s 1) <vfc> Reflectivity weighted terminal velocity (m s 1) w Mean vertical air velocity (m s 1) Z Reflectivity factor (dBZ) Z_D Differential reflectivity (dB) uq DK S-band horizontal reflectivity factor (dBZ) C-band horizontal reflectivity factor (dBZ) Apparent C-band horizontal reflectivity factor (dBZ) Zy, S-band vertical reflectivity factor (dBZ) Zyj C-band vertical reflectivity factor (dBZ) a Canting angle (deg) A<(> Differential phase shift (deg) 6 Boundary layer depth (m) n Reflectivity cross-section density (mm A Parameter of the DSD (mm ^) A Scavenging rate (s_1) X Radar wavelength (mm) p Correlation coefficient Pw Water density (kg m -3) o Surface tension (J m“2) a Extinction cross-section at horizontal polarization (mm2) ^H’ ZH10 Zjj,j Z ' xxxi 2 m -3 ) Extinction cross-section at vertical polarization Backscatter cross-section at horizontal polarization Backscatter cross-section at vertical polarization Fall time of raindrops xxxii CHAPTER 1 INTRODUCTION 1.1 General Nature of the Problem Radar has been an important tool for remote sensing of the atmosphere, since interactions between atmospheric particles and radio waves are significant in the microwave and millimeter wave bands. Backscattered power at these wavelengths can be interpreted to give information about these atmospheric particle scatterers, specifically for detection and characterization of rain and cloud particles consisting of snow and ice crystals, all commonly referred to as hydrometeors. Radar information also has important applications in communication systems and propagation studies, especially along earth-satellite paths, since the communication channels employing these wavelengths are affected by hydrometeors causing cross-talk when orthogonal polarizations are used and attenuation that can signifi cantly degrade channel quality. Radar is unique in the remote sensing of atmospheric scatterers because of its inherent ability to cover large areas from a single location in real time. To approach the same capability otherwise would require installation of a dense network of ground stations, aircraft and other aerial sensing devices which in turn would result in much greater costs and delays in data transmission and analysis. 1 The most recent developments in radar remote sensing include the use of multi-parameter radar measurements (MPRM) to provide independent information about the atmospheric medium and scatterers from polarization, phase, frequency and statistical characteristics of the received echoes in addition to their backscattered power. These measurements usually employ dual polarization, dual wavelength and Doppler spectrum techniques. More than one radar may also be involved in transmitting and receiving various signals, operating either simul taneously or sequentially. One of the most promising techniques among the MPRM's utilizes a dual polarization radar receiving the backscattered returns in two linear, orthogonal polarizations, horizontal and vertical. This scheme relies on measuring the differential reflectivity which was introduced by Seliga and Bringi (1976) and is defined as the differ ence (in dB) in radar reflectivities between returns at these two orthogonal polarizations. hydrometeors: is the result of three properties of (1) their non-spherical shape; (2) their high degree of mutual orientation; and (3) representation of raindrop size distribu tions by models dominated by two independent parameters. assortment of raindrops, Z ^ For an is measured by illuminating the volume at vertical polarization which is aligned along the symmetry axis and horizontal polarization which is aligned along the major axis of the generally oblate-shaped raindrops. The backscattered power is received with the same polarization as the transmitted one. Raindrops tend to be deformed into nearly oblate spheroidal shapes with their axes of symmetry aligned dominantly along the vertical and larger drops are uniformly more deformed than the smaller ones (Pruppacher and Pitter, 1971). This raindrop behavior results in polarization- dependent backscattering properties. When differential reflectivity is combined with the effective reflectivity factor at either hori zontal (Zjj) or vertical (Zy) polarizations, the two parameters of a given raindrop size distribution can be determined. Rainfall parameters such as rainfall rate (R), liquid water content (M) and median volume diameter (Dq ) and propagation characteristics such as specific attenuation (A) and relative phase shift (A<J>) can also be estimated accurately from these polarimetric measurements, resulting in considerable improvement over other radar techniques developed to estimate these parameters using a single radar observable such as reflectivity factor (Z) (Battan, 1973; Atlas et al., 198A). Thus far, the Zqjj method has proven to be useful in several applications. (1) These include: estimation of drop size distribution (DSD) which yields the spatial and temporal evolution of rainfall rate, liquid water content and median volume diameter; (2) discrimination of regions of water, ice and mixed phase hydrometeors and the detection of hail; and (3) other applications such as prediction of cumulative micro wave attenuation, differential attentuation and differential phase shift in rainfall using both attenuating and non attenuating wavelengths. Combined, these applications clearly have major implications for cloud physics, hydrology, weather modification and communications. 4 This study, therefore, was undertaken to examine further the use of the method for rainfall rate measurement and other related applications. It includes: a review of relevant assumptions and theory; three studies comparing radar with ground-based measurement of rainfall; a successful demonstration of using the method to predict specific attenuation and reflectivity at attenuating microwave wave lengths; and simulations which show that the method has potential for rainfall scavenging of aerosols and for determining vertical air motions. 1.2 Previous Related Studies The relationships between the reflectivity and attenuation of microwaves and rainfall rate were first examined by Ryde (1941, 19A6) who was mainly concerned with precipitation as unwanted clutter as noted by Atlas et al. (198A). Wexler and Swingle (19A7), Marshall et al. (1947) and Atlas (1947, 1948) were the first to interpret Ryde's work for radar meteorological applications, and Marshall and Palmer (1948) proposed an exponential size distribution for raindrops to obtain an empirical relationship between the reflectivity factor (Z) and rainfall rate (R) Z = ARb = 200 R 1,6 6 ~3 "1 where Z is in mm m and R is in mm h . (1-1) To arrive at this, they assumed N q in the exponential distribution N(D) = N q exp -(AD) (mm *m ^) (1-2) to have a specific value independent of rainfall (Nq = 8x10 3 mm “1 -3 m ). Marshall et al. (1947) and Austin and Williams (1951) conducted the first experiments on the relation between echo intensity and rain rate. Austin and Richardson (1952) and Blanchard (1953) reported the first signs that there was not a universal relationship between Z and R. Atlas et al. (1953) were the first to demonstrate quantitatively the extent to which particle shape, orientation, phase state, and the polarization and angle of incidence of the transmitted wave affects the reflectivity of precipitation as indicated by Rogers (198A). And, by the mid-1950s, strong evidence had already been gathered (Twomey, 1953) that a satisfactory estimate of R cannot be determined from Z alone through a simple Z-R relationship. Nevertheless, extensive investigations to obtain empirical Z-R relationships continued where the values of the parameters A and b varied widely according to rain type, geographical location, space and time. The result was that by 1970, Battan (1973) reported 69 Z-R relations for different locations around the world. A physical basis for this multitude of relations was given by Atlas and Chmela (1957) in a rain-parameter diagram involving the four basic parameters Z, R, M (liquid water content) and D q (median volume diameter). More recently, Ulbrich and Atlas (1978) extended the same work by adding N q and (optical extinction). They showed the extent of the errors which is possible in estimating any of these parameters using Z alone and recognized the fact that remote measurements of R required at least two independent parameters. indicated that the region spanned by the Z-R relations listed by They 6 Battan extends over three orders of magnitude for N q and more than one order of magnitude for R. The Z ^ method, introduced by Seliga and Bringi, promises to improve the estimation of precipitation parameters to a greater accuracy. Simulations derived from disdrometer measurement, by Ulbrich and Atlas (1984) showed that assuming a gamma DSD model with m = 2 reduced the bias in R, M and D q estimates when compared with results derived using the exponential model of Eq. (1-1). Similar simulations by Seliga et al. (1986) indicated that the technique promises to produce a normalized standard error of better than 13% over the range R from 0.1 to 260 mm h A number of field tests of the method have been performed producing very encouraging results as noted in a review article by Ulbrich (1986). First field experiments by Seliga and Bringi (1978) and Seliga et al. (1979) reported that D q and were in their expected ranges of 0.5-4 mm and 0-4 dB, respectively. Seliga et al. (1980a) and Bringi et al. (1982) constructed a time profile of R from ground-based disdrometer measurements and, after comparing them with the radar estimated values, found good qualitative agreement for a 1978 storm near Chicago, Illinois. Al-Khatib et al. (1979) and Seliga et al. (1980b, 1981) performed radar-raingage comparisons over a dense network of raingages and reported an improvement in estimation of R of around a factor of two for the Z^^ method over Z-R relationships. Clarke et al. (1983) also reported good agreement for this method when comparing radar and raingage derived R. Direskeneli et al. (1983) showed that Z-- derived R and Dn tracked the spatial and temporal variability of disdrometer-derived values very well. Seliga et al. (1984) employed a transformation technique to account for changes in DSD with altitude to demonstrate the agreement between radar and disdrometer derived (Z^, Z ^ ) . Direskeneli et al. (1986) in a preliminary report, used a Cartesian interpolation technique to transform the radar volume into constant altitude plan position indicators (CAPPI's) and compared the radar and raingage-derived R's by accounting for the wind transport and fall time of raindrops in a 1984 Colorado storm with high R. They reported improvements of 14% and 23% in normalized standard error with respect to two other Z-R relationships (see Section 4.3). The above experimental studies outline research by the Ohio State/Penn State radar meteorology group for quantitatively estimating rainfall parameters by the Z ^ method. Experiments have also been carried out by the Rutherford Appleton Laboratory employing the Chilbolton radar in Southern England (Hall et al., 1980). comparison between A and disdrometer-derived D q values led Goddard et al. (1982) to propose a modified relationship between the axial ratio and the equivalent diameter of the raindrops. Goddard and Cherry (1984a) obtained radar-derived rainfall rates from a sample volume 200 m above a disdrometer without accounting for drop size sorting or wind transport of raindrops. They suggested the need for a DSD other than exponential to account for a systematic overestimation of R of 33%. Subsequently, Goddard and Cherry (1984b) employed a gamma model of m = 5 and obtained a standard deviation of 33% between the radar- and raingage-derived R. Cherry et al. (1984) reported general agreement between radar and airborne disdrometer measurements 8 of rainfall parameters; they attributed differences in radar and aircraft deduced (Nq, Dq) of the DSD on the method of measuring the aircraft spectra which placed greater emphasis on the large diameter drops. Although the focus of this work is on rainfall rate, water content and drop size estimation, several other important topics are also included. They are: - application of to predict and compare C-band reflectivity profiles from S-band measurements by estimating C-band attenuation and reflectivity factors from S-band (Z^, measurements (Chapter 5); - simulations on how to estimate aerosol scavenging rates from (Zjj, measurements (Chapter 6); - the potential role of Zqjj as an estimator for reflectivityweighted fall velocity (Chapter 6). Previous related work in these areas is considered within the context of these chapters. 1.3 Research Objectives and Approach This work deals primarily with the applications of the differential reflectivity radar technique to estimating rainfall parameters and predicting microwave attenuation. Case studies, derived from the 1982 Ohio State Precipitation Experiment (OSPE) in Central Illinois and the 1983 and 1984 MAY POLarization Experiment (MAYPOLE) field programs provide the data for the research. Rainfall rate results also include comparisons with estimates from single parameter Z-R methods. In order to make observation volumes of radar and ground measurements compatible, careful attention was paid to spatial and temporal factors due to the large separation and resolution differences between these systems. Potential applications of Z^R in two new areas, namely scavenging by rain washout of aerosols and fall velocity of raindrops are also examined. The results of the study are organized as follows: Chapter 2--Differential Reflectivity Radar Method and Experimental Factors. The theory of the Z^R method is outlined with special emphasis on how the radar measurements can be used to determine rainfall parameters. Major assumptions of the technique and their physical basis are discussed. The specifics of the experimental facilities from which the dual polarization radar data and ground based measurements were obtained are outlined as well as a review of relevant statistical measures. Chapter 3— Disdrometer Based Rainfall Simulations. The findings of the simulations by Seliga, Aydin and Direskeneli (1986) are reviewed to establish the relationships between the radar observables (Zjj.Zp^) and the rainfall parameters R, M and D q . The estimates of the errors in these simulations are described and results are compared to other estimation methods. Chapter 4--Differential Reflectivity Radar Measurements of Rainfall. The major emphasis in this chapter is to demonstrate that the Zq R method results in improved estimation of rainfall parameters. Results obtained from case studies from three different field programs are presented, comparing radar and ground-based measurements. These studies differ experimentally and, consequently, require special 10 techniques to account for volume sampling differences, drop size sorting and wind transport. Chapter 5— Predictions and Comparisons of C-Band Reflectivity Profiles from S-Band Measurements. Simulations to estimate C-band reflectivity factors and attenuation using S-band (Z„ described. » ZDR) are These results are employed to predict successfully the apparent reflectivity factor profiles of a C-band radar employing the S-band radar measurements made at a different site during the MAYPOLE *84 field experiment. Chapter 6— Other Applications. Potential use of Z ^ measurements in two other applications are discussed. These are the determination of the scavenging rates of aerosols by precipitation and a proposed scheme to recover the vertical air motion component of the reflectivity weighted Doppler velocities from Z ^ radar observations. Chapter 7--Conclusions and Recommendations. research are summarized in this chapter. Results of the Recommendations for possible improvements in future studies and a brief discussion of other applications based on the (Z„» Zq ^) radar measurements conclude the study. CHAPTER 2 DIFFERENTIAL REFLECTIVITY RADAR METHOD AND EXPERIMENTAL FACTORS The purpose of this chapter is to outline the basic concepts in radar remote sensing, focusing on the differential reflectivity radar method and its applications for estimating rainfall parameters and microwave attenuation. A review of the relevant radar observables as well as a discussion of the underlying physical basis for these are presented. The experimental facilities that supplied the radar and ground truth data for the studies given in Chapters 4-6 are described. Possible sources of error that can affect comparisons of the radar estimated parameters with ground-based measurements are also discussed. 2.1 2.1.1 Differential Reflectivity Radar Method Radar Observables In this research, radar meterological measurements are obtained by illuminating a medium containing randomly positioned hydrometeors with a finite length electromagnetic pulse and sampling backscattered energy at fixed time intervals or gates (Battan, 1973; Doviak and Zrnic, 1984). The two incoherent radar parameters employed in dual polarization measurements are the effective reflectivity factors at 11 12 horizontal (Zjj) and vertical (Zy) polarizations (Seliga and Bringi, 1976): ^max ~ V ^ TT |k| where A(mm): | 0„ ,,(D)N(D)dD H ’V (mm6 m~3) (2-1) radar wavelength (mm) 2 CM 6 - 1 + 2 m IkI2 I 2 = 0.93 ; refractivity factor at S-band C-band frequencies with m being the complex index of refraction for water a„ ,,(D): H, V bacxscattering cross-sections at horizontal and 2 vertical polarizations (mm ) D: Zjj y equivolume diameter (mm) N(D): raindrop size distribution (mm D maximum drop size, r max : -1 m -3 ) is related to the total backscattered power P from this ensemble of distributed targets through C Iv I2 ? = Zh,V (W) (2_2) where C is a constant which depends on the radar characteristics. When Rayleigh scattering applies, the backscattering cross-section of an individual, spherical scatterer is 1)6 c™"2) and the reflectivity factor for an ensemble of raindrops becomes C2"3) 13 Z = I max A -1 D N(D)dD (mm m -3 (2-4) ) 0 Differential reflectivity ( Z ^ ) can be defined as the difference (in dB) between and Zy (2-5) The differential reflectivity radar method for estimating rainfall parameters utilizes the deformation of raindrops into nearly oblate spheroidal shapes as they fall through the atmosphere. The vertically and horizontally polarized backscattering cross-sections of raindrops differ considerably for raindrops of sizes larger than 0.5 mm, and this difference increases as the raindrop size increases because of the axial ratio dependence of the oblate drops with size (equivalent diameter). For computing Eq. (2-1), the backscattering cross-sections a„ ,,(D) may be determined using Waterman's (1965) (1969) T-matrix method and the axial ratios (r) given by Green (1975). The latter approximation, relating r to D, agrees well with the theoretical and experimental results of Pruppacher and Pitter (1971) and has the analytical form (mm) where pw = 10 a - 3 kg m -3 7.275 x 10 g = 9.8 m s ^ -2 (water density) -2 Jm (surface tension) (2-6) 14 r = a/b; axial ratio where a is the semi-minor and b is the semi-major axis of an oblate spheroidal drop. Fig. 2.1 illustrates the geometry of the oblate' spheroidal raindrops as well as the horizontally and vertically polarized electric field incident on it. Since r depends on D, a radar measurement based on r can in turn yield an estimate of the size of the raindrops. In practice, the maximum drop size D max is assumed to be 8 mm which is based on experimental studies of the critical sizes above which breakup of raindrops occursduring their steady state fall through the atmosphere (Pruppacher and Klett, 1978). 2.1.2 Rainfall Parameters The rainfall parameters to be estimated using radar observables are rainfall rate (R), liquid water content (M) and median volume diameter ( D q .). R and M are given by D max D v (D)N(D)dD (mm h ) (2-7) 0 max (2-8) D N(D)dD 0 where vfc(D) is the terminal velocity of the raindrops (Gunn and Kinzer, 1949). A good approximation to v is given by Atlas et al. (1973) as vfc(D) = 9.65 - 10.3 e"°'6D (m s"1) (2-9) 15 Minor Axis Major Axis (Vertical Polarization E,,JHorizontal Polarization) ~HO Incident Fields Figure 2. 1* Raindrop distortion model: an oblate spheroid is the body of revolution formed when an ellipse is rotated about its minor axis. 16 D q is the diameter such that half the water content is contained in drops with diameters smaller than D q and can be obtained from, fD° 3 1 D N(D)dD - j fDmax 0 2.1.3 3 D N(D)dD (2-10) 0 Specific Attenuation Specific attenuation for propagation of radio waves through the rainfall within the radar volume is defined as D 2 f max Ajj^v = A.343 x 10 i (dB km"1) aER v (D)N(D)dD (2-11) 0 where O otl Uai>V : extinction cross-sections at horizontal and vertical polarizations. 2.1.4 Drop Size Distribution Many drop size distributions (DSD) within the radar volume have been generally assumed to have an exponential form, N(D) = Nn exp(-AD) (0 < D < U — — _1 where ^ ( m m Dmax ) (mm"1 m'3) (2-12) _^ m ) and A(mm ) are the parameters of N(D). This form of the DSD was suggested by Marshall-Palmer (1948), based on their analysis of the drop size spectra obtained by Laws and Parsons (1943). Once DSD is determined, the other rainfall parameters R, M and D q can be obtained from Eqs. (2-7), (2-8) and (2-10). Experimental results indicate that Eq. (2-12) is a good approximation when sufficient spatial and temporal averaging is performed on the drop size spectra 17 (Ulbrich, 1983). More recent studies also indicate that the N q parameter of this model is different times subject to large and sudden changes during within the same stormfor similar rainfall rates (Waldvogel, 1974; Donnadieu, 1982). Since these changes in N q are independent of A» it is necessary to specify both parameters (Nq , A) of the DSD in order to account for rainfall variations during and within a storm. This in turn implies the necessity for using at least two radar observables to obtain an estimate of these parameters. Sekhon and Srivastava (1970) have shown that, for D /Drt> 2.5, max 0 — * the approximation A ® 3.672/Dq is within 2% of its limiting value. This indicates that the exponential model DSD is insensitive to changes in D for large D /Dft. ° max ° max 0 Another improvement in DSD modeling can be achieved by assuming a gamma model DSD (Ulbrich and Atlas, 1984) as N(D) = N Dm exp (-AD) m 0 < D < D — — max (2-13) In this model, N^ is used rather than the notation Nq as proposed by Ulbrich and Atlas, since N (mm -1 m -3 ) as for Nq. m has units of (mm " 1 “ in m “3 ) rather than Note that, when m = 0, N(D) reduces to the exponential form of Eq. (2-12) so the exponential model DSD is a special case of the gamma model DSD. that, for D max Ulbrich and Atlas also indicated /Dn > 2.5, A converges to A = (3.67 + m)/Dn for m > -3. 0 ° 0 Thus, the gamma model DSD is relatively insensitive to changes in D^ y for large D /Dn . * max 0 Simulations of Ulbrich and Atlas (1984) and Seliga et al. (1986) have shown that estimations based on the exponential model tend to 18 overestimate (R, M) and underestimate Dq . A gamma model DSD with m * 2 greatly reduces the bias in these estimates (see Chapter 3). Simi-larly, Goddard and Cherry (1984b) found that a gamma model of m ■ 5 reduced their bias and standard deviation of radar-raingage comparisons. In this research, the empirical relationships to obtain R, M and D q from radar observables do not assume any a priori analytical form for the DSD, although computations of the same rainfall parameters based on a gamma model DSD with m « 2 are also performed for the comparisons. 2.1.5 Single Parameter Estimation of Rainfall Parameters While suggesting the exponential form of Eq. (2-12), as noted earlier, Marshall-Palmer (M-P) assumed N q as a constant and A = A(R). Based on these assumptions, N(D) and all the integral quantities defined in Sections 2.1.2 and 2.1.3 involving N(D) depend only on a single DSD parameter and can be estimated from any one of the other defined quantities. form Eq. (1-1) [Z(mm For R, they developed a Z-R relationship of the m ) * 200 R ' ]. Other investigators also used the empirical form, Z = ARk (mm^ m ^) (2-14) to estimate R from Z, but derived or assumed different values for A and b depending on the precipitation type and location. Battan (1973) listed 69 Z-R relationships from around the world and selected the following as being the most typical for classification according to storm type: - stratiform rain: Marshall-Palmer (A = 200, b = 1.6) 19 - orographic rain: Blanchard (1953) (A = 31, b = 1.71) - thunderstorm rain: Jones (1956) (A = 486, b ■ 1.37). These typical and other Z-R relationships are also employed in this study in the simulations of Chapter 3 and in the experimental comparisons of Chapter 4. Power law expressions have also been extended to Z-M and A-R and A-Z relationships to estimate M and A in the microwave region (Douglas, 1964; Wexler and Atlas, 1963; McCormick, 1970). To demonstrate the physical basis for the wide range of variations of the empirical Z-R relationship parameters, rain parameter diagrams were introduced by Atlas and Chmela (1957) and Ulbrich and Atlas (1978) for related radar and rainfall parameters. Figure 2.2 shows the possible variations in Z, R, N q and D q for different Z-R relationships in a rain parameter diagram along with a group of radar-derived data points. The wide range of variations of these parameters illustrates the need for estimation methods based on at least two observables to account for the two parameter DSD's. Seliga and Bringi (1976) introduced Zq ^ in addition to second radar observable to provide this additional information. 2.1.6 Differential Reflectivity Radar Technique The Zqjj technique of estimating rainfall parameters derives from the following three assumptions: 1. Falling raindrops are not spherical, but assume an approximately oblate spheroidal shape as their shapes are modified by surface tension, gravitational and aerodynamic forces. Also, their oblateness increases with increasing drop size (Section 2.1.1). Radar Reflectivity Factor, Z H(dBz) 20 10° 10' Rainfall Rate ( m m / h r ) Figure 2.2. Rain parameter diagram for exponential drop size distribution model. Radar reflectivity factor versus rainfall rate with isopleths of median volume diameter Do and parameter No. Data points represent estimates inferred from radar measure ments (Seliga et al., 1981), and MP signifies the Marshall-Palmer Z-R relationship. 21 Therefore, their equilibrium axial ratios are a unique function of drop size. Theoretical calculations of Pruppacher and Pitter (1971) and wind tunnel experiments of Pruppacher and Beard (1970) support this argument. However, Jameson and Beard (1982) and Jameson (1983) found the relationship between the axial ratios and D to be different from their equilibrium values after analyzing ground-based photographic measurements of raindrops (Jones, 1959) and attributed the result to oscillations of raindrops due to the energy created by collisions. Johnson and Beard (1984) and Rasmussen et al. (1984) indicated that an existing ice core in melting raindrops would cause greater dampening of these oscillations and result in equilibrium shapes dominating their description. In situ aircraft measurements by Cooper et al. (1983) and Chandrasekar et al. (1984) indicated good agreement between the predicted and experimental equilibrium values of the axial ratios. Thus, there is strong evidence to support the hypothesis that the shapes of raindrops is well-approximated by their equilibrium axial ratios given by Pruppacher and Pitter (1971) and empirically related to drop size by Green's (1975) formula (Eq. 2-6). 2. The symmetry axes of the falling raindrops are mutually aligned along the vertical direction. For raindrops deviating from the symmetry axes, the canting effects can be analyzed in two categories: raindrop canting in the plane of incidence, and perpen dicular to the plane of incidence. Fig. 2.3 demonstrates these propagation conditions in terms of the canting angle a. The corresponding effects of radar elevation angles different than 0° are shown in Fig. 2.4(a), taken from Al-Khatib et al. (1979) who used the 22 S y m m e t r y Axis (a) Figure 2.3. Raindrop canting angle (ft), (a) in the plane of incidence with an angle of incidence (6) .and (b) perpendicular to the plane of incidence. 23 scattering formulation of Evans et al. (1978), to compute the results. For canting angles less than 10° Z^R is underestimated by only 5-6%. Available measurements of raindrop canting angles indicate that mean 10°. a Furthermore, supporting the hypothesis that hydrometeors fall with preferred orientation (McCormick and Handry, 1976). Beard and Jameson (1983), in their theoretical investigations, obtained a mean 1.5° due to wind shear and an rms a <. A general, canting effects on due to turbulence. Thus, in measurements should be negligible for most applications. 3. Raindrop size distributions are dominated by two independent parameters. Previous simulated and experimental results outlined in Chapter 1 and the results of this research (see Chapter A) support this argument. The assumed gamma model of Eq. (2-13) employs three parameters, but Ulbrich and Atlas (198A) indicated a general correlation between N m and m which would reduce that model to a two-parameter one. Based on these assumptions, the polarimetric Z^R method introduces a second radar observable in addition to DSD of raindrops. to estimate the The form of the relationships between parameters are given in Eqs. (3-5) and (3-6); these were computed from disdrometer measurements without any a priori assumptions about the analytical form of the DSD. Eqs. (3-7) through (3-10) are similar relations based on the exponential and gamma model assumptions for DSD. <. ZOR(a)DB a =5 a-0 a =5 CD O a a iO' oc Q N a =l5 (a) Maximum ZOR (DB) (b) Maximum ZDR (DB) Figure 2.4. Variation in with canting angle a (a) in the plane of incidence, and (b) perpendicular to the plane of incidence. Zero canting angle (a = 0) results in maximum Zjjr where Zd r is the differential reflectivity (Al-Khatib et al., 1979). ISJ 2.1.7 Statistical Considerations is expected to have values between 0.5-4 dB in natural rainfall. As seen from Eqs. (3-5) and (3-6), for accurate rainfall parameter estimation has to be measured with a standard error of less than around 0.2 dB. This accuracy is possible, since a high degree of correlation exists between and Zy if rapidly switching H and V polarizations on a pulse-to-pulse basis are employed by the radar. For this research, Z ^ was measured using polarization agile radars (CP-2 and CHILL) transmitting alternate highly-correlated H and V polarized pulses. A single channel receiver was used for co-polar reception, thereby minimizing effects due to differential drift which might occur with different receivers. The major source of error in Z ^ is due to the nature of the narrow band noise signal associated with randomly moving hydrometeors in the scattering volume and their subsequent locations in space over time. For optimum estimation, three estimators of Z ^ have been defined (Bringi and Seliga, 1980). These are 1 - Square-Law Estimator - - m n - Jl ^ ( 2 - 1 5 ) m i=i ^ where A ^ y^, i = l,m for a pairwise set of independent samples. 2 - Log-Ratio Estimator 26 3. Ratio Estimator . . m Aj,. 2 ** ■ - Jx (2-17) The results of Doviak and Zrnic (1984) indicate that, although both the square-law and the log-ratio estimators are unbiased, the square-law estimator results in slightly lower standard errors. example, for a cross-correlation of p = 0.97 between For and Zy, Z ^ can be measured with standard errors in the range 0.1-0.2 dB at a single gate using 40-60 pairs of independent correlated samples. Their results are in agreement with those of Bringi and Seliga which are shown in Fig. 2.5 for different p and m. A square-law estimator is used by the CHILL radar while the CP-2 radar employs a log-ratio estimator which produces a slightly greater error. When the sampling rates used by these radars in the experiments described in Chapters 4 and 5 are combined with additional spatial averaging, statistical variations in Z ^ (and Zjj) are predicted to be of little consequence to the results. Another possibly important source of error for Z ^ absolute (and relative) calibration of (Z^, Zy). in Zpp is minimized by calibrating Z ^ is the The relative error in misty rain or by pointing the radar along the zenith (resulting in Zp^ ;0). CP-2 Z^^ calibrations additionally used solar measurements. Sources of error for Zy include statistical errors similar to those described above for Zp£, errors due to quantization and uncertainties in the radar constant. A description of these error sources were outlined by Al-Khatib et al. (1979). Specific estimates of these errors for the 27 Standard D e v i a t i o n , dB Square Law 20 40 Cross Correlation =0 .0.90 ,0.92 ,0.94 0 .9 6 0.98 100 80 60 Number of Sam ples, m Figure 2.5. Standard deviation (dB) of the square law estimator as a function of sample size m and cross-correlation coefficient p (Bringi and Seliga, 1980). 28 , Zpfl) measurements during the OSPE and MAYPOLE field experiments are given in Chapter A. 2.2 Experimental Facilities 2.2.1 Radars The field experiments outlined in Chapters A and 5 employed the S-band (CHILL and CP-2) and C-band (CP-A) radar systems. In this section, the operation of these radars is briefly described. Complete specifications of these radar systems are given in the Appendix. 2.2.1.1 CHILL Radar (OSPE) The 10.9 cm CHILL radar, operated by the Illinois State Water Survey (ISWS), was employed during the Ohio State Precipitation Experiment (OSPE) in 1982. It operated in a fast polarization switching mode on a pulse-to-pulse basis as required to reduce the standard error in DK estimation. The polarization transmission and reception control on the CHILL system were made possible through electronic control of a high-power switchable waveguide circulator (Seliga and Mueller, 1982). This circulator had four ports with energy propagating in either a clockwise (CW) or counterclockwise (CCW) direction depending on the switching state of the circulator. Circulator switching time was less than 5 ys and resulted in loss of data for targets within 750 m of the radar which was not important for this study. 29 2.2.1.2 CP-2 and CP-A Radars (MAYPOLE »83. *84) The CP-2 and CP-4 radar systems with wavelengths of 10.7 cm and 5.A5 cm, respectively, were operated by the National Center for Atmospheric Research (NCAR) during the 1983 and 198A MAY POLarization Experiments (MAYPOLE). The CP-2 radar, similar to the CHILL, employed a high power, pulse-to-pulse switching between linear, orthogonal, horizontal and vertical polarizations. The switch- as vith the CHILL radar, was provided by the Ohio State research group for implementa tion by NCAR or the CP-2 radar. 2.2.1.3 Antenna Performance One of the major factors for both the CHILL and CP-2 radars is the influence of the antenna illumination function characteristics on Zpjj measurements. Herzegh and Carbone (198A) examined these for CP-2 and reported that, although a very good symmetry for the illumination patterns at orthogonal polarizations was obtained in the main lobes, the top and bottom sidelobes are stronger in horizontal with respect to vertical polarization and left and right sidelobes are stronger at vertical with respect to horizontal polarization, respectively. Their simulations of this mismatch of illumination patterns resulted in a positive bias for in regions of vertical reflectivity gradients and a negative bias in regions of horizontal gradients. These effects are also present with the CHILL radar, since the antenna and feeds are of identical design (Johnson, 198A). exercised in using Consequently, care must be measurements in regions of strong reflectivity gradients with these radars. Fortunately, this problem does not appear to be important in the case studies considered in this study. 30 2.2.2 Ground-Based Facilities 2.2.2.1 Disdrometer The disdrometer which was used in the simulations and experimental studies was an electromechanical instrument developed by Joss and Waldvogel (1967). It sorts drops into 20 size ranges, the smallest range being 0.3 < D(mm) < 0.4 and the largest being D(mm) > 2 5; its sampling cross-section area is 50 cm . N(D) averaged over 30 s is derived by, N ( 2- is ) ' ^ AD± > « V = A......... At v^(D'i) where N(D^) : the size distribution of the i'th range : number of drops counted during the time interval At in the i'th range At : averaging interval (30 s) v t^i^ : term*na^ velocity of the drops in the i'th range : size interval of the i'th range. The discrete relationships for R, M and D q estimation from these are given by Seliga et al. (1986), and additional information on the operational characteristics were reported by Joss and Waldvogel (1970) and Waldvogel (1974). The estimated fractional deviations (FSD) for disdrometer-derived values of (H, Zjj, are outlined in Table 3.1. 31 2.2.2.2 Portable Automated Mesonet. (PAM) The PAM system was operated by NCAR to provide surface mesoscale data during MAYPOLE '83 and '84. data with an accuracy of of meteorological data. It provided rainfall accumulation ±0.25 mm and 19 other surface measurements The data were also available in real time using the GOES satellite that linked the remote stations to a base station in Boulder, Colorado, which collected and archived the data and generated graphic displays for system control and scientific analysis. A detailed description of the PAM system is given by Brock et al. (1986). CHAPTER 3 DISDROMETER BASED RAINFALL SIMULATIONS In order to use differential reflectivity ( Z ^ ) as an additional radar parameter to obtain improved estimates of the rainfall parameters, rainfall rate (R), liquid water content (M) and median volume diameter (Dq ), relationships between the radar observables (Z„, Z-r,) and these parameters are required. n UK These relationships were derived by Seliga, Aydin and Direskeneli (1986) from numerical simula tions linking rainfall drop size distributions (DSD) to the rainfall parameters and'radar observables. This chapter reviews these findings in detail, since they establish the expected lower bounds on errors of the radar estimates presented in Chapter 4 for three case studies which compare radar estimates of R with ground-based raingage and disdrometer measurements. 3.1 Disdrometer Measurements The DSD's used by Seliga et al. (1986) were obtained during an intense rainfall event that occurred on 6 October 1982 in Central Illinois during the Ohio State Precipitation Experiment (OSPE). plots of R, M and D q for this event are shown in Fig. 3.1. continuous plots at 30-s Time The time intervals represent 2 min running averages of the disdrometer data. This averaging was used to obtain a large enough number of drops per DSD sample to reduce the variance in 32 0 M (gm '3 ) -1 o' 0 o -2 0 0 Content, 0 Wat er Rai nf a l l Rat e, R ( m m h " 1) 0 -3 O -1 I0 0 20 40 60 80 Tim e Figure 3.1(a). I00 I20 I40 I60 I80 (min) Time records of R and M during the 6 October 1982 rainfall event in central Illinois. Solid lines are actual disdrometer measurements representing 2 min running average of 30 s recordings. Crosses are the simulated radar estimates of R and M computed for Eq. (3-5) using disdrometer-derived (Zr , Zr r ). Zero time indicates values averaged over 1513:30-1515:30. R is the rainfall rate, M water content, Zr reflectivity factor and Zr r differential reflectivity. u> u> Do (mm) Median Volume Diameter, 3.5 3.0 2.5 2.0 0.5 20 40 60 80 100 120 140 160 180 Time (min) Figure 3.1(b). Time record of D q during the 6 October 1982 rainfall event in central Illinois. Solid lines are actual disdrometer measurements representing 2 min running averages of 30 s recordings. Crosses are simulated radar estimates of D q computed from Eq. (3-15) using the disdrometer-derived Z ^ . Dq is the median volume diameter and ZpR differ ential reflectivity. u> ■S' 35 the derived radar and rainfall parameters to acceptable levels. Zero time in these plots corresponds to the measurements averaged over the period 1513:30 to 1515:30. A deviations (FSD) of ^ The estimated fractional standard A a A an(* a Z D R ^ D R at ^ = an(* 1,11,1 h ^ for these DSD sampling conditions were computed, based on the approach of Joss and Waldvogel (1969) and Gertzman and Atlas (1977) and are given in Table 3.1. 3.2 3.2.1 Relationships between Rainfall Parameters and Radar Observables Rainfall Rate and Water Content For two-parameter DSD models such as the truncated exponential or gamma, the Z ^ technique can be employed to estimate R and M from (Zr » Zjjr) measurements, since R/Z^ and M/Z jj are unique functions of Zp^ in these models (Chapter 2). When the variation of the DSD parameters such as the order of the gamma model (m) or the maximum drop size C®max) are insignificant. To determine the applicability of the aforementioned ratio relationships with Z^^ under natural rainfall conditions, Seliga et al. (1986) used simulations derived from the wide ranging, highly variable Illinois rainfall event to examine and determine the empirical dependence of R/Z^ and M / o n Z^. These results are plotted in Figs. 3.2 and 3.3 for R/Zg and M/Z jj, respectively. Corresponding plots versus D q , instead of Z^^, are given in Figs. 3.4 and 3.5. The strong correlations between the variables on these graphs suggest power law relationships of the form: 36 Table 3.1. Estimated fractional standard deviations (FSD) of rainfall rate (R), horizontal reflectivity factor (Zjj) and differential reflectivity (Zd r ) in thunderstorms at R = 1, 10 and 100 mm h“l. Here Zjj is in mm^m--* and Zd r = Zji/Zy where ZV is the vertical reflectivity factor. Rainfall Rate (mm h“l) FSD 8 r /r % r /Zd r 1 10 100 0.15 0.09 0.06 0.50 0.24 0.12 0.06 0.06 0.06 R ( m m h 'V Z M t m n r ^ m 3 ) 1-2 i-« I0'1 Figure 3.2. Scatter plot of R/Zjj versus ZpR for the data set shown in Fig. 3.1(a). The fitted curve corresponds to Eq. (3-5). R is the rainfall rate, Zp reflectivity factor and Zp^ differential reflec tivity. Figure 3.3. Scatter plot of M/ZH versus ZpR for the data set shown in Fig. 3.1(a). The fitted curve corresponds to Eq. (3-6). M is the water content, Zfl reflectivity factor and Zpjj differential reflectivity. io-; ICT 10 '6 *E E I0': N Z N 1i 0 E o» 10-’ 10° 10* 10-’ Median Volume Diameter, C\,(mm) Figure 3.4. Scatter plot of R/Zg versus Do- The fitted curve corresponds to the 2-section relationship given in Table 3.3. R is the rainfall rate, Z|i reflectivity factor and Do median volume diameter. Median Volume Diameter, (}, (mm) Figure 3.5. Scatter plot of M/Zh versus D q The fitted curve corresponds to the 2-section relationship given in Table 3.3. M is the water con tent, Zfl reflectivity factor and D q median volume diameter. 0 39 R/ZH - aR (ZD R )bR (>1) M/ZH ’ R/Z„ - m/ zh (>2) cR (D0 )dR (3-3) = <« (Do)dM (3' 4) where the corresponding units are R(mm h 6 -3 Z^(mm m ) and ZpR (dB). “1 ”3 ), M(g in ). Tables 3.2 and 3.3 summarize the results of regression analyses based on the standard method of linearizing the relationships with logarithms to the base 10 (Yevjevich, 1972). The tables give the estimated value of the coefficients (a^, bR , c^, b^, CR* CM* anc* ^ e i r confidence limits for two cases, one for the entire range of parameters and the other for two regions separated by high and low values of ZpR and D q as indicated in the tables. The latter two-section piecewise linear approach is preferred since it better accounts for the variations between the parameters than the relationship derived over the entire range. The resultant relationships were assumed to apply for even higher values of Z^R and D q than those indicated, since the regression analysis results (not shown), obtained from the original 30-s disdrometer data with maximum (Zq ^, D q ) values of (2.9 dB, 3.2 mm), produced nearly the same empirical relationships. An interesting observation is that the dependence of the ratios on D q exhibits more scatter than their corresponding Z^R dependence. This shows that Zq R that Zq R , when used with Z„, is a better estimator of R than even an a -priori knowledge of V Table 3.2. (R/ZR )- and (M/Zh )-Zd r relationships derived from regression analyses. The estimated con stants for these power law relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for "log (R/Zr ) and log ZpR ] and [log (M/Zr) and log ZDR] are also listed. R is the rainfall rate, M water content, ZR reflectivity factor and ZpR differential reflectivity. R/ZH aRZDR l A A /\ SR aRl A P PS D a t a Range (dB) " bR2 0.2 < ZDR < 2.6 1.51 • 10-3 1.49 10-3 1.52 • 10-3 -1.55 -1.52 -1.57 -0.99 0.2 < ZDR < 0 . 7 1.95 • 10-3 1.84 • 10-3 2.07 • 10-3 -1.04 -0.94 -1.14 -0.95 0.7 < ZpR < 2.6 1.59 • 10-3 1.57 • 10-3 1.61 • 10-3 -1.67 -1.64 -1.70 -0.99 bM2 P • aR2 bR bM M/ZH = aMZDR A aM A aMl aM2 A A bM bMl 0.2 < ZgR < 2.6 7.38 • 10“ 5 7.26 • 10-5 7.49 • 10-5 -1.92 -1.88 -1.95 -0.99 0.2 < Zq R < 0.7 1.04 • 10~4 9.43 • 10-5 1.14 • lO-4 -1.29 -1.13 -1.44 -0.92 0.7 < Z^R < 2.6 7.81 • IQ”5 7.64 • IQ-5 7.98 • 10“5 -2.04 -2.00 -2.09 -0.98 o Table 3.3. (R/Zjj)- and (M/Zjj)-Dq relationships derived from regression analyses. The estimated constants for these power law relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for [log (R/Zfl) and log Do! and [log (M/Zh ) and log Do] are also listed. R is the rainfall rate, M water content, Do median volume diameter and ZR reflectivity factor. dR r /z h ■ c rd o A /A A dR dRl dR2 P -2.29 -2.23 -2.34 -0.98 4.85 • 10~3 -2.20 -2.00 -2.40 -0.91 5.86 • 10"3 -2.45 -2.36 -2.53 -0.96 A /V A CR CRl CR2 0.7 < DQ < 3.0 4.80 • 10“3 4.62 • 10~3 5.00 • 10-3 0.7 < D0 < 2.1 4.54 • 10-3 4.26 • 10~3 2.1 < DQ < 3.0 5.47 • 10"3 5.11 • 10"3 Date Range (mm) m /z h - cm d o A /\ A A CM CM1 CM2 dM dMl dM2 P 0.7 < D q < 3.0 3.16 • 10"* 3.02 • 10"4 3.29 • 10"4 -2.86 -2.80 -2.92 -0.98 0.7 < D0 < 2.4 3.01 • 10“4 2.80 • 10-4 3.24 • 10“4 -2.82 -2.59 -3.04 -0.93 2.4 < D q < 3.0 3.54 • 10~4 3.29 • 10“4 3.80 • 10~4 -3.00 -2.90 -3.09 -0.97 42 To illustrate use of the empirical relationships, the estimated R and M values in the Illinois rainfall event from the two-section (Zjj, ZpR ) relationships. R = 1.95 x lO^ZjjZjjn"1,04^ h"1), 0.2 < ZDR < 0.7 R - 1.59 x 10"3 ZHZD R -1*67(mm h'1), 0.7 < ZDR < 2.6 M = 1.04 x 10"4 ZjjZpn"1 *29(g m~3), 0.2 < ^ M * 7.81 x 10_5 ZHZ])R"2,0A(g m'3), 0.7 < ZDR < 2.6 are superimposed on the time plots of Figure 3.1. (3-5) < 0.7 (3-6) For reference purposes, these relationships may be compared with those derived by Ulbrich and Atlas (1984), given by R/Zjj = 1.93 x 10“3ZDR“1,5(mmh ^ / a n A a " 3) (3-7) M/Zjj = 1.28 x 10‘4ZDR"1,94(gm"3/mm6m"3 ) (3-8) for the exponential model DSD, and R/Zh = 1.70 x 10"3ZDR"1,5(mmh_1/mm6m"3) (3-9) M/Zjj = 9.90 x 10_5ZDR‘1,94(gm ‘3/mm6m'3) (3-10) for the gamma model DSD where Z^R is in dB. 3.2.2 Median Volume Diameter One of the hypotheses of the Z^R method is that Z^R = ZjjR (Dq ) ar*d is relatively independent of the other DSD parameters such as Dmay and 43 m. To test this hypothesis, Seliga et al. (1986) examined Z ^ ( d B ) versus DQ(mm) as shown in Fig. 3.6 on both linear and logarithmic scales. The high correlation between Z q R and D q is evident; therefore, by using linear and power law relationships, D q may be estimated from Z^R and vice versa as originally proposed by Seliga and Bringi (1976). Regression analyses, applied to the Illinois DSD data set, were performed to determine coefficients for both the linear and logarithmic relationships, giving (3-11) ZDR(dB) " aLD0 (nm) + bL ZDR(dB) = ap (D0(mm))bP (3-12) DQ(mm) - cLZQR (dB) + dL (3-13) D 0(mm) = cp(ZDR(dB))dP (3-14) where subscripts L and P indicate linear and power law relationships, respectively. In Eqs. (3-11) and (3-12), D q is the independent parameter, and in Eqs. (3-13) and (3-14), Zq R is used as such. The results of these regression analyses are summarized in Table 3.4. Different relationships for employing Z^R and D q as the independent parameters are used rather than obtaining one and deriving the other, since in linear regression analysis the coefficients which are obtained using mean square estimation are different from the corresponding reciprocal coefficients. D q values, estimated from Z^R using the form of Eq. (3-14) in Table 3.4, D q = 1.68 Zdr° ’6A Cn®») (3-15) 2.5 - i. 2.0 © © E 10° o Q © E ,2 3 c g T3 Median Volume D iam eter,D 0 (mm) 3.0 © 2 0.5 10-' (a) Figure 3.6. 0.5 1.0 2.0 2.5 (b) Scatter plots of D q versus on (a) logarithmic and (b) linear scales obtained from the data set shown in Fig. 3.1. The fitted curve corresponds to Eq. (3-15). D q is the median volume diameter and Zq r differential reflectivity. 30 Table 3.4. ZpR(dB)-Do(nnn) relationships derived from regression analyses. The estimated constants for these relationships and the corresponding 95% confidence limits are given. Correlation coefficients (p) for the linear (Zpg and Do) and power law (log Z^r and log Do) relation ships are also listed. Results were obtained from data in the ranges 0.2 < Zj)p < 2.6 and 0.7 < Dq < 3.0. Zjjg is the differential reflectivity and D q median volume diameter. Regression Parameters ZDR * aLD0 + bL ZDR * A A aL aLl /\ aL2 0.902 0.934 D0 ■ C',ZDRdP A A bL bLl bL2 0.966 -0.511 0.444 -0.577 P 0.96 A A A A aP 3P1 aP2 bp bPl bp2 P 0.505 0.469 1.43 1.38 1.48 0.95 0.487 /V CL D0 = CLZDR + dL A 0.983 A A CL1 CL2 0.949 1.02 A A CP CP1 /s CP2 1.68 1.66 1.69 A A A dL dLl dL2 P 0.617 0.715 0.96 0.666 A A dP dPl dP2 P 0.613 0.659 0.95 0.636 •p* in 46 are superimposed in the time plot of D q in Fig. 3.1(b) to illustrate the performance of the relationship. Other relationships of the same form were derived by Seliga et al. (1983), Z ^ = 0.54 D0 1,39 (dB) (3-16) and by Ulbrich and Atlas (1984), ZDR = 0.76 D q 1,55 (dB) (3-17) Zq R « 0.58 D0 1,55 (dB) (3-18) for the exponential and gamma model DSD's, respectively, and where D q is in mm. 3.3 Error Computations In order to quantify the comparisons between radar estimates of rainfall parameters and ground-based measurements, a number of error measures are available. These include Sample Bias (SB), Normalized Bias (NB), Normalized Standard Error of Difference (NSED), Average Difference (AD) and Average Absolute Difference (AAD). These are defined as follows: Sample Mean X - I f X (3-19) ” i=l Sample Bias A /\ SB = *R - *D (.3-20) 47 Normalized Bias NB * B/Xp (3-21) A X^ - radar-derived parameters A Xp - disdrometer-derived parameters Normalized Standard Error of Difference N N S E D - - - [ “ I (Xr - X - B)2]1/2 Xp N i=l i i (3-22) Average Difference ad ■ - jx Average Absolute Difference N (3-24) AAD i' J 1. X NB and AD are closely related while NSED is considered a more useful measure of the scatter of the estimators than AAD, since the effects of the bias are removed with NSED while AAD incorporates the bias in the measurements as an overall error figure. Thus, AAD does not significantly differ from AD for large bias values. Ulbrich and Atlas (1984), Goddard and Cherry (1984a), Seliga et al. (1986) and Ulbrich (1986) used various combinations of these measures in their simulations and radar-ground-based rainfall comparisons. This work emphasizes use of NB and NSED for the error analyses, since they are relative measures commonly used in statistics. 48 3.3.1 Simulated Comparisons of Rainfall Parameters The rainfall rates obtained by the method using the disdrometer-derived radar observables (Zg» ^q ^) are compared with the actual rates in Fig. 3.7. The scatter is very low throughout the entire range of R indicating a very good theoretical applicability of the two-section empirically-derived relationship of Eq. (3-5). Liquid water content estimates for the same rainfall event employing the empirical relationship of Eq. (3-6) are shown in Fig. 3.8, also demonstrating a very good agreement with the actual disdrometer values. Fig. 3.9 shows the comparison of the disdrometer-derived median volume diameter estimates with the actual measurements. that The figure indicates is a good estimator of D q and can be used to determine this important DSD parameter. 3.3.2 Choice of Relationships Since a number of relationships for estimating rainfall parameters from (Z„, Z ^ ) measurements are available, it is important to establish the most appropriate ones for use in the case studies presented in Chapter 4. The intercomparisons given by Seliga et al. (1986) provide an excellent criteria for this choice: first, by comparing the errors produced by various relationships in simulations using the Illinois rainfall data of 6 October 1982, and second, by observing the performance of the same relationships when applied to two independent rainfall events in Boulder, Colorado, on June 8 and 13, 1983. Tables 3.5, 3.6 and 3.7 present these findings for the 6 October 1982 event and include results for seven rainfall relation- 10° o> IO« 10-* R tmrnh'1) Figure 3.7. Scatter plot of Re derived from the empirical relationship given in Eq. (3-6) versus disdrometer-derived where R is the rainfall rate. Figure 3.8. Scatter plot of Me derived from the empirical relationship given in Eq. (3-6) versus disdrometerderived where M is the water content. VO 50 4 3 ( UUUJ) ®°Q m• 2 4m. 0 D0 (mm) Figure 3.9. Scatter plot of DQe derived from the empirical rela tionship given in Eq. (3-15) versus disdrometerderived where D q is the median volume diagemeter. 51 ships, six water content relationships and six median volume diameter relationships, respectively. The R relationships include the one- and two-sectional empirical relationships of Seliga et al. (1986), the exponential and gamma model relationships of Ulbrich and Atlas (1984) and three Z-R relationships. The latter includes: the Marshall-Palmer (1948) relationship which is commonly used for characteristic stratiform rain Z - 200 Rjjp6 (mm6m ‘3) (3-25) the.Joss and Waldvogel (1970) widespread rain relationship Z - 300 Rjy1 '5 (mm6m -3) (3-26) and the empirical relationship derived from the Illinois data set Z = 388 Rzr1,36 (mm6m -3) (3-27) The results for R in Table 3.5 are given for three ranges of R: R <. 5, 5 < R <. 50 and R > 50 mm h These show that, overall, the two-section empirical relationships yield the best results. That is, they produce the smallest NB and NSED of NB = 1.3%, -1.3% and 2.9% and NSED = 7.6%, 5.7% and 4.2% within the ranges outlined above. Examination of Table 3.6 shows that the two-section empirical relationships for M are the preferred choice yielding NB = 1.5%, 0.1% and 2.9% and NSED - 12.6%, 11.8% and 8.0% within the same ranges. In addition to the empirical relationships, these comparisons include the exponential and gamma relationships of Eqs. (3-8) and (3-10) and Table 3.5 Rainfall rate errors for the heavy rainfall event of October 6, 1982 in central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24 ). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2 and Eqs. (3-5, 7, 9, 25, 26, 27) are used in obtaining rainfall rates from the simulated radar measurements. The disdrometer-derived rainfall rates are treated as reference values. R(nn/h) < 3 5 < R(mm/h) < 50 R - 2.12 mn/h NSED(Z) AD(Z) 50 < R(mm/h) < 220 R - 19.5 un/h AAD(Z) NB(Z) HSED(Z) AD(Z) R - 102.6 mm/h AAO(Z) NB(Z) NSED(Z) AD(Z) AAO(Z) Rainfall Race Estimation Method NB(Z) Two section empirical (Zjj, Zpp) (Eq. 3-5) 1.3 7.6 0.6 6.1 -1.3 5.7 -1.1 4.9 2.9 4.2 2.1 3.5 Caoma model (Eq. 3-9) 11.8 11.4 12.1 14.6 13.6 13.5 11.7 12.3 23.9 12.5 23.0 23.0 Marshall-Palmer (Eq. 3-25) 38.6 49-.0 48.7 55.4 2.1 16.1 1.5 17.5 -24.9 23.3 -20.5 20.7 5.6 44.5 9.3 37.9 4.3 21.6 1.3 20.4 -0.9 16.3 3.0 11.5 One section empirical (Zjj, ZDR) (Table 3.2) -0.2 8.7 0.2 7.7 -1.3 5.6 -2.4 4.7 6.3 5.4 5.5 6.0 Exponential model (Eq. 3-7) 27.1 17.8 27.5 28.4 29.2 23.5 27.0 27.0 60.9 19.7 . 39.8 39.8 Joss-Waldvogel (Eq. 3-26) 14.6 44.1 21.4 40.3 -7.8 16.3 -6.9 20.2 -23.2 22.0 -19.3 19.5 Empirical Z-R (Eq. 3-27) Ln NJ Table 3.6 Water content errors for the heavy rainfall event of October 6, 1982 in central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24 ). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2 and Eqs. (3-6, 8, 10, 28, 29) are used in obtaining water contents from the simulated radar measurements. The disdrometer-derived water contents are treated as reference values. M(g/m3) < 0.1 M • 0.066 g/m3 Water Content Estimation Method Two section empirical (Zg, (Eq. 3-6) zd r ) Gamma model (Eq. 3-10) Douglas (Eq. 3-29) DapIrleal Z-M (Eq. 3-28) One section empirical (Zjj, ZDR) (Table 3.2) Exponential model (Eq. 3-8) 0.1 < M(g/m3) < 1 1 < M(g/m3) < 9 fi " 0.37 g/m3 M " 2.88 g/m3 NB(Z) NSED(Z) AD(Z) AAD(Z) NB(Z) NSED(Z) AD(Z) 1.5 12.6 0.9 11.0 0.1 11.8 0.4 36.9 21.2 37.5 40.3 30.1 23.0 122.6 84.9 124.7 124.7 22.0 28.7 57.3 27.8 54.0 1.6 13.4 2.0 76.8 31.9 77.6 AAD(Z) NB(Z) NSED(Z) AD(Z) 8.6 2.9 8.0 0.9 5.0 31.0 31.5 39.8 30.8 36.8 36.8 36.6 34.2 42.3 -9.6 27.2 -0.6 14.8 -6.0 35.4 -3.2 36.6 4.1 18.6 8.7 14.1 12.0 -2.8 10.5 -2.3 8.8 6.1 9.8 3.6 6.3 78.4 68.1 44.9 69.2 69.2 80.5 56.8 76.6 76.6 AAD(Z) Ui 54 the empirical Z-M relationship derived from the Illinois data set Z - 2.83 x 10A M zm1,47 (3-28) plus Douglas1 (1964) equation Z - 2.4 x 10A Mp1 ’82 (3-29) The D q comparisons in Table 3.7 show little difference between the NB and NSED of any of the empirical relationships, each of which has a comparable NB and a significantly lower NSED than the expo nential DSD model (Eq. 3-17) and the gamma DSD model (Eq. 3-18). The results of the above comparisons support the use of Eqs. (3-5), (3-6) and (3-15) for the case studies in Chapter 4. To test these assumptions, the two independent disdrometer-measured rainfall events in Colorado of June 8 and 13, 1984, provided a convenient test. The R, M and D q simulations for these cases produced the error mea sures given in Tables 3.8, 3.9 and 3.10, respectively. showed that the choice of the two-section R and M are the best These conclusively empirical relationships for choices and that either of the empirical Zq R -Dq relationships outlined in Table 3.4 is preferred over the exponential and gamma model relationships. Thus, the following set of relation ships were chosen to perform the case studies presented in Chapter 4: R = 1.95 x 10-3 ZjjZq ^ 1,04 (mm h'1) , 0 . 2 < Z D R <0.7 R * 1.59 x 10-3 ZRZDR"1,67 (mm h"1) , 0 . 7 < Z D R <2.6 (3-30) Table 3.7 Median volume diameter errors for the heavy rainfall event of October 6, 1982 In central Illinois in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24). Differential reflec tivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.4 and Eqs. (3-17, 18) are used in obtaining median volume diameters from the simulated radar measurements. The disdrometer derived median volume diameters are treated as reference values. Median Volume Diameter Estimation Method D0(mm) < 1.5 1.5 < Dp/on) < 2.5 2.5 < I>0(a») < 3.0 Dq - 1.18 in D0 - 2.05 am DQ - 2.67 am NB(Z) NSED(Z) AD(Z) NB(Z) NSED(Z) AD(Z) Bnplrlcal (Table 3.4, Eq. 3-11) 4.6 13.1 4.8 9.3 -2.4 8.5 -2.5 Baplrlcal (Table 3.4, Eq. 3-12) 2.1 15.6 2.1 11.9 -0.8 8.2 Empirical (Table 3.4, Eq. 3-13) 9.9 12.1 10.2 10.6 -2.4 Daplrlcal (Table 3.4, Eq. 3-14) 6.3 14.8 6.3 10.8 Gamma model(Eq. 3-18) -10.3 12.7 -10.2 Exponential model (Eq. 3-17) -24.9 10.9 -24.8 AAD(Z) AAD(Z) AAD(Z) HB(Z) NSED(Z) AD(Z) 7.3 2.1 4.0 2.1 3.4 -0.8 6.5 1.5 3.4 1.5 2.9 7.8 -2.3 6.7 -0.1 3.7 -0.2 2.8 -1.3 7.4 -1.2 6.0 -1.5 3.0 -1.5 2.8 15.0 -16.1 6.8 -16.0 16.3 -16.0 2.7 -16.0 16.0 25.7 -29.7 6.8 -29.7 29.7 -29.6 2.5 -29.6 29.6 Ln Table 3.8. Rainfall rate errors for two independent rainfall events that occurred on June 8 and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24). Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2, and Eqs. (3-5, 7, 9, 25-27) are used in obtaining rainfall rates from the simulated radar measurements. The disdrometer derived rainfall rates are treated as reference values. June 8 Event June 13 Event R = 1.17 mm/h-^ R = 2.42 mm/h-l Rainfall Rate Estimation Method NB(%) Two section empirical (Z^, Zp^) (Eq. 3-5) -0.1 11.8 -5.7 8.1 -3.5 8.5 -2.2 6.3 Gamma model (Eq. 3-9) 12.4 16.0 25.6 28.3 4.8 7.8 5.9 7.5 Marshall-Palmer (Eq. 3-25) -2.2 28.1 19.6 27.4 43.5 22.5 65.7 66.2 1.9 12.4 16.3 22.5 -7.5 8.9 -6.5 7.4 27.8 33.0 42.9 43.8 19.2 13.9 20.4 20.4 -21.9 40.2 -11.8 20.9 19.9 21.2 35.6 39.6 One section empirical (Zjj, Zp^) (Table 3.2) Exponential model (Eq. 3-7) Joss-Waldvogel (Eq. 3-26) NSED(%) AD(%) AAD(%) NB(%) NSED(%) AD(%) AAD(%) Ln ON Table 3.9. Water content errors for two independent rainfall events that occurred on June 8 and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 - 3-24) . Reflectivity factor and differential reflectivity data are simulated from disdrometer measurements of raindrop size distributions, and the relationships given in Table 3.2 and Eqs. (3-6, 8, 10, 29) are used in obtaining water contents from the simulated radar measurements. The disdrometer-derived water contents are treated as reference values. June 13 Event June 8 Event _3 M = 0.106 gm J Water Content Estimation Method NB(%) Two section empirical (Z^, Zpj^) (Eq. 3-6) -1.3 Gamma model (Eq. 3-10) Douglas (Eq. 3-29) One section empirical (Zjj,Zj)^) (Table 3.2) Exponential model (Eq. 3-8) M = 0.064 gm-3 AD(%) AAD(%) NB(%) 17.9 -10.5 14.1 -3.3 12.8 -1.3 9.3 40.8 43.3 57.3 59.5 23.6 18.3 25.9 26.2 20.5 27.5 42.9 46.4 100.1 38.4 140.2 140.2 3.4 17.9 14.4 24.0 -7.7 13.0 -6.0 9.3 81.8 85.6 103.1 103.8 59.6 37.7 62.6 62.6 NSED(%) NSED(%) AD(%) AAD(%) Table 3.10. Median volume diameter errors for two independent rainfall events that occurred on June 8 and 13, 1983 near Boulder, Colorado, in terms of NB, NSED, AD and AAD (see Eqs. 3-19 3-24). Reflectivity factor and differential reflectivity data are simulated from dis drometer measurements of raindrop size distributions and the relationships given in Table 3.4 and Eqs. (3-17 - 3-18) are used in obtaining median volume diameters from the simulated radar measurements. The disdrometer-derived median volume diameters are treated as reference values. Median Volume Diameter Estimation Method June 8 Event June 13 Event 72 mm 5o = 1 - DQ = 1. 01 mm NB(%) NSED(%) AD(%) AAD(%) NB(%) NSED(%) AD(%) AAD(%) (Table 3.4, Eq. 3-11) -1.1 8.4 -0.5 7.1 3.1 11.7 4.7 9.4 Empirical (Table 3.4, Eq. 3-12) 0.9 8.5 1.5 7.2 -6.5 14.5 -7.4 14.3 Empirical (Table 3.4, Eq. 3-13) 0.3 8.3 1.1 7.0 10.8 11.7 13.2 14.0 Empirical (Table 3.4, Eq. 3-14) 1.8 8.3 2.5 7.2 -0.9 13.9 -1.2 11.3 Gamma model(Eq. 3-17) -13.6 8.2 -13.1 13.7 -16.5 12.1 -16.9 19.5 Exponential model(Eq. 3-18) -27.6 8.4 -27.2 27.2 -30.1 11.6 -30.4 31.2 Empirical Ui 00 59 M = 1.04 x 10-A ZHZDR"1,29 (8 m "3 ) » °-2 ^ ZDR ^ °-7 N = 7.81 x 10"5 Zh Zd r "2 *04 <8 m ”3) . 0.7 < ZDR < 2.6 (3-31) D q = 1.68 Zdr°*6A (ram) (3-32) 6 *3 where the corresponding units are ZR(mm m ), Z^R (dB) and DQ(mm). CHAPTER A DIFFERENTIAL REFLECTIVITY RADAR MEASUREMENTS OF RAINFALL The preceding chapter showed that comparisons of rainfall parameters obtained from disdrometer measurements with the same parameters estimated by the disdrometer-derived radar observables (Zjj, Zpjj) gave encouraging results for the applicability of the differ ential reflectivity radar rainfall estimation technique. This chapter presents the results of case studies from three different field programs to test the aforementioned simulated results. The first occurred in central Illinois on 29 October 1982 during the Ohio State Precipitation Experiments (OSPE), and the two others in Boulder, Colorado during the MAYPOLE '83 and '84 field programs on 4 June 1983 and 15 June 1984. The studies consisted of comparisons between ground-based measurements and radar estimates of rainfall parameters. A brief description of these case studies follows: (1) OSPE: Comparisons of the rainfall parameters R, M, and D q , estimated from the radar observables (Z^ ^DR were made with in-situ measurements using a disdrometer located at a site 47.1 km away from the radar. (2) This study is given in Section 4.1. MAYPOLE *83: Similar disdrometer comparisons site that was only 6.35 km away from the radar. are made for a This case differed from the Illinois case in that the width of the radar beam was 60 61 considerably smaller and the rainfall event was of short duration and transient in nature. (3) the MAYPOLE *84: The results are given in Section A.2. Comparisons of rainfall rates estimated using method are made with measurements from two ground-based rain gauges located at distances of 28.6 km and 35.2 km from the radar. These data were from the same storm and differed from the other case studies in that they are for heavier rainfall rates than the other two cases. Each of the studies required special techniques to account for sampling differences between the radar and the ground truth measurements. Temporal to spatial transformations as well as schemes accounting for effects of advection and drop size sorting are included in the analyses. A .1 OSPE Case Study This experiment took place on 29 October 1982 during the Ohio State Precipitation Experiments (OSPE). The rainfall event of 6 October 1982 consisted of only disdrometer measurements whereas on 29 October both the CHILL radar and the disdrometer were operational. Descriptions of the CHILL radar and the disdrometer are given in Chapter 2. The radar was located in Central Illinois at the airport of the University of Illinois near Champaign-Urbana, and the disdrommeter was located at the Clinton site (227 m MSL) at a distance of A7.1 km away from the radar and an azimuth angle of 285.6° from relative to the radar. One degree E- and H-plane half power beam widths of the radar antenna corresponded to an approximately 820 north m beam diameter at the disdrometer site. During this rainfall event, CHILL radar operations began from 2220 PM CST on 28 October and continued for nearly 8 h until 0630 on the 29th. A tipping-bucket rain gauge verified the total rainfall amount at the disdrometer site. The disdrometer recorded several rainfall events throughout this period, and, since the radar was calibrated at 0135 CST, the period 0018-0054 was chosen for analysis. radar errors affecting the results. This reduced the probability of During this period, the radar operated in the plan-position indicator (PPI) mode performing narrow sector scans between the azimuth angles 280.7°-290.5° at a fixed elevation angle of 0.9° with an angular velocity of l°s The large number of sector scans over the 36 min time period of interest provided an excellent radar data base from which comparisons with disdrometer measurements could be made. The CHILL radar was operating in a pulse-to-pulse fast switching mode between the alternating H and V polarizations every 1 ys, and the data were recorded after power averaging of 32 pulses at each polarization. The drop size distributions (DSD's) producing the rainfall parameters were recorded by the disdrometer every 30 s. For this analysis, the disdrometer data were averaged over 5 recording periods which extended the sampling periods to 2.5 min; this procedure produced 2.5 min running average samples every 30 s. It was used to reduce the standard error in the rainfall parameters and also made the averaging period of the disdrometer records more compatible with the vertical extent of the radar beam. This is seen by considering the fall speed of the event's mean median volume diameter, D q , of 1.7 mm. 63 These raindrops would traverse the radar beamwidth in around 1A0 s which matches closely the 150 s disdrometer averaging period. Thus, a single radar sample at the range of the disdrometer is compatible with a 2.5 min average ground-based observation. The fractional standard deviation (FSD) of rainfall rate under these circumstances is about 0.13 for R ■ 1 mm h * 1969). and 0.10 for R ■ 5 mm h * (Joss and Waldvogel, The radar scanned the sector in approximately 10 s, so every 3 consecutive radar scans were averaged and compared with the 30 s (2.5 min averaged) disdrometer recordings. The fall time of the raindrops introduced a delay .time which caused the disdrometer data to lag the radar measurements. This delay tiri** was defined to be the difference between the time of the second scan in each radar triad and the mid-point of the 2.5 min averaging period of the disdrometer data. In order to determine the corresponding spatial location of the radar data for comparison, the speed and the direction of the storm had to be accounted for by using the PPI scans of the reflectivity factor contours. A track of the 30 and 35 dBZ contours of at a 0.9° elevation angle during the rainfall event is shown in Fig. 5.1. This indicates that the storm was moving in the NE direction at about A5 ° from the north with a speed of around 30 ms In addition to the bulk motion of the storm, frictional effects in the atmospheric boundary layer can cause the wind direction and speed to change with height in the lower atmosphere, deviating counter-clockwise with a decreasing speed as height decreases. The comparisons depend on the accurate prediction of the location of those raindrops aloft which eventually were recorded by the ground-based instruments. A 64 0.0*o 3* I3 DISDROM ETER 00:20:26 CHILL R A D A R Okm 00:12:32 Figure 4.1. The relative locations of the CHILL radar and the disdrometer for the 29 October 1982 rainfall event in central Illinois. contours of a rain cell obtained from three different PPI scans are also shown which were used to estimate storm speed and direction. The times indicate beginning of the scans. Zjj is the reflectivity factor. 65 cross-correlation scheme of comparing the radar-observed and the disdrometer-derived is used to determine the location of the appropriate radar volume for the comparisons; details of this procedure are outlined in Section 4.1.1. The radar data were organized into an equivalent surface network of cells forming parallelograms as shown in Fig. 4.2. The axes, defined by the numbers 1 through 7 in each row, are in the radial direction from the radar with the first range gate in each cell noted. The axes, represented by the letters A-D in each column, are aligned in the direction of the storm track with the corresponding azimuth angles shown along the track. Spatial averaging within each cell site corresponds to 3 radar rays and 6 range gates, forming cell sizes of around 1 km (3 rays spanning 1.28° at 47.1 km range) by 900 m (6 gates of 150 m length per gate). This choice of spatial averaging created non-overlapping radar cells having comparable dimensions along both axes. The ray averaging was accomplished by averaging each ray with its two adjacent rays. The azimuth angle represents the middle ray, and the numbers in the cells designate the first of six range gates averaged within that cell. The disdrometer was located at site A4. This averaging pro duced standard errors of (Zg» 2 ^ ) within each cell of (0.5 dB, 0.1 dB). During the 36 min of this rainfall event, 179 radar scans were analyzed. 4.1.1 Cell Selection Since the columns of the radar cell network (numbered 1-7) are aligned with the estimated storm track (45° from the north) and IKm Ra n g e 340 344 3 48 35 2 35 6 330 334 33 8 342 320 32 4 326 3 32 3 36 300 30 4 308 32 2 3 26 290 29 4 298 - 284.4 284 288 285.6 2 8 3.2 - 282. 0 30 2 306 .280, 292, 296 - 2 80.8 Figure 4.2. The spatial cell network used in the cross-correlation analysis of the radar versus disdrometer data for the central Illinois rainfall event (see Section 4.1). Columns 1-7 are along the storm track, whereas rows (A-E) are along the radar rays at the indicated azimuth angles. The numbers in each cell correspond to the first of the six range gates to be averaged. Disdrometer is located at the center of cell A4. On O' 67 assuming that the effects of wind shear and advection were negligible, column 4 would be the expected path through which the raindrops would fall from the observed radar volume onto the disdrometer. However, if wind shear and advection are important, then an analysis based on these claims might possibly result in comparisons between unrelated drop size distributions (DSD's). Also, choice of the section of the column that contributed to the ground data depends on the averaging time of the disdrometer and the estimate of the average storm speed over the path of descent. Sampling time governs the section length, while storm speed governs the location of the section. Complete information on the vertical and horizontal wind profiles was not available, although ground observations, consistent with frictional effects, showed the surface wind speed to be considerably less than the 30 ms * estimated speed of the storm scan obtained from radar at a height of 740 m. Each of the parallelogram cells shown in Fig. 4.2, representing the corresponding radar observation cells, was considered for the cell selection. The procedure requires examination of the cross-correlation coefficients (p^^* ^z d r ^ between the radar-averaged and the disdrometer-derived (Zjj, Z ^ ) time series for all the sites at different time delays. (Pz h > ^ZDR^ were chosen for this purpose since (Z„, ZnD) are the independent radar parameters of interest. n UK Also, if the correlation procedure for choosing the radar cells is correct, then Pz d r ) should both exhibit maxima in the same cells. Thus, a test of the methodology results from cross-correlating both , Zj^) as opposed to selecting either one of these or another single parameter such as rainfall rate. Considering the different 68 delay times between the radar and the ground measurements was necessary, since the fall time of raindrops from the radar beam height of 740 m can cause a significant delay between the radar and disdrometer observations. The problem may be further complicated by the terminal velocity dependence on drop size and vertical winds (updrafts and downdrafts). To implement the process, the maximum (Pz h * ^ZDR^ were determined for each cell. The lag times at which these maxima occurred were taken to represent the optimum time delay between the radar and disdrometer observations. for all cells in Fig. 4.2. Fig. 4.3(a ) shows the maximum values of In calculating p ^ , the time delays were limited in range from 0.5 min to 3.5 min by physical considerations. The disdrometer-measured DSD's were not expected to contribute to radar observations outside the time window due to computations based on beam height, beamwidth and raindrop fall speeds. For example, a spatially uniform distribution of raindrops in the radar volume would contribute to a measured DSD only between the times represented by the minimum fall time of the largest raindrops from the lower section of the beam and the maximum fall time of the smallest raindrops from the upper section of the beam. As expected, optimum time delays increased for the radar cells located farther away from the disdrometer. Also, for each row peaks along a single column (4), supporting the storm track analysis which showed the general storm direction to be toward the Northeast at 45°. Column 4 p ^ values were high and ranged between 0.94 to 0.95. Fig. 4.3(b) shows the corresponding cross correlation values of P™™, for all the cells. £DK The delay times for the 69 0.9 x N 0.8 0.7 Range (a) 0.9 ZDR D/ /E, 0.8 0.7 (b) Figure 4.3. Range Cross-correlation coefficients for (a) Zjj and (b) Z^ r time series data obtained from radar and disdrometer measure ments shown for optimum delay times for radar measurements. Zji is the reflectivity factor and ZpR differential reflectivity. 70 peak values of and P2DR fro*“ each other in only two out of 35 cells, thereby confirming the procedure of radar cell selection for comparisons with the disdrometer measurements. Note that PgpR exhibits less uniformity in range than Pgg* hut its peak values (0.84-0.86) again concentrate along column 4. Columm 4 cells, although having different optimum delay times of 0.5, 1.0, 1.5, 2.0 and 3.0 min for the sites A4, B4, C4, D4 and E4, respectively, have all comparable (P^h * maximized both the Pa*rs t^ie cell and p ^ ^ ; its delay time matching the result of the swath analysis presented later in this section. The difference in p_„and p_n_ in the ranges 1-7 are significantly higher than the ZH ZUK differences along the storm tracks A-D, indicating greater variability normal to the storm track than along the storm track. The optimum time delay (highest correlation) at site D4 is 2 min. This is consistent with an estimate based on the fall speed of drops of 1.7 mm diameter which was assumed while determining the averaging period of the disdrometer giving an average lag time of 126 s, consistent with the time lag of the D4 site. The cross-correlation analysis was also extended to p^, p^ and p^Q with the rainfall parameters (R, M, D q ) estimated using the 2-region relationships of Tables 3.2 and 3.3. Maximum p^, p^ and tively. p^ q were 0.90, 0.87 and 0.83 for site D4, respec Figs. 4.4(a)(b)(c) and 4.5(a)(b) show comparison scatter plots for the radar and the disdrometer-derived parameters for site D4 (see also Section 4.1.3 and Tables 4.1 and 4.2). 0.21 0.18 R e (mmh 3 - 0.15 fI O 0.12 E 2 - O' ixi 0.09 ♦♦ **♦ * + ♦+ ♦ + ♦♦ ♦ 0.06 I 0.03 * ±±. 0.03 R d (mmh ) (b) 0.06 0.09 0.12 _L 0.15 _L 0.18 M0 (gm‘ 3) Figure 4.4. Cell D4 scatter plots of (a) Rg derived from the radar (Zh , Z^r ) using Eq. (3-5) versus disdrometer-derived Rj) and (b) Mg derived from the radar (Zh , Zjjr) using Eq. (3-6) versus disdrometer-derived MD . R is the rainfall rate, M water content, Zh reflectivity factor and ZpR differential reflectivity. 0.21 72 2.8 2.4 ++ ^ ++ D0e (mm) 2.0 0.8 0.4 0 .4 0.8 2.0 2.4 2.8 DoD (mm) Figure 4.4(c). Cell D4 scatter plot of D q e derived from the radar Zd r using Eq. (3-15) versus disdrometer-derived D q d where D q is the median volume diameter. RADAR Z H (dBZ) 40 35 .6 30 .4 ♦ + + 25 V* v ♦ : ♦* *«* XJ O' Q N CC 20 .2 < Q < 0.8 VC I5 ♦♦ 10 0.6 5 5 (a) 10 20 25 30 DISDROMETER Z H (dBZ) 15 35 40 0.4. 0.4 0>) 0.6 0.8 1.0 1.2 1.4 1.6 DISDROMETER Z DR (dB) Figure 4.5. Cell D4 scatter plots of radar measured (a) and (b) Zjjr versus their corresponding values derived from disdrometer measurements. Zjj is the reflectivity factor and ZpR is the differential reflectivity. 74 4.1.2 Swath Selection In order to improve on the results using cell D4, consideration must be given to the path length of the radar sample along the storm track which contributes to the disdrometer measurements. That is, the spatial extent of the storm track that contributed to the ground measurements must be matched to the averaging time of the disdrometer (150 s). Each of the cells cover 1.2° in azimuth angle and about 1.1 km along the storm track; ranges to the disdrometer change from 47.1 km for the cell A4 to 49.5 km for the cell E4. The exact horizontal speed of the raindrops along their descent is not known, and, instead of initially estimating their transit time from the radar volume to the ground from the storm speed of 30 ms * and other assumed wind behavior, swaths of different extents were analyzed using the same cross-correlation procedure. All the possible contiguous swath combinations extending over a various number of sites were analyzed to find the maximum cross-correlation coefficients between the (Zjj, time series of the radar volumes and the corresponding disdrometer values. The best match occurred for sites (B4, C4, D4, E4) with an optimum delay time of 2 min which was identical to the delay time of the single cell D4 and consistent with the earlier single cell correlation results. The cross-correlation values for this swath are 0.95, 0.89, 0.94, 0.92 and 0.88 for P ^ , PZDR» P^» Pj^ and P^q , respectively. It is of interest to test the physical consistency of this result. A disdrometer sampling time of 150 s and a constant horizontal wind speed of 30 m s * would imply a swath length of around 75 A.5 km. 4.2). Swath (B4, C4, D4, E4) is approximately 4.4 km wide (Fig. Assuming the radar swath represents a sample from a steady state storm being advected across the earth's surface, the 4.4 km length is then consistent with the sampling time transformed to a spatial scale of 30 m s * x 150 s * 4.5 km. The correlation results may also be examined in terms of raindrop trajectories to determine what portion of each disdrometer size category emanates from the radar swath. This is done by considering the delay time between radar and disdrometer sampling, the duration of the disdrometer sample, the storm velocity and the terminal velocity of each drop size. Assume the storm moves at the wind speed u which varies with height z according to u(z) = u q [1 - exp(-z/6)] (m s 1) (4-1) where uQ(ms *) is the horizontal wind velocity above the boundary layer and 6(m) is depth of the boundary layer where u(z) = 0.632 [e.g., see Stern (1968)]. uq If the terminal velocity of the drop does not change very much with z, the height of the raindrops originating at z = z o z = after time t would be (z q - vt t) (m ) (4-2) These approximations lead directly to an estimate of the horizontal distance traveled by the raindrops during their fall to the ground. x (t ) = u(z)dt (m) (4-3) 76 x(t) = t-j + exp(-ZQ/6)-l] where r = z /v„ is the fall time. o t Fig. 4.6 for (4-4) The results for x(x) are plotted in parameters most likely representative of the experimental conditions: u o = 30 m s * zq * 330, 740, 1150 m (lower, mid and upper beam heights) v “ 3, 4, . . . , 9 m s * (corresponding to drop diameters of 0.75-5 mm) 6 = 100, 200, 300, 400 m The choice of the boundary layer depths model data given in Stern for night time conditions. Also shown in the figure are the horizontal extent of the swath and selected disdrometer drop size categories superimposed on the terminal velocity axis. The plots indicate the expected approximate horizontal distance of origin of the raindrops within the radar swath that arrived at the disdrometer site without any sampling period considerations. greatly with 6. The results do not vary In this experiment, the drop sizes of greatest interest center around D q « 1.7 mm and have velocities between around 4-7 m s * . Fig. 4.6 s hows that the disdrometer sampled raindrops in this range come from all parts of the radar beam's vertical extent over most of the 4.4 km wide swath. Also, note that the swath contains over 50% of the disdrometer samples for raindrops of all sizes represented by v in the range 3-9 m s * . 77 8(m) h ■ 740m h ■ 330m 100 10 200 9 300 a 400 7 100 6 £ 200 X \ 5 300 + E4 400 4 + 04 \ 3 100 + C4 2 200 300 400 + B4 0 0 2 3 4 5 6 7 8 9 V t ( m s * 1) i_________ l_____________ i_________ i_______i---- 1 0.75 1.50 2.25 3.15 4.75 0.35 0,(m m ) Figure 4.6. Horizontal distance X traveled by raindrops of different sizes during their fall to the ground versus terminal velocity v t of the raindrops. Results are shown for different boundary layer depths 6 and for raindrops originating from upper, mid and lower beam heights h. The horizontal extent of the radar swath and the disdrometer drop diameter corresponding to the Vt axis are also superimposed. 78 Fig. 4.7 shows the time of impact on the disdrometer of drops originating from within the radar beam. The duration of the disdrometer time sample relative to the equivalent radar sampling period (vertical transit time through the radar beam) is indicated for the lower, mid and upper beam heights. As expected, the time delay increases for smaller drops due to smaller fall velocities. From Fig. 4.6 and 4.7, the disdrometer sample duration and the radar swath length are shown to be highly comparable for 6 % 200-300 m. The percentage of disdrometer sample observed by radar is above 55% for all drop sizes, and greater than 74% for drops between 1.0-2.5 mm in equivalent diameter. The results of the analysis of drop trajectories relative to the disdrometer sampling times and radar sample swath and the comparative results indicate that choices of the swath length and the disdrometer sample period are compatible. In addition, they corroborate the correlation analysis used originally to determine the swath size and its location. The time series plots of the swath/disdrometer R, M and D q values are shown in Fig. 4.8 while Fig. 4.9 gives the corresponding radar Scatter plots of the radar and disdrometer values for these are given in Figs. 4.10 through 4.13. In these figures, the radar observations were shifted 2 min in time to account for the fall time of the disdrometer-sampled raindrops. Gaps in the time records resulted from periods where the radar performed wider sector scans than normal. The corresponding time plots follow the I20(s) DISDROMETER TIME SAMPLE PERCENTAGE of DISDROMETER SAMPLE OBSERVED BY RADAR — — 5 5.3% I50(s) 4.75 - 9 3.1 5 - D .lm m ) 2.25 i/> h=330m (LB) h=740m (BC> h= I I50m (VB) 8 66 .0 % 7 78.0% 6 9 1.3% 5 86 .0 % 4 74.7% 1.50 - 0.75 - 3 200 100 RADAR SAMPLING TIME Figure 4.7. 300 56.7% T IM E (s) Time of impact on the disdrometer of the raindrops originating from lower, mid and upper beam heights, h plotted for raindrops with different terminal velocities, and disdrometer drop diameters. The direction of the dis drometer time sample with respect to radar sampling time and the percentage of disdrometer sample observed by radar for different v t are also shown. 0.08 0.04 2.5 R(mmh I 0.5 0 4 8 I2 I6 20 24 28 32 36 TI ME( mi n ) Figure 4.8(a). Time records of R and M during the 29 October 1982 rainfall event in central Illinois. The solid lines represent 2.5 min running averages of 30 s disdrometer samples with zero time corresponding to values averaged over 0018-0020:30. The points indicate radar estimates derived from (Zjj, Zp^) using Eqs. (3-5) and (3-6) delayed by 2 min. R is the rainfall rate, M water content, Zjj reflectivity factor and ZpR differential reflectivity. oo ° 2.4 2.0 E E ■ s ■\ y o O 0.8 0 4 8 12 16 20 24 28 32 36 TIME(min) Figure 4.8(b). Time record of D q d u r i n g the 29 October 1982 rainfall event in central Illinois. The solid lines represent 2.5 min running averages of 30-s disdrometer samples with the zero time corresponding to values averaged over the time interval 0018—0020:30. The points indicate radar estimates derived from (Zg, Zdr) using Eq. (3-15) delayed by 2 min. Do is the median volume diameter, Zjj reflectivity factor and Z^r differential reflectivity. (mm) 2.4 2.0 o Q 0.8 0 4 8 12 16 20 24 28 32 TIME(min) Figure 4.9. Time records of Zjj and Zjjr for the rainfall event shown in Fig. 4.8. The points are obtained from the radar measurements and the solid lines are the disdrometer-derived values. Zjj is the reflectivity factor and Zjjjj differential reflectivity. 36 0 0.5 (a) Figure 4.10. I 1.5 2 R o l m m h * 1) 2.5 3 3.5 0 (b) 0.5 1.0 1.5 2.0 2.5 3.0 Rolmmh'1 ) Swath scatter plots of (a) Rg derived from the empirical relationship of Eq. (3-5) and (b) Rg derived from the gamma model relationship of Eq. (3-9) using radar (Zh , Z^r ) versus Rj) obtained from the disdrometer [see next page for (c) and (d)]. R is the rainfall rate, Zh reflectivity factor and Zj)R differential reflectivity. 3.5 4.0 3.5 ---- r—r t 1---------- 1--------- r t r 3.5 * -i 3.0 - 2.5 - 25 -C (mmh i 20 n E oc 1.5 m r-1 - " « - If »«« ■ 0.5 - O5 05 (c) ■ 1.5 - 1.0 ><'•1 •* ■ I 15 R0 ( m m h *1 ) 2.5 3.5 O (d ) 0.5 1.0 J_____ I _____ I_____ L 1.5 2.0 2.5 3.0 3.5 4.0 R jjtm m h '1 ) Figure 4.10. Swath scatter plots of (c) RZR derived from the empirical Z-R relationship of Eq. (4-6) and (d) Rm s derived from the Mueller-Slms (1966) relationship of Eq. (4-5) using radar Zr versus Rj) obtained from the disdrometer [see previous page for (a) and (b)]. R is the rainfall rate and ZR reflectivity factor. 00 4S 0.21 0.18 - o.i 5 - (gm*3) ro 0.12 i E UJ ^ - 0 09 O' o 0.09 - 0.06 0.06 - 0.03 0.03 0 (a) Figure 4.11. 0.03 0.06 0.09 M d ( g m ' 3) 0.12 0.15 - 0.06 0.09 0.12 0 .2 I M0 (gm '3 ) Swath scatter plots of (a) Mg derived from the empirical relationship of Eq. (3-6) and (b) Mg derived from the gamma model relationship of Eq. (3-10) using radar (Zg, Zpg) versus Mg obtained from the disdrometer. M is the water content, Zg reflectivity factor and Zd r differential reflectivity. 00 Ui 2.4 2.4 2.0 2.0 Dqg (mm) K K E E XX X Lxi o ***** X * * 0.8 0.8 (a) Figure 4.12. 1.2 Q ** 1.6 D oD (mm) 2.0 2.4 0.8 0.8 a) 1.2 I .6 2.0 2.4 D oD (mm) Swath scatter plots of (a) DoG derived from the gamma model relationship of Eq. (3-18) and (b) D q £ derived from the empirical relationship of Eq. (3-15) using radar versus D0j) obtained from the disdrometer. D q is the median volume diameter and Zjjr is the differential reflectivity. 00 O' 35 m RADAR Z u (dBZ) 30 GO *o 25 tr 1.0 o N cr 20 < 0.8 Q < or 0.6 I5 I0 (a) 20 25 30 DISDROMETER Z H (dBZ) Figure 4.13. 35 0.4 0.4 (b) 0.6 0.8 1.0 1.2 1.4 DISDROMETER Z DR (dB) Swath scatter plots of radar measured (a) Zjj and (b) Zp^ versus their corresponding values derived from the disdrometer measurements. Zjj is the reflectivity factor and ZDr is the differential reflectivity. 00 -vj 88 same peaks and valleys and are also comparable in their values as seen in the scatter plots. The rainfall rate scatter plots are given in Fig. A.10. In addition to showing results for the (Zg, Z^g) 2-region empirical relationship (Eq. 3-5) and gamma model Rg Rg relationship (Eq. 3-9), they also include results for the Mueller and Sims (1966) Z-R (R^g) relationships Z derived for Champaign-Urbana (A-5) = 372 I^gA7 (mm6m~3) and an empirical R^g relationship derived from the entire rainfall event of 28-29 October 1982 as „ Z ._c 0 l.A5 , 6 -3 n = A25 R^ (mm m ) (A-6) The liquid water content scatter plots in Fig. A.11 utilized the empirical Mg relationship (Eq. 3-6) and gamma model relationship (Eq. 3-10). Dg scatter plots in Fig. A.12 used the logarithmic relationship (Eq. 3-15) for the empirical gamma model Dgg Mg of Eq. 3-18. Dgg and the The time series and scatter plots show good comparisons between the radar- and disdrometer-derived rainfall parameters. These are discussed in greater detail in the following sections along with a comparative examination of different schemes of estimating selected parameters. A.1.3 Radar-Disdrometer Comparisons From an original 179 radar scans taken at approximately 10 s intervals, 59 (Zg, Z^g) values were obtained for comparison with the 89 disdrometer samples. These data produced the results given in Tables 4.1, 4.2 and 4.3 where the disdrometer values were taken as the ground-truth reference. Tables 4.1 and 4.2 relate to single cell A4, and Table 4.3 is for the swath. The errors were analyzed in terms of NB, NSED, AD and AAD as defined by Eqs. (3-19), (3-20), (3-21) and (3-22). The parameters AD and AAD are given primarily for comparison with previously reported results in the literature. In this discussion emphasis will be on the use of the NB, NSED pair, since NSED is a measure of the scatter of the data with the bias effects removed, and NB is a direct measure of bias. The sample means of 6 *3 and Zy are obtained using linear averaging in units of mm m , and Z ^ from the difference of Z^(dBZ) and Z^(dBZ). The spatial and temporal averaging of the radar data leads to several schemes of interpreting rainfall parameters. These depend on whether Z^ ^ are power-averaged over space and time to final values from which (R, M, D q ) are derived or whether the space and/or time partitioned values of Z„ .. are used to estimate their respective n, v rainfall parameters from which the overall averages are obtained. These procedures are illustrated by considering how, for example, Z^ is derived from spatial and temporal averaging: ^ O m n V 3) > ^ (mm6m~3) (4-7) where (i,j) correspond to time and space indices, respectively, representing the N sample scans occurring in each 30 s period and the M cells making up the swath. As noted previously, for this experiment 90 N ranged between 2-A, and M = A (cells BA, CA, DA and EA). Eq. (A-7) may be expanded into its parts; this results in ZH " M *N E ^iil + N E ^ 1 2 + ’ ' • + N ^MiA^ i=l i=l i-1 ZH “ M *N ^ 1 1 (4“8) + ^ 2 1 + • • * ^ N l ^ + N [ZM12 + ^f22 + * ’ ' + ^1N2^ + • * * + N t^MlA + ZM2A + * * * ^IN A ^ (A—9) For. each Z^ term in the above expressions there is a corresponding Zy and Z ^ . Similarly, each (Z^, Zj^) pair may be used to estimate (R, M, D q ). Thus, there are at least three possible averaging schemes to estimate these parameters. For example, R may be found from either of the following: »E = W ZDR> (4 - 10) M h n m S j , RJ 3 M (4-u ) N where the R. and R. , values are derived from their corresponding (Z„, J ij n Zp^) values as illustrated in Eqs. A-8 and A-9. Note that when dealing with a single cell such as DA, the above reduces to two alternative schemes, 91 ^ " W and *» - 1 X ri ( 4 - In order to determine i 3 ) which procedure is mostappropriate for this experiment, comparisons between the disdrometer measurements of rainfall rate R^ and Rg, Rg^ and which are given in Table 4.3. were performed, the results of Rg clearly gave the least errors as measured by NB, NSED, AD and AAD and therefore is chosen as the preferred radar parameter throughout the rest of this case study. A comparison between R^ and Rg and Rg^ for cell D4 (Table 4.2) yielded similar results with Rg being the preferred radar estimate. Since R is considered the most important parameter of interest, all other radar-derived rainfall parameters were obtained using the same scheme as for Rg, that is M = MCZg, Zjjg) (4-14) D q - D0 (ZnR) (4-15) Similarly, all other radar estimated rainfallparameters, such as those computed from Z-R and Z-M relationship and gamma model (Zg, Z^g) relationships for (R,M,Dq ), are derived using the same averaging technique. The cross-correlation procedure which was used to match the radar volume to ground based measurements can also be tested using the results of Table 4.1. When the NB and NSED from column 4 are compared Table 4.1. Radar-disdrometer comparisons of rainfall rates for the 29 October 1982 event. The error rates NB (Eq. 3-21), NSED (Eq. 3-22), AD (Eq. 3-23) and AAD (Eq. 3-24) are given for selected cells shown in Fig. 4.2. The disdrometer is located at the center of cell A4. Rainfall rate, R (mm h ^), R = 1.03 mm h ^ Duration = 35 min Range 3 4 5 Azimuth NB % NSED % AD % AAD % NB % NSED % AD % AAD % NB % NSED % AD % A 28.3 44.6 34.3 50.0 17.7 31.7 14.6 27.7 16.9 49.6 9.1 32.8 B 13.4 30.5 12.9 28.8 13.9 35.2 10.0 29.5 13.0 52.4 4.4 35.6 C 21.7 35.0 16.7 30.5 13.8 34.0 6.6 31.9 7.1 45.9 1.6 36.4 D 19.4 34.8 13.0 29.2 6.9 35.9 0.1 29.6 7.2 52.0 -0.1 39.4 E 22.2 39.8 15.6 36.8 11.0 39.9 3.6 35.9 -7.8 41.5 -14.5 38.5 AAD % VO N> 93 with values in adjacent columns (3 and 5) at all sites, column 4 is seen to produce the smallest errors with column 3 results being slightly better than those in column 5. Among the single radar sites, D4 gave the overall best result, although all the adjacent sites in column 4 are comparable, demonstrating the earlier conclusions about the storm track, optimum column and site choices. 4.1.3.1 Rainfall Rate Tables 4.2 and 4.3 present the comparisons for cell D4 and the swath consisting of cells (b 4, C4, D4, E4), respectively. In addition to the empirical and Mueller and Sims (1966) Z-R relationships, the tables include results for the Z-R relationships of Joss and Waldvogel (1967) (Eq. 3-26) which is used for widespread rain and the M-P relationship (Eq. 3-25). Also listed are results from the gamma model for interpreting (Zg» ZpR ) radar measurements (Eq. 3-9). Comparing the Rg results of Tables 4.2 and 4.3 shows that the swath averaging of (B4, C4, D4, E4) significantly reduces NSED by around 11.5% when compared to the results obtained for cell D4, although NB is slightly greater by around 2%. The gamma model relationships showed very similar relative behavior. For the Z-R relationships, denoted by RgR , R ^ , R^p and R_j, swath averaging improves NSED by 5-8% while NB increases by 3-5%. These results show that all the R estimates benefit from smaller standard errors when comparable spatial averaging of the radar volumes with the disdrometer time averaging is used. This improvement is more significant in the (Z^, ZpR ) relationships than for the Z-R relationships. As a consequence 94 Table 4.2. Cell D4 radar-disdrometer comparisons of rainfall rate, water content, median volume diameter, reflectivity factor and differential reflectivity for the 29 October 1982 rainfall event. Rg, Rgjj, Rq, Mg, Mq employ radar observed (ZH» ZDR) whereas Rgg, R ^ , Rtfp, Rjy and Mpo use ZH only. D0g and Dqq are estimated from Zdr. Disdrometer values are the reference values for all entries. Cell IM Duration (35 min) Estimation Method Rainfall rate AD % AAD % (Eq. 3-5) 6.9 35.9 -0.2 29.6 ren (Eq. 4-13) 9.1 38.5 1.5 30.8 rg (Eq. 3-9) 15.6 40.4 7.8 31.8 rzr (Eq. 4-6) 26.4 40.5 21.4 31.0 (Eq. 4-5) 37.5 46.2 32.6 39.4 (Eq. 3-25) 93.7 72.5 92.6 92.6 RJW (Eq. 3-26) 56.9 56.6 52.5 56.7 (Eq. 3-6) 14.0 41.1 6.5 32.8 (Eq. 3-10) 46.2 60.1 27.3 51.7 (Eq. 3-29) 165.0 102.8 171.6 171.6 (Eq. 3-15) -3.3 10.0 -3.4 8.6 (Eq. 3-18) -18.0 8.9 -18.1 18.5 -1.6 7.3 -2.6 6.3 8.5 15.9 10.2 15.0 r ms r mp me M = 0.049 gm“^ Mg m do Median volume diameter D q = 1.65 mm NSED % Re R ■ 1.03 mm h-^ Water content NB ^ doe dog Zy = 26.6 dBZ ZH (radar measurement) Z„R - 0.87 88 ZDR (radar measurement) Table 4.3. Swath radar-disdrometer comparisons as in Table 4.2, except the results of for the swath averages of cells (B4, C4, D4, E4) shown in Fig. 5.2. RgM and R g ^ employ (Zg, Zjjr) for rainfall rate estimation with different averaging considerations (see Section 4.1.3). Zg is the reflectivity factor and Zpg differential reflectivity. Swatch Averaging of Cells $4, C4, 04, E4) Duration (35 min) Estimation Method NB ^ NSED Rg 9.1 24.4 6.2 25.6 R e m (e 9* 4-11) 11.5 25.9 8.6 25.9 Re M n (e 9- 4-12) 14.2 28.2 10.5 28.6 Rq (Eq. 3-9) 17.8 28.6 14.0 29.2 RZR (e 9* 4-6) 30.0 35.8 31.3 33.4 RjlS (Eq • 4-5) 41.4 40.9 43.6 44.3 (Eq. 3-25) 99.3 65.0 108.6 108.6 Rjjj (Eq. 3— 26) 61.4 50.3 65.1 65.1 Mg (Eq. 3-6) 15.9 28.5 12.2 29.1 Mq (Eq. 3-10) 48.0 44.4 43.1 50.5 Md0 (Eq. 3-25) 172.9 94.0 192.2 192.0 Median volume diameter D q * 1.65 mm D q e (e 9* 3—15) -2.5 7.4 -2.3 6.4 Doc (Eq. 3-18) -17.3 7.0 -17.2 17.2 ZH “ 26.6 dBZ (radar measurement) 0.6 4.9 0.6 4.2 9.5 13.2 12.1 14.8 Rainfall rate R ■ 1.03 mm h-^ Rm p Water content M - 0.049 gm"3 ZDR - 0.87 dB (Eq. 3-5) (radar measurement) Z AD % AAD % 96 of these swath versus cell comparisons, all the remaining results will focus on the swath findings. The small increases in dB for the swath are not considered as important as the larger improvements in NSED. If the empirical Rg and the gamma model Rg estimates are compared, Rg is better by 8.7% in NB and A.2% in NSED which are similar to the results of the simulations in Chapter 3 which indicated an expected 10.5% reduction in NB and 3.8% in NSED for R < 5 mm h The empirical Rg had an NB of 9.1% and an NSED of 2A.A%. The only comparable experiment employing (Zg, Z^g) was performed by Goddard and Cherry (1984b) which produced a similar bias and a 33% standard deviation, which is about 9% more than NSED obtained here. Their results required them to assume a Zg bias of 1.5 dBZ and a gamma model of m ■ 5. Rg errors can also be compared to Z-R relationships utilizing the same Zg time series. The improvements of the Rg over the empirical Z-R relationship derived for this event (Eq. 5-2) are 20.9% in NB and 11.4% in NSED. These improvements are consistent with the simulation results of Chapter 3 which predicted an improvement of 4.1% in NB and 36.9% in NSED. The improvements of Rg over R computed from the other Z-R relationships are 32.3%, 90.2% and 52.3% in NB and 16.5%, 40.6% and 25.9% in NSED for the R^g (Mueller-Sims), R^p (Marshall-Palmer) and Rj^ (Joss-Waldvogel) rainfall rates, respectively. Again, the simulations in Chapter 3 predicted similar improvements: 37.3% and 13.3% in NB and 41.4% and 36.5% in NSED for Rgp and respectively. Rg errors of 9.1% in NB and 24.4% in NSED differ considerablly from the simulated results of Chapter 3 which are 1.3% and 7.6% in NB and NSED, respectively. The increase in these 97 experimental errors over those predicted from the disdrometer-derived simulations may be due to a number of reasons, including (a) the large difference in the radar and the disdrometer sampling volumes (about 3 x 10 9 m 3 for the radar versus 4.5 o m (b) for the disdrometer); statistical and measurement errors such as bias and calibration in both the radar and disdrometer; (c) errors in determining and accounting for the horizontal and vertical wind motion; (d) other factors such as higher order DSD effects which might require more than two radar parameters to estimate R; and effects of spatial and temporal gradients on the measurements. 4.1.3.2 Liquid Water Content In addition to R, Tables 4.2 and 4.3 give the liquid water content comparisons for cell D4 and the swath (A4, B4, C4, E4). The swath averaging improves NSED by 12.6% and 15.7% for the empirical Mg (Eq. 3-6) and the gamma model Hg (Eq. 3-10), respectively, while NB increases slightly by about 2% for both. This result, as for R, again suggests using the swath results for comparisons. The swath Mg computations resulted in 15.9% and 28.5% in NB and NSED, respectively, while the gamma model Mg resulted in 48.0% and 44.4%. These show improvements of 32.1% in NB and 15.9 in NSED for Mg over Mg which are comparable to the improvements shown in the simulations of Chapter 3. The simulated results are 1.5% and 12.6% 98 for VL and 36.9% and 21.2% for Mg in NB and NSED, respectively, for _3 M < 0.1 g m . The differences, when compared with the simulations, are 14.A% and 15.9% for Mg and 11.1% and 23.2% for Mg. The differences between the simulated and experimental results are most likely due to the same factors outlined in Section 4.1.3.1. The single M-Z relationship used for comparison here is due to Douglas (1964) [the only one reported by Battan (1973)] and resulted in excessive errors of 165.0% in NB and 102.8% for NSED. 4.1.3.3 Median Volume Diameter Comparative results for the median volume diameter D q at cell D4 and the swath are also included in Tables 4.2 and 4.3. The swath shows improvements of only 0.8% and 2.5% for the empirical relation ship (Dqe, Eq. 3-15) and 0.7% and 1.9% for the gamma model (Dq G > Eq. 3-18) in NB and NSED, respectively. Although the improvements are not as great as those for R and M, for consistency the comparisons which follow again use the swath results. The NB and NSED results for the swath are -2.5% and 7.4% for D^g and -17.3% and 7.0% for D q q » respectively, indicating comparable NSED errors while D^g shows an improvement of 14.3% in NB over D ^ . Goddard and Cherry (1984b) reported a bias of -5% and a standard deviation of 15% in their radar-disdrometer comparisons assuming a gamma model of m = 5. Their bias errors are comparable to those of Dgg while their standard error (presumably similar to NSED) is twice as large. The simulated results in Chapter 3 were -1.3% and 7.4% for DQg and -16.1% and 6.8% for Dqq in NB and NSED, respectively, for 99 1.5 mm < D q .£.2.5 mm which holds for nearly all the data of this event. The experimental results for D0E are very comparable to their simulated counterparts which contrasts with the empirical Rg and Mg results which both showed significant differences of around 16% in NSED and slight increases in NB when the simulated and the actual radar-disdrometer resuts are compared. If the relationships derived for Rg, Mg and D^g in Tables 3.2 and 3.3 are representative, R and M are dependent on both (Zg, Zgg), whereas Dq is in principle only related to Z^g. Whether this one-to-one relationship between Z^g and Dq accounts for the very similar experimental and simulation results cannot be directly ascertained, but the results are very encouraging. One possible explanation may be found in the form of the DSD which may be approximated by the gamma model given in Chapter 2. If this form is representative, for a given m, R and M are dependent on both N^ and Dq. Large spatial and temporal variations in Nm within a storm have been reported by Joss and Waldvogel (1970); such variations in the storm would produce large changes in Zg (or R and M) but not necessarily in Z^g (or D q ). Nevertheless, utilizing (Zg, Z^g) resulted in significant improvements for R, M and Dq estimates over single parameter relationships under experimental conditions. 4.1.3.A Reflectivity Factor and Differential Reflectivity Radar measured and disdrometer-derived (Zg, Z^g) are in very good agreement as seen in Tables 4.2 and 4.3. The swath averaging improved NSED by only 2.7% in Z^g and 2.4% in Zg with respect to cell D4 while NB's were comparable. These correspond to (0.64 dBZ, 0.023 dB) 100 reductions in NSED for the mean (Zg, Zpjj) which in turn translate into a decrease (3%, 16%) in NSED for (Rg, Mg) computed using the empirical relationships of Eqs. (3-5) and (3-6). The Zg error improvements were 6 —3 computed using units in mm m (power averaging) while computations for Zjjg were made in dB. These improvements are comparable to the improvements of about 16% found for swath averaged Rg and Mg outlined in Sections 4.1.3.1 and 4.1.3.2. 4.1.4 Remarks The simulations of the (Zg , Zgg) two parameter estimation method for R, M and D q rainfall parameters in Chapter 3 were tested in the 29 October 1982 central Illinois experiment. The radar derived rainfall parameters were compared with disdrometer measurements located 47.1 km away from the radar. The results of 179 radar scans at a constant elevation angle of 0.9° produced very good agreements between radar estimates and disdrometer measurements. The empirical Rg and relationships utilizing both radar parameters showed significant improvements over both gamma model (m « 2) and Z-R or Z-M relation ships. Rg produced errors of 9.1% for the normalized bias (NB) and 24.4% for the normalized standard error of difference (NSED), whereas, the best of the Z-R relationships, empirically derived from the same rainfall event, gave 30.0% for NB and 35.8% for NSED. These results strongly support use of Z^g as an additional estimation parameter in radar rainfall rate and water content measurements. In order to perform the comparisons correctly, a systematic approach to select the appropriate radar volume was undertaken. This analysis included 101 performing a cross-correlation to optimize the matching of the disdrometer temporal averaging with the radar spatial averaging. This approach was confirmed through an examination of raindrop trajectories which demonstrated that the disdrometer samples were derived from the radar swath which maximized the cross-correlation coefficients of the radar-measured and disdrometer-derived (Z„ , Zj^) values. This approach is considered useful for future radar rainfall comparisons with the ground based measurements as well. 4.2 Radar and Disdrometer Comparisons: Experiment 4 June 1983 MAYPOLE The MAY POLarization Experiment in 1983 (MAYPOLE '83) in Boulder, CO provided additional opportunities to test the differential reflectivity method of estimating rainfall parameters using the CP-2 radar. MAYPOLE was a collaborative research program between The Ohio State University, National Center for Atmospheric Research (NCAR) and Colorado State University. Its main objective was to perform experiments with the CP-2 radar in the newly modified multiple polarization mode including S-band reflectivity factor (Z^) and differential reflectivity X-band reflectivity factor linear depolarization ratio (LDR) in addition to S-band Doppler velocity measurements. A description of the CP-2 radar is outlined in Chapter 2 and the Appendix. The disdrometer was in operation throughout this program and supplied a continuous record of rainfall events in the Boulder area. One of the main objectives of MAYPOLE '83 was to evaluate the Z ^ method of estimating rainfall rates and area-wide cumulative rainfall. To realize this, the CP-2 radar made measurements whenever a rainfall event had been detected in the vicinity of the disdrometer. In this section, the 4 June 1983 rainfall event was selected for comparisons between the radar estimated rainfall parameters and the same parameters measured by the ground-based disdrometer. The main characteristic of this event was the short range of the radar to the disdrometer resulting in a smaller radar volume compared with the other events discussed in this study. Thus, the rainfall parameters measured by the disdrometer were trans formed to the corresponding radar altitudes to make meaningful comparisons. Because of the nature of the rainfall event, in addition to transport, this transformation had to account for drop size sorting which occurs as the raindrops descend from the radar height to the disdrometer. 4.2.1 Radar and Disdrometer Measurements The rainfall event occurred between 1948-2008 MDT. The disdrometer was the same one used in the Central Illinois study and was located in the vicinity of the Boulder Atmospheric Observatory (BAO) meteorological tower. The CP-2 radar was 6.35 km away from the disdrometer at an azimuth of 173° from true north. Both the radar and the disdrometer was at 1540 m MSL elevation which alters the empirical , Zj^)-R relationship which was derived previously in Chapter 3. The considerable elevation increases the fall velocities of the raindrops and affects the analysis in two different respects. The disdrometer is an electromechanical instrument estimating the equivalent diameter of the raindrops from their momentum assuming a 103 mean sea level elevation. The increase in raindrops fall speeds results in a different set of equivalent drop sizes due to increased momentum for each drop size. Therefore, a new set of horizontal and vertical backscattering cross-sections and other disdrometer drop size coefficients were used to analyze the disdrometer data. Another effect of the increased terminal velocities is the resultant modification of the empirical relationship which is used to estimate the rainfall rate from (Z„ , The rainfall rate as defined by Eq. (3-5) is dependent on the terminal velocity v of the raindrops, and an adjustment is necessary as these velocities increase. The pressure dependence of v^ (Eoote and du Toit, 1969) and an assumed mean atmospheric pressure of 827 mb for the radar and the disdrometer location gives v t * 1.085 v. to (4-3) where vfc and vfc are the terminal velocities for this experiment and for MSL, respectively. Since R is proportional to vfc and since all drops would increase their terminal velocities by the same percentage, the empirical relationships are simply multiplied by the factor 1.085. For example, the 1-section empirical relationship which was used for this rainfall event [Eq. (3-1), Seliga et al. (1983)] becomes R « 1.79 x 10"3 Zjj Z ^ " 1,52 (mm h"1) (4-4) The rainfall event at the disdrometer site began at 1945 MDT and developed rapidly, reaching 45 dBZ Z^ and an 8 mm h * rainfall rate intensity within 2 minutes. The intensity of the event continued 104 until 1952 MDT after which time the cell moved away from the dis drometer site and began dissipating. The radar performed 28 sector PPI scans between the azimuth angles 342°-10°, covering the volume over the disdrometer location with the elevation angles changing between 1° to 6° in 1° steps with an angular velocity of 2° s * between 1951-2007 MDT. The CP-2 radar was operating with a PRF of 960 in a pulse-to-pulse fast switching mode, and the data were recorded after pulse averaging of 256 pulses in each polarization resulting in 2 records per second. Horizontal and vertical wind profiles were obtained from the BAO tower (300 m in height) measurements and by an examination of the Doppler velocities corresponding to the same radar scans. The event most likely consisted of only rainfall, in that the vertical structure of (Z^, Z_„) indicated that the melting layer was at a height of 1.2 km. In order to compare the ground-based measure ments with the corresponding radar volumes at different elevations, the horizontal wind speed and direction were estimated from the BAO tower measurements and were found to be nearly constant at approxi mately 12 ms *7205° over the tower height of 300 m. For heights above 300 m the winds were taken to be 15 ms Vl80°, same as the highest measurement on the BAO tower. The radar Doppler velocity measurements were in agreement with the tower and also showed very little change in winds with heights above 300 m in the region of interest. The disdrometer measurements indicated that a diameter of 1.5 mm is representative of the event. median volume This implies a terminal velocity of around 6 ms * which, together with the wind speed, was used to determine the approximate radar elevation 105 angle-dependent location of the radar volumes from which the disdrometer-sampled raindrops originated. This analysis indicated that the disdrometer samples originated from radar volumes at eleva tion angles 1°, 2°, 3°, 4°, 5° and 6° which in turn translate into height/range locations of 100 m/6.55 km, 250 m/6.875 km, 400 m/7.20 km, 550 m/7.575 km, 700 m/7.95 km and 850 m/8.325 km, respectively, from the CP-2 radar. The path of the raindrops, the location of the radar volumes to be used for different elevation angles and the radar rays and the range gates which were used for averaging are illustrated in Fig. 4.14. Three successive rays and two range gates were averaged resulting in a 420 m x 400 m horizontal extent of the radar volume at 6° elevation, the linear dimensions of which compared favorably with the transformed range resolution of the 30 s disdrometer samples (12-15 m s ^ x 30 s * 360-450 m). Six radar volume scans produced 33 data samples corresponding to six elevation angles (l°-6°) which were used to compare with the ground-based measurements. The disdrometer time records, showing the variations of the computed radar observables (Z„, Z™), plus R and D q , are shown in Fig. 4.15. Time t = 0 corresponds to 1948:45 MDT. The variation in these plots indicates that the rainfall event was locally transient and may have been a dissipative stage with strong gradients in all the rainfall parameters. Over the period of 20 min shown in these plots, the peak values of 45 dBZ, 2.7 dB, 12 mm h and 3.5 mm for Z„, ^DR’ R and D q decreased to 2 dBZ, 0.3 dB, 0.1 mm h * and 1.0 mm, respec tively. The high rate of change in these rainfall parameters, coupled with a narrow radar beamwidth, necessitated the transformation of the 106 352* 354* 356* 358* 0* I0 km ELEVATION • I* ■ 2* A • 3* 3*,4* • • m 4* 5* 5*.6* • 6* TRAJECTORY RANGE GATE 39 BAO TOWER DISDROMETER 34 CP- S km Figure 4.14. Relative locations of the CP-2 radar and the disdrometer during the 4 June 1983 rainfall event in Boulder, Colo rado. The trajectory of the raindrops, the location of the radar volumes used for different elevation angles and the radar rays and the range gates used for averaging are also shown. o N — «n O — O I ” N o o 16 TIME IMIN.) • TIME IMIN.I o V E J c K TIME IMIN.I 20 TIME (MIN.) Figure 4.15. Time records of the computed radar observables (a) Zh and (b) Zjjr corresponding to the disdrometer measurements for the 4 June 1983 event in Boulder, Colorado. Also shown are (c) R and (d) D q measured by the disdrometer for the same event. ZH is the reflectivity factor, Zdr differential reflectivity, R rainfall rate and Do median volume diameter. 108 ground-based measurements to the radar measurement heights as explained in the next subsection. A.2.2 Transformation of Disdrometer Time Records to Radar Altitudes The half power beamwidth of the CP-2 radar is 0.96°, resulting in a beam diameter of 140 m at the radar volume of interest at 6° elevation angle (range 8.325 km). The vertical beam-crossing time of raindrops of 1.7 mm in diameter would be 23 seconds which is comparable to the disdrometer sampling period. But unlike the previous rainfall study in central Illinois where the descent time of the raindrops was less than the disdrometer averaging period (150 s), in this event raindrops in different size categories having different fall velocities were sampled during different disdrometer periods. For example, 2.5 mm drops, originating from 850 meters in height at 6° elevation angle reach the surface 104 s later, whereas 1.3 mm drops take 160 s to reach the surface. The time difference between these is of the order of two sampling periods. Even for the drops originating at the height corresponding to the 3° elevation angle, the arrival times for these same sizes differ by a full sampling period. The resultant differences in the arrival times of different size drops indicate that the rain drop size distribution, which filled the radar volumes during the successive scans, changed during their descent and were sampled as different DSD's by the disdrometer. This phenomenon, which is generally described as being due to drop size sorting, must be accounted for when the disdrometer records are compared with the radar measurements. This is accomplished hereby transforming the 109 ground-based measurements to their respective radar elevation heights. The steps in this transformation are outlined below: (1) Upper and lower height limits for the radar beam at different elevation angles are computed using the locations of the radar volumes determined in Section 4.2.1 (43-157 m for 1°, 190-310 m for 2°, 337-463 m for 3°, 484-616 m 4°, 630-770 m for 5°, (2) for 777-923 m for 6°). For a particular time of interest T during the rainfall event, the heights in the atmosphere of the raindrops within each size category for all the disdrometer record are computed. The transformation consists of mapping each drop size category, recorded during each 30 s disdrometer sampling period and assumed to occur at the midpoint of this period, into heights determined by the product of the appropriate terminal velocity and time interval between T and the disdrometer sample times. In order to ensure adequate spatial coverage of the disdrometer measurements within the vertical limits of the radar volumes, each drop size category vertical distribution was replicated at T + 15 s. This procedure is illustrated in Fig. 4.16 which indi cates the height of the raindrops in each size category contributing to the radar sampling volumes at the 6 eleva tion angles. (3) The drop size categories within the beamwidth limits of different radar elevation angles are determined from those samples which intersect the vertical extent of the radar no ELEVATION ANGLE 04 io o o r 900 04 RADAR BEAMWIDTH 800 03 HEIGHT(m) 700 03 600 500 D2 400 D2 300 200 100 Vj (ms*1) I____________ I____________________ I_________________ I------- 1 0.34 0.74 1.66 3.08 5.36 De(mm) Figure 4.16. Vertical distributions of raindrops with different terminal velocities and their corresponding disdrometer size cate gories at 15 s intervals to determine the raindrops con tributing to the radar sampling volumes at the six elevation angles. Pairs of drop size distributions averaged to obtain 30 s disdrometer samples and the radar beamwidth at different elevation angles are also indicated. Ill volumes. If two or more disdrometer samples in any size category are contained in the volume, the average of the samples are used to represent that size. (A) In order to obtain the time history of the event correspond ing to the radar volumes at the six elevation angles, the disdrometer records were transformed to height profiles at 30 s intervals according to the procedures outlined in (2) and (3). The resultant DSD1s were then used to compute rainfall and radar parameters R, M, D q , and as functions of time for comparison with the radar measure ments . A.2.3 Disdrometer-Radar Comparisons Disdrometer records of the transformed rainfall parameters are shown in Figs. A.17 through A.22. corresponding to successive elevation angles of 1°-6°(1°). Disdrometer derived (Zjj, Zq r ) as well as (R, D q ) are identified as (a) through (d), respectively, in each figure. Radar measurements are indicated'by the discrete data points. Note that the transformation process accounts for the delay times between radar and disdrometer samples at each of the elevation angles, and that the radar parameters are separated by approximately 2 min and AO s which is the duration of each volume scan. ments (Z^, For radar measure- are the observed parameters where (R^, D q ) are estimated using Eqs. (A-A) and (3-15), respectively. In general, good agreement between the time plots of the disdrometer and the radar parameters are obtained. The radar parameters follow closely the occ •IEWUIflH • I OEC * n w — « £4 SC N to 1 n IB TIME (MINJ TIME IMIN.I- OEC OEC 1 E C K T F ^ TIME IMIN.I io TIME IMIN.I Figure 4.17* Time records of the transformed rainfall parameters (a) Zg, (b) Zjjp, (c) R and (d) Do derived from the disdrometer measurements corresponding to 1° radar elevation angle. Zh is the reflectivity factor, Z^r differential reflectivity, R rainfall rate and D q median volume diameter. 113 K cwmioh • g'otc occ N aa x N a TO re TIME (MIN.) I (C ) Rn(mm/hr) 'LCVAUON • 2 OEC ItlVBTtON * 2 OEC . \ 1 1 TIME Ml IMIN.I TIME IMIN.I Figure 4.18. Time records of the transformed rainfall parameters (a) Zh, (b) ZD R , (c) R and (d) D q derived from the disdrometer measurements corresponding to 2° radar elevation angle. Zh is the reflectivity factor, ZpR differential reflectivity, R rainfall rate and D q median volume diameter. oce o ec N at a x N M 1 12 TIME (MIN.) TIME (MIN.) XEVBTIBW « 3 OEC DEC in* «Qo«q « K cu N O O0 TIME IMIN.I TIME IMIN.I Figure 4.19. Time records of the transformed rainfall parameters (a) Zh , (b) Z d r » (c ) R and (d) D q derived from the disdrometer measurements corresponding to 3° radar elevation angle. Zh is the reflectivity factor, Z^p differential reflectivity, R rainfall rate and D q median volume diameter. ■LEVATIiON • 4 oec OEC c _ e n r* * a Is "" o le N « TIME [MIN.I TIME IM IN.I : le»»tibh . n oec OEC RR(mm/hr) 'LEVAT « Oc o ft 20 TIM E IMIN.I 20 TIME IMIN.I • . Figure 4.2 0. Time records of the transformed rainfall parameters (a) ZH , (b) Zdr, (c) R and (d) Do derived from the disdrometer measurements corresponding to 4° radar elevation angle. ZR is the reflectivity factor, Zj)R differential reflectivity, R rainfall rate and D q median volume diameter. ore ore TIME (MIN.) TIME (MIN.) ELEVBTjOH . j OEC ILEVHTOOH . S OEC H E YU I I OH « S n in « SE e o TIME IMIN.1 Figure 4. 2L TIME IMIN.I • Time records of the transformed rainfall parameters (a) ZH , (b) ZD R , Cc) R and (d) Do derived from the disdrometer measurements corresponding to 5° radar elevation angle. ZH is the reflectivity factor, ZpR differential reflectivity, R rainfall rate and D q median volume diameter. IbJ 1 ELfvflT HON . t OCC d occ n eS d i ( Z Q Q ) **Z m 1 TT /I r • V • • o . V ei Q. w--- TIM E (M IN ) OEC qevBTiBM . » ote ( J i | / u i u i ) Mtj in E E mcz p) TIM E IMIN.I TIME IMI N.I Figure i.22. Time records of the transformed rainfall parameters (a) Zr , (b) Zd r , Cc ) R and (d) D q derived from the disdrometer measurements corresponding to 6° radar elevation angle. Zr is the reflectivity factor, Zd r differential reflectivity, R rainfall rate and Do median volume diameter. 50 40 N 30 rsi rsi 20 0 (a) 10 20 30 Z°(dBZ) 40 50 (b) H R D Figure 4.23. Scatter plots of radar-observed (a) ZR and (b) ZgR versus their corresponding values ZH and z [jR obtained from the results shown in Figs. 4.17-4.23(a) and 4.17-4.23(b), respectively. ZR is the reflectivity factor and Zjjr is the differential reflectivity. 10 £ 45 0£ 0.1 0.1 M-P aoi 0.01 0.01 (a) 0.1 10 R (mm/hr) o.oi (b) o.i i 10 RJmm/hr) Figure 4.24. Scatter plots of radar-derived rainfall rates computed from (a) the empirical (Zg, Z]jR) relationship and (b) Marshall-Palmer relationship versus disdrometer-derived rainfall rates shown in Figs. 4.17-4.23(c). ZH is the reflectivity factor and ZDR differential reflectivity. D 0 (mm) 120 2 D n(mm) T> Figure 4.25. Scatter plot of D q derived from the radar measurements of ZDR versus disdrometer-derived values shown in Figs. 4.174.23td) where D q is the median volume diameter. 121 dissipating trend of the rainfall event as observed with the disdrometer. In Fig. 4.23, radar-observed and disdrometer-derived are compared. Radar estimated R and D q are also compared with their disdrometer derived counterparts in Figs. 4.24 and 4.25. These scatter plots are obtained using the data in the time plots of the same parameters, by matching each radar value to the best fit disdrometer value within one disdrometer sampling period away from the radar sampling time (±30 s). The superscripts R and D refer to disdrometer and radar, respectively. The scatter plots of the radar and disdrometer rainfall parameters indicate a very close agreement between measurements. It is also of interest to compare the (Z^, derived estimates with R obtained from the Marshall-Palmer (1948) relationship of Eq. 3.25. The latter results are shown in Fig. 4.24(b) and, when compared with Fig. 4.24(a), indicate that a much greater bias (overestimate) in R results when using the Marshall-Palmer relation ship. Table 4.4 is a statistical summary of the results. For each radar and disdrometer-derived rainfall parameter, the mean value (X) and the standard deviation cr^, given by, <v24 are computed. ? *2 - *2 <4- 5> i=l The linear, least-squares fit parameters of the corresponding data points are also given in Table 4.4, including the correlation coefficient (p) and the slope (A) and the intercept (B) of the linear regression coefficients. The results show that using 122 Table 4.4. Statistical summary of radar- and disdrometer-derived parameters including mean values (x), standard deviations (s), correlation coefficients (p), and the slope (A) and the intercept (B)* of the linear regression coefficients. The superscripts D and R for Zjj, Zq r and D q and the subscripts D and R for R refer to disdrometer- and radarderived values, respectively, where Zji is the reflec tivity factor, ZpR is the differential reflectivity, R is the rainfall rate and D q is the median volume diameter. Linear Regression Parameters s p A 2? (dBZ) cl 21.77 11.69 21.29 11.38 zjJR (dB) 0.85 0.43 zL “DR 0.79 0.44 1.33 1.61 Rr (Eq. 4-4) 1.35 1.65 R^ 2.10 2.67 4 Rjj (mm h -i ) (Eq. (3-25) D q (mm) 1.56 0.49 D q (Eq. 3-13) 1.32 0.52 0.985 0.959 0.41 0.864 0.885 0.040 0.973 0.996 0.023 0.950 1.577 0.006 0.834 0.874 -0.040 123 , 2-^) results in significantly improved estimates of radar estimated rainfall rates over conventional Z-R methods. A .2.4 Remarks Simultaneous CP-2 radar and disdrometer measurements were compared during the rainfall event of 4 June 1983. The short distance between the radar and the disdrometer resulted in a narrow beamwidth making the effects of different fall velocities of the drops in a radar volume important. The transformation of the disdrometer measurements to radar altitudes was used to account for this drop size sorting. Effects of horizontal wind transport of the raindrops were also approximately accounted for using the known wind speed to estimate the region where the radar measurements were most representa tive of the disdrometer measurements. The comparisons between the radar-estimated and disdrometer-derived rainfall parameters were very good, supporting 4.3 method of rainfall estimation. Radar-Raingage Comparisons: 15 June 1984 MAYPOLE Experiment During MAYPOLE 1984, evaluation and further development of the differential reflectivity technique for precipitation measurements continued. The CP-2 radar made measurements over the Portable Automated Mesonet (PAM) network whenever rainfall occurred over the network which was established to supply ground observations of rain fall rate and other atmospheric parameters for comparison with radar observations. The rainfall event of 15 June 1984 provided an excellent opportunity for such comparisons and was unique in that the 12A rainfall rates were considerably higher peak (R > 120 mm h *) than the other case studies and since raingages, rather than disdrometers, furnished the ground truth. In this study, time changes of rainfall rate over two PAM stations are compared with the radar estimates of the same parameter obtained from the volume scans spanning an approximately 35 min time period. The comparisons are performed by using a spherical to Carte sian interpolation technique to obtain constant-altitude PPI's (CAPPI's) at different heights. Consideration of the wind speed and direction, mean fall velocity of the raindrops,height of the CAPPI's and the appropriate radar volumes to be compared with the raingage sampling period yielded ground-based raingage measurements. The analysis is done for both the two-parameter Z„ -Zd r estimation method and the single parameter Z-R method utilizing two commonly used relationships. A.3.1 Raingage Measurements During this event the PAM stations supplied the wind vector, air temperature, humidity, barometric pressure and other atmospheric parameters in addition to the rainfall rate. The precipitation gages at each site were of the tipping bucket type where the accumulation is measured in increments of 0.25 mm. The resolution of the wind speed is 0.1 m s * and the wind direction is 0.1 . The time diagrams of all the parameters are recorded in 1 min intervals. the PAM stations is given in Chapter 2. More information on 125 The PAM stations selected for analysis in this case study were the two which received the most amount of rainfall (stations 11 and 15). Their locations relative to the radar are shown in Fig. 4.26. PAM 15, at the Brighton site, was co-located with the CP-4 radar where personnel confirmed that the event consisted of heavy rain as opposed to mixed phase hydrometeors or hail. The altitude of both stations were at 1.49 km MSL whereas the CP-2 radar location was at 1.75 km. The gage measurements are given in Section 4.3.3. 4.3.2 Radar Measurements During this event the CP-2 radar operated continuously in a volume scan mode with the measurements broken into two portions. From 1703-1726 the sequence consisted of PPI sectors of 52° between azimuth angles of 42°-94°, an angular velocity of 4° s * and elevation angle increments of 1.1° between the angles 0.5°-8.2°. This observational time period produced 10 volume scans with each volume scan lasting around 1 min 50 s and comprising 8 elevation angles. During the time period 1727-1735, 9 other volume scans were completed when the radar operated between the azimuth angles of 52°-74° with an angular velocity of 2° s * and covering the elevation angles between 0.5°-2.0° in 3 steps. The radar was in the similar pulse-to-pulse fast switching mode as during the MAYPOLE '83 case study with a PRF of 960. Data were recorded after pulse averaging 128 pulses in each polarization during the first 15 volume scans and 256 pulses in each polarization during the last 5 scans. PAM I I S T A T I O N ( 3 5 .2km ,64.6°) P AM I 5 STATION ( 2 8 .6km ,77.4°) C P - 2 RADAR I Okm Figure 4.26. The relative locations of the CP-2 radar and the two PAM stations during the 15 June 1984 rainfall event in Boulder, Colorado. The radar data were obtained in the Universal Format (Barnes, 1980) which was suitable for processing using SPRINT and CEDRIC software (Mohr et al., 1981; Mohr and Miller, 1983). SPRINT is an interactive program that transforms the data values from radar space to 3-dimensional Cartesian coordinates. For each selected Cartesian grid point (x, y, z) with the spherical coordinates (R, 6,<p), four radar beams surrounding its location in space from successive PPI scans are determined. A sequence of bilinear interpolations of the eight surrounding data points from the adjacent constant elevation angle planes leads to an interpolation of the radar data to each of the selected (x, y, z) grid points. CEDRIC enables the user to perform various functional operations on the Cartesian data sets generated by SPRINT. Since radar scattering or reflectivity factor measurements are 6 "3 only linear when in units of mm m rather than in dBZ, the preferred method of interpolation should employ ^ 6 —3 (mm m ) after which Z^R is derived from Z^R = 10 log Z^/Zy as opposed to interpolating Zjj ^(dBZ) and ZpR (dB). Thus, in this study all (Z^, Z^R ) Cartesian data points were obtained using the preferred method, that is, the 6 "3 (Zjj, Z ^ ) spherical data points were transformed to (Z^, Z^) in mm m and interpolated to Cartesian grid points at 200 m intervals in the (x, y) planes located at constant altitudes (z) separated by 300 m, ranging from 2.1 to A.5 km MSL. Fig. A.27 shows CAPPI's obtained from the volume scan between 1705:36-1707:31. the areas where Z^ In Fig. 4.27(a) note 50 dBZ indicating high reflectivities and Z^R > 2 128 ZHldB Z I 20 liiilij'!. 30 • 40 30 E 20 > *.- 20 OJ i CL O 10 0 1 IQC O Z I _ /'•‘v *c1 20 25 35 30 EAST of CP-2 (km) (a) Zqr (dB) K TniniiiiiM ::!:::ioi:iii::::::: slilil> il!!!!l!!!& i1 iiHmiMSh h jiiS?!: L Ift \ nnifTTU J 20 r 25 .......... . . . . T.::: 30 EAST of CP-2 (km) Figure 4.27. Constant altitude (2.4 km MSL) PPI's of (a) Zjj and (b) Z])r generated from the value scan between 1705:36-1707:31 MDT during the 15 June 1984 event. Zr is the reflectivity factor and Zd r differential reflectivity. Rlmmh' ) 20 50 I5 I0 NORTH of CP-2 (km) 10 ::::::::: :::::: V :K :I. I5 20 25 30 35 E A S T of C P - 2 (km) 129 Figure 4.27(c). Constant altitude (2.4 km MSL) PPI of R generated from the volume scan between 1705:36—1707:31 MDT during the 15 June 1984 event where R is the rainfall rate. 130 dB which shows that the event consisted of rainfall containing drops of large diameter. To compute the R field (Fig. 4.27(c)), corresponding to the same area, the 1-section empirical relationship of Table 3.2, modified to account for the decreased atmospheric pressure in Colorado and corresponding increased terminal velocities, was used. Radar- estimated rainfall rates were obtained for all the CAPPI's between 2.1 km-3.0 km in 300 m increments using the CEDRIC software. Based on the vertical profiles of the (Zy, Z^^) fields, heights above 3.0 km most likely contained mixed phase hydrometeors, including hail and graupel particles as opposed to rainfall. Consequently, the average height of the CAPPI rainfall computations is 2.55 km which has a corresponding mean atmospheric pressure of 742 mb. This reduced pressure alters the terminal velocities of raindrops (Foote and du Toit, 1969) by, v t = 1.12 v tQ (4-6) (m s ' 1 ) where v is the velocity of interest and vq is the velocity at MSL. This changes the 1-section empirical relationship of Table 3.2 (used for convenience to accommodate CEDRIC) to (4-7) R « 1.69 x 10"3 Zjj Zj^"1 *55 (mm h"1) This is the relationship used to obtain the rainfall rates shown in Fig. 4.27(c) at the height of 2.4 km. area of R The figure describes a wide 50 mm h 1 surrounding PAM station 15. The series of CAPPI's derived from the volume scans provide a time history of the 131 were obtained for the 19 volume scans, each consisting of A heights which contain Cartesian grid points in 200 m (x, y) increments. A.28 shows (Z-j, Fig. , R) 2.A km CAPPI's for a later volume scan which occurred during the times 1716:A0-1718:31. By comparing the CAPPI's in Figs. A.27 and A.28 storm motion and development can be tracked. For example, the storm area described by the high R values in Fig. 3.27 over PAM 15 moved over the PAM 11 station resulting in the heavy rainfall rates recorded by this gage. Thus the same region of the storm was responsible for the event as recorded by both PAM stations. Fig. A.29 shows a North-South vertical cross-section of the radar observables (Zr * passing through the PAM 15 location during the volume scan between 1705:36-1707:31. This and other RH1 scans indicate that the regions below 3 km consisted primarily of rainfall. This information was used to establish the CAPPI's to be used for radar-rain gage comparisons. As seen in this figure, although the high 55 dBZ Z^ core of this storm extends up to A km in height, low Zp^ ( 0.5 dB) values above 3.5 km indicate that hydrometers other than rainfall, most likely dominated throughout the storm. The estimation of the wind vectors, needed to locate the radar volumes at different elevations for comparison with ground-based measurements, was achieved in two ways. First, the surface wind speed and direction data are obtained from the two PAM stations. Their time records indicate a significant shift in both parameters during the event. The surface wind speed V(m s *) and direction 6(deg) were found to be 132 20 20 CM 5 QO I0 a: 25 30 35 EAST of CP-2 (km) (a) Zq r (dB) ft m \ ,:X®. N' ^ V 20 ({ Cv* *& A ' \ *X*' rA J , , 25 .........r>V; 'ft (£) - 1'? 1 ( 0 * 30 EAST of CP-2 (km) Figure 4.28. Constant altitude (2.4 km MSL) PPI's of (a) Zr and (b) Zjjr generated from the volume scan between 1716:40-1718:31 MDT during the 15 June 1984 event. Zr is the reflectivity factor and Zd r differential reflectivity. 20 V « 50 of CP-2 (km) 10 I5 :S:-' A : 10 NORTH 50 20 25 30 35 E A S T of C P - 2 (km) Figure 4.28(c). 133 Constant altitude (2.4 km MSL) PPI of R(mm h -1) generated from the volume scan between 1716:40-1718:31 MDT during the 15 June event where R is the rainfall rate. 134 Z M (dBZ) ffi 1111 k"'il i1111! 5 7 .5 10 NORTH of CP-2 (Km) (a) 4 .5 i 0.5 3.5 0.25 liiil? : 0 (b) 2 .5 5 7 .5 10 I 2 .5 I5 NORTH of CP-2 (km) Figure 4.29. RHI's of (a) Zjj and (b) Zjjr generated from the volume scan between 1705:36-1707:31 MDT during the 15 June 1984 event which shows a North-South vertical crosssection of (Zjj, Zd r ) passing through the PAM 15 site located 27.8 km east of CP-2. ZH is the reflectivity factor and Zd r differential reflectivity. 135 V * 5.7 m s"1 ; 0 - 202° for t < 1728 MDT V = 3.3 m s'1 ; 0 - 101° for t >_ 1728 } MDT J V * 9.4 m s ^ ; 0 = 173° for t <. 1713 MDT V - 5.5 m s"1 ; 0 - for t > 1713 MdT for PAM 11 and 86° after averaging once the Indicated time periods. } J for PAM 15 The results were also compared with the wind vectors obtained from the movement of the storm cell as seen in the time history of the CAPPI's at different heights. For PAM 11, the storm speed and direction were estimated to be 5.8-6.1 m s * at 197°. This result compares very favorably with early portion of the average surface estimation for PAM 11. Applying the same approach to PAM 15 produced a wind speed of 9.6-10.1 m s * at 190°-200° which again matched very closely the radar-derived storm motion estimates and provided evidence to support use of the PAM wind measurements in the analysis. The comparisons between the time records of the radar and rain gage data involved estimating the delay times of the raindrops, corresponding to CAPPI's at different heights. The method of averaging the PAM rainfall rate data also affects the choice of the volume from which the radar data comes. Representative values of for each CAPPI height in the vicinity of the PAM stations led to estimatesof corresponding median volume drop sizes (Eq. 3-15) from which approximate bulk terminal velocities are obtained (Eq. 4-6). Expected fall time of raindrops are then computed and added to the radar observation times in order to match the radar estimated rainfall 136 estimates from different CAPPI's with the PAM rainfall rates. For example, for CAPPI data at 3.0 km, a representative Z ^ of 2 dB indi cates that D q * 2.62 mm. This leads to a bulk terminal velocity of 8.5 m s * and an estimated time for the raindrops to reach the surface (1.5 km MSL) of 176 s, a delay time of nearly 3 min for this CAPPI. Horizontal wind speed and direction indicate the grid points where the radar data from this CAPPI should be selected. This process was repeated for every volume scan and CAPPI height of interest. As in was chosen Section A.2, the horizontal resolution of the radar data to accommodate the spread of the expected fall velocities caused by different drop sizes. was found to be 8.5 m s * Since the expected bulk fall velocity for a 2.A km CAPPI (mean height), this would correspond to a representative fall time of around 105 s. A fall velocity spread of A m s * would then result in a horizontal resolution of around A20 m which compares favorably with the 200 m x 200 m square grid from which the radar data are derived for comparison with the gage. The radar and PAM data are both averaged to decrease their variability and to obtain comparable spatial (radar) and temporal (raingage) resolutions. After the initial interpolation, the radar data at four adjacent Cartesian grid points on the constant-z plane were spatially averaged; the overall radar averaging procedure is estimated to yield standard errors for and Z^^ and 0.1 dB, respectively (Sirmans et al., 198A). of less than 0.5 dBZ To establish an appropriate PAM data averaging time duration, the vertical resolution of the interpolated radar data was taken into consideration. The 137 combined vertical angular width of the interpolated elevation scans and the radar beamwidth is around 2.1 , corresponding to a vertical resolution of 1.3 km at the range of PAM 11. Taking 8.5 m s * as the representative terminal velocity for the raindrops, gives a transit time of around 153 s. This analysis led to a choice of using running averages displayed every minute for both PAM station raingage data sets to compare with the radar estimates. 4.3.2 Raingage-Radar Comparisons A comparison of the radar estimated rainfall rates with those obtained from the rain gages is shown in Figs. 4.30 and 4.31 for the PAM 15 and PAM 11 stations, respectively. Radar estimates include the Marshall-Palmer (1948) (Eq. 3-25) and the Jones (1956) thunderstorm Z-R relationships, Z - 486 R 1,37 (mm6m'3 ) (4-8) in addition to those obtained from the 1-section empirical Z^ relationship. As for the (Z„ , Zp^)-R relationship of Eq. 4-7, the Z-R relationships should also be modified for increased fall velocities of raindrops due to altitude. However, this was not done in this study, since it would have increased the estimated rainfall rates (by about 7%) which are already overestimated using the unaltered Z-R relationships (see Table 4.5). Rain gage data are 3 min running averages of the 1-min PAM rainfall data. The rainfall event spans different time periods for the PAM 11 and 15 stations. For PAM 15, the rainfall rate reaches a peak value of 122 mm h * at 1708 within 3 10 15 20 TIME(min) (a) 150--- A. ; \ 4* PAM 15 * RZ0(* O Rj R(mmh 100-- 50-- 0--0 (b) 5 10 IS 20 TIME(min) Figure 4.3G. Time record of R obtained from PAM 15 raingage measurements. Also shown are the radar estimates R z d r derived from the empirical relationship using (Zjj, Zpp) and (a) R^p derived from the Marshall-Palmer relationship and (b) Rj derived from the Jones(1956) relationship of Eq. (4-8). Zero time corresponds to 1700 MDT. R is the rainfall rate, Zjj is the reflectivity factor and Zpp is the differential reflectivity. ao-r- Muiiujy 40--- 20- - 20 40 TIME(min) (a) 00-r- + PAM I * rid* O Rj 60-- (( tjujuj)y 40--- 20-- O; 20 (b) 25 30 40 TIME(min) Figure 4.31. Time record of R obtained from PAM 11 raingage measurements. Also shown are the radar estimates R z d r derived from the empirical relationship using (Zr , Zjjr) and (a) Rj^p derived from the Marshall-Palmer relationship and (b) Rj derived from the Jones (1956) relationship of Eq. (4-8). Zero time corresponds to 1700 MDT. R is the rainfall rate, Zjj is the reflectivity factor and Zpp is the differential reflectivity. 1A0 min after the beginning of the event. accumulated a total of 9.9 mm. _ h It lasted around 14 min and For PAM 11, the peak R reached 60 mm i at 1729 after a slower, more steady increase of around 12 min. The event lasted around 23 min and also accummulated 9.9 mm. Examination of the plots show that R^ d r f ° H ° ws the variations in the surface data more closely than do the Z-R relationship estimates. Similarly, the NSED result of 30.6% for R^DR indicates an improvement of 14.8% and 23.3% over R^p and Rj which are 45.4% and 53.9%, respectively. Regarding the PAM 15 comparisons in Fig. 4.30, the significant Z-R overestimates in the beginning of the storm deserve special examination. This result is believed to be attributable to the presence of very large raindrops in the radar scattering volume which are not accounted for through an averaging procedure of rainfall estimation as is represented by use of a Z-R relationship. In this case, Z^p accommodates for this large drop size and accordingly modifies the rainfall rate estimation by reducing the Zpp dependent proportionately constant between R and Zp. a Zg of 55dBZ at Z^p = 2 . 5 and 3.2 R(55, 2,5) - 129 mm h"1 and R(55, 3.2) - 88 mm h'1 compared to R^p = 100 and Rjy = For example, dB would give 146 mm h At the beginning of this event, Z^p was quite large and exceeded 3.0 dB. Thus, the data and sample computations support the explanation given here to explain the behavior of Z-R relationships relative to the Z^p method of rainfall 141 150 100 -C E E cr o M CL 50 0 50 100 150 R ( m m h " ') Figure 4.32. Scatter plot of RgjjR derived from the empirical rela tionship using (Zfl, Zd r ) versus R obtained from the measurements of both PAM 11 and 15 raingages where R is the rainfall rate. 150-r- 1 0 0 -- 100--- (mmh (mmh 150 -T- a_ 2 a: oc 5 0 --- 50--- ir 0 100 50 150 R l m m h ' 1) Figure 4.33. Scatter plot of Marshall-Palmer R obtained from raingages where rate. Rjjp derived from the relationship versus the PAM 11 and 15 R is the rainfall 0 100 50 150 R l m m h ' 1) Figure 4.34. Scatter plot of Rj derived from the Jones (1956) relationship of Eq. (4-8) versus R obtained from the PAM 11 and 15 raingages where R is the rainfall rate. N) 143 rate estimation. Interestingly, this same phenomenon may be applicable to the time centered around 20 min in the data for PAM 11 in Fig. 4.31. It can be argued from the time plots of R^p and Rj that the raingage measurements lagged R^p and Rj by an interval of around 1 min. Accordingly, R^p and Rj were moved forward by 1 min in time, but their standard error results improved only slightly (43% for R^p and 51% for Rj in NSED), while NB, as expected, remained the same. Therefore, adjusting the Z-R results to match better an apparent discrepancy in timing did not significantly affect the conclusions. 4.3.3 Remarks The results obtained in this experiment illustrate that the (Zjj-Zpp) method of estimating rainfall rates works very well in heavy rainfall and also improves the estimates obtained from Z-R relation ships employing a single radar parameter. This experiment differs from the other case studies described previously, since it employs raingages for ground truth and presents results for significantly higher rainfall rates. The rainfall rates are comparable to the simulated Central Illinois event, the conclusions of which are also tested in this case study. Those simulations predicted an improvement in the normalized standard error between the Z^p technique and the M-P relationship of more than 10% in the range 5 <. R (mm h *) < 50 and 12% in the range 50 £ R (mm h *) < 220 as opposed to the 15% improvement found in this case study. The results of this experiment are also comparable to other case studies. The 29 October 1982 Central Illinois experiment described in Section A .1 resulted in a 9.1% NB and 2A.A% NSED for and 35.8% NSED for the best Z-R rainfall estimation. and 30.0% NB Goddard and Cherry (198Ab) obtained 11% bias and 32% standard deviation for their RgQ£ computed from a gamma model relationship with M * 5 and A0% in standard deviation for their best fit Z-R relationship. As expected, all of these results are higher than the errors found in the simulations of Seliga et al. (1986) [A-6% in NSED for 5 220]. R (mm h *) Factors affecting the experimental results and the possible error sources were outlined in Section A.1.3.1. CHAPTER 5 PREDICTION AND COMPARISONS OF C-BAND REFLECTIVITY PROFILES FROM S-BAND MEASUREMENTS 5.1 Introduction The reflectivity factors measured by a radar operating at an attenuating wavelength can be adequately predicted by using the reflectivity factors at horizontal and vertical polarizations measured at a non-attenuating wavelength (Goddard and Cherry, 1981, 1984a; Leitao and Watson, 1984; Aydin et al., 1983a; Bring! et al., 1986). This capability has important ramifications for understanding rainfall effects on microwave communication systems when propagation through storms occurs. In this chapter, the predicted and measured reflec tivity profiles of a C-band radar (5.45 cm wavelength) are compared to test this hypothesis. The prediction employs the horizontal reflec tivity factor (Zjjiq ) and differential reflectivity (Zj^) obtained from the dual polarization measurements of an S-band radar (10.7 cm wave length) combined with an approximate geometry describing the problem. C-band radars are currently used in many cloud physics and precipitation studies and also as part of multiple-Doppler radar systems. At this wavelength, attenuation effects often have to be taken into consideration, since the observed reflectivity factor at a given range gate includes effects due to the two-way attenutation experienced by the propagating electromagnatic wave along the path within the storm to that gate. For this reason, it is convenient to 145 146 denote the observed C-band reflectivity factor, including attenuation effects, as "apparent." Thus, is defined as the apparent or measured C-band horizontal reflectivity factor in contrast to the unattenuated Z^,.. Attenuation effects at C-band are significant for high rainfall rates while at S-band they are negligible, typically less than 0.1 dB km at R ■ 100 mm h ^ (Battan, 1973). Radar studies of attenuation were considered extensively by Battan and Doviak and Zrnic (1984). Following the pioneering work of Hitschfeld and Bordan (1953), Joss et al. (1974) and Atlas and Ulbrich (1974) reported on comparisons of the theoretical and experimental results of radar attenuation within rainfall cells. Prediction of reflectivity factors at different wavelengths using an attenuation-correction technique was considered in various dual wavelength studies to distinguish hail from rainfall within a storm. For example, Eccles (1975, 1979), Jameson (1977), Jameson and Heymsfield (1980) and Tuttle and Reinhart (1981) employed empirical techniques using either the returned powers at an attenuating and a non-attenuating wavelength or a single attentuation-reflectivity relationship to compensate for attenuation and correct the hail signal. S-band polarization measurements were utilized in a rayprediction technique for 3.2 cm radar reflectivities by Aydin et al. (1983b, 1984) to confirm the presence of hail along the ray. Other attenuation studies using dual polarization were reported by Leitao and Watson (1984), Goddard and Cherry (1984), Goddard et al. (1981) and Bringi et al. (1986) at 3 cm and smaller wavelengths. 147 This chapter outlines and tests a generic approach to obtain the complete reflectivity profile of a storm cell at an attenuating wavelength from non-attenuating The procedure is demonstrated at 5.45 cm wavelength, but is also applicable to other attenuating wavelengths such as at X-band and possibly K -band. 5.2 Simultaneous Operation of CP-4 (5.45 cm) and CP-2 (10.7) cm Radars During the MAYPOLE '84 project in Boulder, Colorado, on 30 June 1984, a storm cell had been synchronously tracked by the CP-2 S-band radar which is capable of dual polarization measurements and the CP-4 C-band radar operating in horizontal polarization at a location 28.6 km nearly due East of CP-2. Both radars operated simultaneously during the time period 1400-1443 MDT from which a single volume scan from each radar was chosen for analysis. The storm cell was fully mature, having reflectivity factors above 50 dBZ during the selected time period. in Table 5.1. A listing of the measurements for both radars are given Note that CP-2 was operating in a pulse-to-pulse fast switching mode where the number of pulses averaged for each record was 128 at each polarization. Other radar specifications are given in Chapter 2 and the Appendix. Since the CP-2 and CP-4 radars were at different locations, the data from these radars can't be compared in their radial coordinate systems. The elevation for the data from each radar changes independently from the other as the range varies, and, although both radars have comparable half-power beamwidths (0.96° for CP-2, 1.06° for CP-4), the storm volumes corresponding to each radar beam differ 148 Table 5.1. Description of radar measurements Volume scan period Total volume scan time Range of sector PPI azimuth angle (deg) Angular velocity (deg s Elevation angles (deg) CP-4 (5.45 cm) CP-2 (10.7 cm) 1418:33-1421:12 1418:52-1422:02 2 min 39 s 3 min 10 s 268°-32° 12°-60° 15 4 o 0 1 -ts o Radar 0.5°-23° Elevation steps (deg) 2° l°-3° Number of pulses averaged (each polarization) 64 128 PRF 1667 960 Elevation (km) 1.49 1.75 Location: Date: Project: Boulder, Colorado 30 June 1984 MAYPOLE '84 149 considerably due to differences in their ranges from the storm cell and the elevation scan patterns. Therefore, to compare the radar data within the same volume along the path originating from CP-4, data from both radars are analyzed using the interactive software CEDRIC (see Section 4.3) for transformation from radar space to 3-dimensional Cartesian coordinates, using the code's successive bilinear interpolation scheme. Linear values of Z ^ employed with this technique, and interpolated Z ^ q and Z ^ q values. q , an(* ^H5 are values are obtained from the After the transformation, the processed data are described in CAPPI's at chosen grid locations. From the original radar space data, the volume between the heights 2.1 km-4.5 km was processed in 300 m elevation steps. Two hundred m horizontal grid spacings in each constant altitude plane were chosen to make the interpolation compatible with the radar range gate resolution. CAPPI's for both radars can then be used for comparison. This is a reasonable approach, since the propagation paths of CP-4 rays (at 4° elevation angle) within the chosen CAPPI (z ■ 3 km) for this storm are such that the CP-z radar data, as described in this CAPPI, are representative of what these CP-4 rays experience as they propagate through the storm. This experimental condition is illustrated in Fig. 5.1 which indicates that the region of interest is dominated by a single CP-4 elevation angle (4 ) PPI scan. Note that most of the 3 km CP-4 CAPPI is interpolated by CEDRIC from this scan. The applicability of this approach was verified by comparing CP-2 CAPPI's at different heights around 3 km which were found to be very similar. Thus, using a more sophisticated approach (see Section 4.2) (Km) 3 .5 - MSL 4 .0 - ALTITUDE 4 .5 - CP-4 E L ^ = 2 CAPPI 3.0 2 .5 - 2. 0 «— STORM LOCATION— J (CP-4J O 10 20 30 40 50 RANGE FROM CP-4 (km) 150 Figure 5.1. Demonstrating the applicability of using CAPPI's for deriving CP-4 reflectivity fields affected by attenuation along ray paths. 151 for predicting attenutation effects along CP-A rays in this storm was deemed necessary. Figure 5.2(a) shows the CAPPI of Z ^ obtained from the CP-2 radar. q at a height of 3.0 km MSL All radar plots in this chapter are shown in a coordinate system taking the CP-2 radar as their origin. This enables the data from both radars to be compared without additional spatial transformations. The contour lines for every 10 dBZ are indicated, and a high reflectivity core with values exceeding 50 dBZ and a peak value of 55.5 dBZ is also visible. 3.0 km is chosen to compare Z ^ q with Z ^ The height of and Z^^' as this height is high enough not be affected by the ground clutter but lower than the melting layer where the phase change from raindrops to mixed phase hydrometeors occurs, since the attenuation effects deal with the rainfall effects only. In order to verify that the storm cell consisted of only rainfall at this height, an examination of the CAPPI's of Z^£ and R at this height, RHI scans of CP-2 data through the storm cell and ground observations was performed. shows the Z ^ contours for the same CAPPI. Fig. 5.2(b) A wide area of Zp^ values exceeding 2 dB gives the indication that the central core of the cell consisted of raindrops of large diameter (Z^^ = 2 dB implies D q = 2.62 mm from Eq. 3-15). The R contours of this data shown in Fig. 5.2(c) which are computed using the empirical (Z^, Z ^ ) relationship of Eq. (3-5) and indicate a heavy rainfall core of R > 50 mm h ^ within the storm. The maximum R in this core was computed to be R ■ 1A0 mm h Fig. 5.3 shows the apparent horizontal reflectivity Zjj,.' contours as derived from the CP-A measurements. Although both CP-2 and CP-A 35 50 30 30 20 25 NORTH of CP-2 ( km) 40 v 20 5 20 E A S T o f C P - 2 ( k m) 25 30 152 Figure 5.2(a). Constant altitude (3.0 km MSL) PPI of Zh i q generated from the CP—2 volume scan between 1418:52-3 422:02 during the 30 June 1984 event. ZHio is the S-band reflectivity factor. 153 35 05 E 30 _x: OJ I CL Z 25 o X f- tr o z 20 I5 10 15 20 25 30 EAST of CP-2 (Km) (b) 35 50 <\J l CL O 25 o X h- cn O Z 20 10 (c) I5 20 25 30 EAST of CP-2 (km) Figure 5.2. Constant altitude (3.0 km MSL) PPI's of (b) Zd r and (c) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event. Zjjr is the differential reflectivity and R is the rainfall rate. 35 30 30 20 v • * *V Q_ 30 O *.v • 25 X o jUinnc|j3rpi Z 2 0 5 10 15 20 E A S T of C P - 2 25 30 ( k m) Figure 5.3. Constant altitude (3.0 km MSL) PPI of Zjj5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event. Zjj5 is the C-band reflectivity factor. . !j£ 4.8 50 40 :':K 30 X Ul ^ 20 'P.-.Or x’.'i '«: 2 I0 i-Ot 20 25 30 EAST of CP-2 (km) E 4. 50 JXl 40 x 30 CO 20 LiJ 2. I0 20 25 30 EAST of CP-2 (km) Figure 5.4. RHI's of (a) Zhio generated from the CP-2 volume scan between 1418:52-1422:02 and (b) ZH 5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event Ui showing an East-West vertical cross-section of (Zflio* ZH5) at y = 20 km. ZjjlO aiM* Zjj5 m are the S-band and the C-band reflectivity factors, respectively. 4.8 Zonfe®) -i— i— i— i— i— i— i— i— i— |— i— i— i— i— i— i— i— i— i— |— i— i— i— i— r %. 0 .5 • .......................... p i C p i i « » ■ » » I5 20 30 EAST of CP-2 (km) (a) 4 .8 50 10 5 (b) 10 I5 20 25 30 EAST of CP-2 (km) 156 Figure 5.5. RHI’s of (a) ZDR and (b) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event showing an East-West vertical cross-section of (R, Zjjr) at y = 20 km. Zjjr is the differential reflectivity and R is the rainfall rate. 157 reflectivities exceed 50 dBZ, the high reflectivity contour area is greatly reduced in the CP-A C-band reflectivity profile indicating that the attenuation effects on Z ^ ' are significant. Additional information on the structure of the storm cell is described in the RHI plots of the radar parameters from both radars. Fig. 5.4(a) is an RHI plot for Z ^ q at y ■ 20 km for the storm cell. Figs. 5.5(a) and (b) show the Z ^ and R fields for the same data set. showing a vertical cross-section Within the storm volume where the high reflectivities ( Z ^ q > 50 dBZ) are observed, Z^^ > 2 dB and heavy rainfall rates can be observed in the same region. dB at x * 16.5 km corresponds to a region where Z ^ likely is in a region of melting graupel. The dip of Z^^ < 2 < 40 dBZ and most q This should not affect the analysis very much since it is a very small region within the storm and since melting graupel is expected to behave similarly to rainfall in its scattering properties (Aydin and Seliga, 198A). the Zjjg1 corresponding to the same RHI plots. Fig. 5.4(b) is Note that the Z ^ ' > 50 dBZ region is significantly reduced in size from the Z ^ q contours described in Fig. 5.4(a), although occurring at the same location. Fig. 5.6(a) is an RHI plot of Z ^ at y ■ 22 km and the Z ^ q q showing the vertical cross-section > 50 dBZ core above the surface. The plot outlines a wider section of the storm where the 3.0 km altitude contains the Z^ > 40 dBZ region throughout most of the cell. Z ^ and R plots in Figs. 5.7(a) and (b), corresponding to the same plot, indicate high Z ^ values and heavy rainfall rates throughout much of this same height. These results support the premise that the storm at z ■ 3.0 km consisted primarily of rainfall. Fig. 5.6(b) is the .8 Cf 50 40 hX 30 O ;! 20 CD LlJ »;=v-•|-8-|-S-8t»-i|«-W' X 20 10 (a) 25 30 EAST of CP-2 (km) Z h 5WBZ) I5 (b) Figure 5. 6. 20 EAST of CP-2 (km) RHl's of (a) ZH io generated from the CP-2 volume scan between 1418:52-1422:02 and (b) Zjj5 generated from the CP-4 volume scan between 1418:33-1421:12 during the 30 June 1984 event showing an East-West vertical cross-section of (ZHio» ZH 5 > at y = 22 km. ZH io and ZH 5 are the S-band and the C-band reflectivity factors, respectively. Ln 00 Zno(dB) 4 .8 0 .5 CD Ll I =1=2 S: / ; :-Sc n. 7: 20 10 (a) 25 30 EAST of CP-2 (km) R(mmh’ ) 4.8 50 na - 10 ZE CD Ll I =^2 20 10 (b) EAST 25 30 CP-2 (km) 159 Figure 5.7. RHI's of (a) Zjjr and (b) R generated from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event showing an East-West vertical cross-section of (R, Zjjr) at y = 22 km. Z^r is the differential reflectivity and R is the rainfall rate. 160 corresponding Z^,.' RHI plot deduced from CP-A measurements indicating the decreased horizontal reflectivities due to attenuation. the > 50 dBZ core does not exist and that the Z ^ 1 is considerably smaller in extent. Note that > 40 dBZ core Fig. 5.8 shows the ( Z ^ q , Zjjr) scatter plot from the CP-2 radar for this volume scan. The solid curve in the figure is taken from Aydin et al. (1986) who described an hail signal to differentiate rain and hail phase hydrometeors from (Zh i q > Zpp) measurements. region The radar measurements are all in the lower of the curve, suggesting the presence of rainfall as based on their findings from disdrometer simulations. Thus, the CP-2 radar data strongly support the presence of rainfall throughout the entire 3.0 km CAPPI. 5.3 C-Band Specific Attenuation and Reflectivity Factor from S-Band Measurements The prediction of the C-band reflectivity profiles from S-band utilizes empirical relationships relating the C-band specific attenuation Ajjg and the reflectivity factor Zjj^) measurements. Z^,. to S-band ( Z ^ q , The relationships used here were derived from drop size distributions (DSD) collected during the field projects in central Illinois in 1982 (OSPE) and in Boulder, Colorado, in 1983 and 198A (MAYPOLE). More than 1800 DSD's with R > 0.1 mm h * were employed for these derivations using 2 min running averages of 30 s samples in order to reduce sampling errors in the DSD-derived parameters. The radar observables Z ^ g , Zy^g, Z ^ , Zjj,., Zy,., Ajj,. and Ayj are computed from the DSD's utilizing the backscatter and extinc tion cross-sections for each drop size at 10°C. The technique is (dBZ) 70 C Figure 5.8. 161 Scatter plot of ZR versus Zj)R obtained from the CP-2 volume scan between 1418:52-1422:02 during the 30 June 1984 event. The solid line is the rainfall boundary defined by Aydin et al. (1986). Both negative and large values of ZDR at low ZR are thought to be due to ground clutter. ZH is the reflectivity factor and Zd r differential reflectivity. 162 similar to the simulations used to compute the empirical R/Zy, M/Z jj and D q versus relationships described in Chapter 3. Although the prediction procedure in this study involves only A^,., Z^,. and in relation to Zj^, other combinations of horizontal and vertical polarizations for the same parameters were also obtained and are presented here for possible future reference. Fig. 5.9 shows the variation of A ^ / Z ^ g , A ^ / Z ^ q , ^ 5 ^ 1 0 versus Z^^ where (dB). ^ are in (dB/km), y^g in (mm^ m ^ and Z^^ in The variations of these plots suggest that a least squares polynomial fit in the form V v 5 " ^ . V I O ^ O + al^DR + • • • + ajfon ) (dB/km) (5-1) would suffice to describe the relationship between parameters. The order of the polynomial was decided after fitting polynomials of increasing order to the actual plots, computing the fitted values for each data point and examining the difference between the empirical fits and the actual data. The results of the polynomial fit of order m = A are tabulated in Table 5.2 which gives the coefficients of the polynomials for each of the Ay versus Z ^ relationships. Fig. 5.10 shows the fitted curve for A ^ / Z ^ g versus Z^^ used in the predictions. The curve follows very closely the plot of Fig. 5.9(a) showing the actual disdrometer simulations. the error Fig. 5.11 shows the magnitude of between the actual and the predicted values of the attenuation A jj,. ) for a polynomial fit of order m = A. This procedure (A^.- was used for different m values, and the errors were found to decrease as m 0 1 K) 0.9 0.9 0.8 0.8 0.7 0.7 0.6 Ji 0.6 (c Ui g U J U J j O I H z / j u i ^ / g p ) in 0.5 0.5 0.4 >0.4 0.3 CD 0 -3 « 0.2 0.2 0.5 (a) Figure 5 . 9 . 2.5 I5 2.0 D I S D R O M E T E R Z 0R (dB) .0 3.0 3.5 0.5 (b) .0 1.5 2.0 2.5 3.0 D I S D R O M E T E R Z 0 r (<1B) Variation of (a) A h s / Z j h o a n d A H 5 / z v l O versus ZDR for disdrometer-derived distributions [see next page for (c) and (d)]. Ajj5 is the C-band specific attenuation at horizontal polarization and Z m g , Zy^g S-band horizontal and vertical reflectivity factors, respec tively. is the differential reflectivity. 0.9 0.9 o .e O.S 0.7 0.7 £ £ 0.6 0.6 A V3(dB/km)/Zmo(mm6 m io 0.5 <0 0.3 0.4 > 0.4 3 CD 0.3 0 in 0.2 0.2 0.1 0.5 (c) 1.0 2.0 D I S D R O M E T E R Z DR (dB) 3.0 3.3 0.5 (d) 0 1.3 2.0 2.3 30 D I S D R O M E T E R Z 0„ ( d B ) 164 Figure 5.9. Variation of (e) Av s /Zjj^q and A y S ^ ^ l O versus Zp^ for disdrometer-derived distribution [see previous page for (a) and (b)]. Ayj is the C-band specific attenuation at vertical polarization and Zh ^q » ZV10 S-band horizontal and vertical reflectivity factors, respec tively. Zp^ is the differential reflectivity. 165 0.9 0.8 0 .7 Z 0.6 rO 0.5 x 0 .4 Q-X 0.2 0.5 0 1.5 2.0 2 .5 3 .0 DISDROMETER ZnR (dB) p Figure 5.10. Variation of predicted Ah 5 /Zhj_q versus ZpR for the P disdrometer-derived distributions where Ajj5 is derived from the empirical relationship given in Table 5,2 in the form of Eq. (5-1). Ajj5 is the predicted C-band specific attenuation at vertical polarization, S-band horizontal reflectivity factor and Zqr differential reflectivity. 166 to-I . + :* 2 ? % W M 8P) ( s2 v - SHV) >"3 ^ iju +#** ± + *♦ M -*i-4 10 * & M T^fr‘^3§t^35Er f y s ^ + +. + ++ + * < ii5 p fs & fs £ ? + ' fit* v *-t ' * *;{ ^ 0.5 + + +• jCu^ri-«"*L •f> + + 10 * +H- + a.* 1.0 1.5 2.0 2.5 3.0 D ISD R O M E TE R Z 0R (dB) Figure 5.11. Errors between the actual and the predicted values of the attenuation (Ah5 -A§ 5 > versus Zjjr for disdrometer derived distributions. aJj5 is derived from the empirical relationship given in Table 5.2 in the form of Eq. (5-1). Afl5 is the C-band specific attenuation and Zp£ differential reflectivity. 167 Table 5.2. Disdrometer-derived specific attenuation empirical formulas* for 5.45 cm specific attenuation - 10.7 cm reflectivity factor and differential reflectivity relationships. Coefficients al ao a 2 a4 a3 (I) 6.460xl03 1.109xl05 3.441xl05 -2.117xl0S 3.325xl04 (II) -7.559xl0 2 1.636xl05 1.895xlOS -1.557xlOS 2.754xl04 (III) 7.494xl03 1.042xl05 3.861xlOS -2.017xl0S 2.902xl04 (IV) 7.690xl02 1.528x105 2.424xlOS -1.654xlOS 2.702xl04 Fig. 5.8(a): (II) Fig. 5.8(b): (III) Fig. 5.8(c): (IV) Fig. 5.8(d): ^H5 = ZH10/(a0+alZDR+a 2ZDR+a3 ZDR+a4 ZDR^ ^ 5 = ZvlO/(aO+alZDR+a2ZDR+a3ZDR+a4ZDR) \5 " ZH l 0 ^ a0+alZDR+a2ZDR+a3 ZDR+a4 ZDR^ ii m (I) Zvl0/(a0+alZDR+a2ZDR+a3ZDR+S4ZDR) 168 increases to A after which they remained relatively stable. 2 % of the predicted values exhibit errors of more than 0.01 Less than dB/km with p the highest error being 0.0A dB/km for • The error rates of the fitted curves for m ■ A are outlined in Table 5.2, using Eq. (3-21) and Eq. (3-22) for NB and NSED. the predicted A a r e For A^,. (dB/km) > 0.05, the errors in 1.8% in NB and 3.3% in NSED. For 0.01 < Ajj,. (dB/km) < 0.05, the errors are 0.1% in NB and 6.9% in NSED. the empirical polynomial fit procedure predicts A ^ p Clearly, very closely to actual A^^. The prediction of C-band profiles also necessitated a scheme for deriving from Zjj values from observed ( Z^g* Z^^), since Zjj y^ differs due to raindrop shape and possible Mie-region (large electrical size) effects. Effective reflectivity factors for the 5.A5 cm and 10.7 cm measurements can differ by more than 1 dB for large drop diameters as observed from the ratio plots given in Fig. 5.12 which are plots of the ratios Zjjj/Zj^q, ^ Zys/ZviQ versus Z^^. 5 ^ 1 0 ’ ^ and 5 ^ 1 0 A polynomial similar to Eq. (5-1) in the form ^H,V5 " ^H,V10^0 + biZDR + • • • + is suggested from these DSD-derived simulations. ^mm m ) (5-2) The results of the polynomial fit of order m * A for these relationships are tabulated in Table 5.3; as with the previous results, m s A was found sufficient to describe the curves. The Z^ ^ polynomial fits to these curves resulted in smaller errors than the previous attenuation relationships due to the less complex behavior and spread of the curves. For reference, the fitted curve of Zjjj/Zjjjq versus ZDR is shown in Fig. 5.13. 169 ZV5 (mm6 m 3)/Zv 10(mm6 m'3) 1.4 1.2 1.0 0.8 HH- 0.6 0 0.5 Zvs (mm6 m'3)/Zn i olmm6 m"3) <a> 1.0 1.5 2.0 2.5 3.0 3.5 3.0 3.5 DISDROMETER Z0R(dB) 0.8 0.6 0.4 0.2 0 (b) Fipure 5.12. 0.5 1.0 1.5 2.0 2.5 DISDROMETER ZDR (dB) Variation of (c) Zvs/Z^iq and (d) 2v5/^KlO versus Zrip for disdrometer-derived distributions [see previous page for (a) and (b)]. Zy 5 is the C-band vertical reflectivity factor and Zjjiq» ^VlO S-band horizontal and vertical reflectivity factors, respectively. Zpp is the differential reflectivity. 170 .4 fO I <0 E E .2 ~o > N .0 ro I tf> E E 0.8 in > N 0.6 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.0 3.5 DISDROMETER ZDR(dB) (c) ro 'E E 0.8 E u> "o X N \ 0.6 in' *E E E <0 m > N 0.2 0 (d) Figure 5.12. 0.5 1.5 2.0 1.0 DISDROMETER Z 0R 2.5 (dB) Variation of (a) Zj^/Zhio and (b) Zns/Zyio versus Z^r for disdrometer-derived distributions [see next page for (c) and (d)]. zH 5 is the C-band horizontal reflec tivity factor and ^VlO S-band horizontal and vertical reflectivity factors, respectively. ZpR is the differential reflectivity. 1.25 ro i E ID E 1.0 E o '"H H + *H- -H+ + vl 0.75 ro 'e CD | 0.5 in CL X N 0.25 0.5 0 1.5 2.0 2.5 3.0 3.5 D I S D R O M E T E R Z np ( d B ) p Figure 5.13. Variation of predicted Zh 5/Zh 10 versus Zjjr for the disdrometer-derived p distributions where Zr 5 is derived from the empirical relationship given p in Table 5.3 in the form of Eq. (5-2). Zj^ is the predicted C-band horizontal differential reflectivity. is the 171 reflectivity factor, ZRl0 S-band horizontal reflectivity factor. 172 Table 5.3. Disdrometer-derived reflectivity factor empirical formulas* for 5.45 reflectivity factor - 10.7 cm reflectivity factor and differential reflectivity relationships Coefficients bo bl b2 b3 b4 (I) 1.011 -2.548xl0"2 1.150xl0-1 -4.749xl0~2 7 .067xl0~3 (II) 1.008 -2.362xl0-1 1.033X10**1 -3.823xl0“2 5.356xl0~3 (III) 1.005 2.368X10”1 1.009xl0_1 -1.503xl0“2 6.499xl0“3 (IV) 1.004 1.786xl0"2 4.712xl0-2 -1.083xl0-2 2.305xl0~3 (I) Fig. 5.11(a): (II) Fig. 5.11(b): (III) Fig. 5.11(c): (IV) Fig. 5.11(d): ZH5 ZHl0/(b0+blZDR+b2ZDR+b3ZDR+b4ZDR) ^ 5 " Zvl0/(b0+blZDR+b2ZDR+b3ZDR+b4ZDR) Zv5 " W (b0+blZDR+b2ZDR+b3ZDR+b4ZDR) Zv5 " ZvlO/(bO+blZDR+b2ZDR+b3ZDR+b4ZDR) 173 5.A Prediction Procedure This section describes the procedure to predict the 5.A5 cm reflectivity factor profiles from the 10.7 cm ( Z^g, measurements. (1) Z^) This procedure is performed in five steps: For each ray, Z ^ is estimated using Eq. (5-12) (Table 5.3) for pre-selected range gates from the S-band ( Z^p, Z ^ ) measurements. (2) The C-band specific attenuation A jj,. for the same range gates are estimated using Eq. (5-1) (Table 5.2). (3) Once Z^,. and are computed for all gates, the computations to find Z^ 1 are initiated at the leading edge of the storm cell defined as Z ^ q “ 20 dBZ. Z^' is then computed at each range gate using the equation ^n' " ZH5n “ 2r \ i*k *1151 ' r *H5n (5‘3) where, r * the path length of the range gate k = the leading range gate Zjj,j " C-band reflectivity factor as predicted from ( Z^g* Z ^ ) before attenuation (mm 6 m “3 ) Zjjj1 = apparent C-band reflectivity factor differing from because of attenuation along the ray path in the storm , 6-3. (mm m ) (A) The process is then repeated for all rays of interest propa gating through the storm cell. 174 (5) Reflectivity profiles can then be obtained by determining the contours of Z ^ ' from the individual range gate values. In order to test the procedure, ^ 5 ' values, corresponding to rays originating from CP-4 and separated by 2.5° in azimuth throughout the core of the storm (30°-45° wide) and 5° at the edges, were determined from the CP-2 predictions. Fig. 5.14 illustrates this procedure as applied to the storm of interest. The contours outline the predicted C-band apparent reflectivity factors ( Z ^ 1) using the CP-2 S-band measurements. In order to compare these to the actual measurements from the CP-4 radar, the Z^,.' values at all range gates were grouped in increments of 10 dBZ as noted in the legend. values in this figure were obtained from the (Zj^q, The Z^,.' values corresponding to nearest neighbor CAPPI grid points to the pre selected range gate locations of the CP-4 rays chosen for the analysis. For rays passing through the storm's core, CP-2 grid point data within around 200 m of the gate locations were averaged to arrive at (Zjj^q, Zjj^) profiles along the simulated CP-4 rays. for these rays were taken to be 400 m apart. Gate locations For rays outside the core, a similar procedure was performed except that the gate spacing was 600 m and data were averaged from grid points within around 300 m of the gate location to obtain the (Z^g, Z ^ ) profiles along the simulated CP-4 rays. Typically, the procedure required averaging 2-4 CAPPI grid points for every gate value along the CP-4 rays. Fig 5.14 includes the resultant storm cell features of Z^,.'. These are outlined in 10 dBZ increments within an area bounded by the o 175 X Zhs (dBZ) predicted from C P - 2 (S-band) x < 2 0 dBZ • 2 0 dBZ A 3 0 dBZ 4 0 dBZ 5 0 dBZ CP -4 (C-bond) Figure 5.14. Predicted CP-4 reflectivity values derived from CP-2 (^HlO* Zdr) measurements. The azimuth angles and the gate spacing used in the prediction scheme for rays along paths originating from CP-4 are also indicated. Azimuth angles are measured CCW from north. Zjjio Is the S-band reflectivity factor and Zdr differential reflectivity. 176 20 dBZ contour corresponding to where the cumulative attenuation computation was initiated. 5.5 S-Band Predictions and C-Band Measurements Due to uncertainties in the absolute bias and the calibration of CP-2 and CP-A radars, the Z^ 1 values predicted from CP-2 values have to be matched before the comparisons. The possible sources of errors in the radars are explained in Chapter 2. Two methods have been used to determine the necessary calibration: (1) The predicted and measured Z ^ ' the range 20 Z^ 1 (dBZ) are compared for all rays in 30 in all rays since the attenua tion effects within this range are negligible. The bias is determined from, ~ B - ZH5 pi ^ Ml 'hs (dB) ( 5 ’ A) /n p' ~ m1 where Z^^ and Z ^ are the mean predicted and measured Zjjj', respectively, assuming that the relative calibrations of the radars are correct. The computed B = 3.5 dB indi cates that CP-A reflectivity factor measurements under estimate the reflectivity factors obtained from CP-2 by this amount. (2) This method applies a linear regression between all the predicted and measured Z^ , . 1 values for the rays intersecting the core of the storm (30° <_ 0 <. A5°). The regression equation of the form Zjj^' = m Z ^ * ' + B (dBZ) (5-5) 177 is used to determine the bias B. In this form, a slope m sufficiently different from unity would have indicated a bias error for the Zj^q measurements as well, since this would lead to erroneous attenuation predictions. The regression analysis resulted in a slope of unity and a bias of 4.0 dB, in good agreement with the previous estimation. The measured, results presented here for Z^ 1 were corrected by increasing the radar values by 3.5 dBZ. Fig. 5.15 shows the predicted 5.45 cm reflectivity factor (Z^^1) as an overlay on the actual CP-4 measurements. The boundaries of the predicted contours are in very good agreement with the measurements, duplicating most of the features. reflectivity areas, Z ^ ' The size and magnitude of the high > 50 dBZ, are well matched. Two two-way accumulated attenuation is highest along the rays through the core of the storm reaching 2.5 dB for the 35° CP-4 ray (see Fig. 5.14). that ray the maximum Z ^ q is 55.5 dBZ with Along = 2.56 dB, indicating a one-way specific attenuation of 0.84 dB * km and a rainfall rate of 140 mm h ^ from Table 5.2 and the empirical relationship, Eq. (3-5). For reference purposes, it is of interest to compare this result from A-R and A-Z relationships. The closest any A-R relationship listed by Battan (1973) comes to the (Ztt.q , Zpjj)-predicted value of 0.84 dB km ^ is due to Wexler and Atlas (1963). predicts a value of A ^ Their relationship (A = 0.004R) = 0.56 dB km * which is 33% less than the polarimetric-predicted value. The A-Z relationship [A ■ 1.12 x 10 -4 A Z ] of McCormick (1970) which assumes a M-P distribution results in Ajjg ■ 0.31 dB/km which is 63% smaller. The maximum Z^^ of 3.12 dB is 3 5 r — -i—i— ■— n — r— |— i— i—i—i— n — i i i Zh5 (dBZ) (PRED.) (MEAS.) 20 40 30 - V. .. Hill, 50 NORTH of CP-2 ( k m) 30 2 5 7 m 20 ; .........I I 10 5 i i . i i i I i i i ■ i i i i » I i » .i.«» i i i i I i i i i i i i i j_ 15 20 25 30 EAST of CP-2 (km) 5. The predicted C-band CP-4 reflectivity factor contours (Fig. 5.14) superimposed as an overlay on the actual CP-4 measurements (Fig. 5.J) for the 15 June 1984 event 178 Figure 5. 179 along the 40° ray from north (with a corresponding Z ^ g ■ 53.4 dBZ) indicating that Dq * 3.48 mm from Eq. (3-15). These CP-2 values of (Zhiq» Zj)r) map into a Z^,. of 52.3 dBZ which 1.07 dB lower than Z ^ q . The corresponding one-way A^,. ■ 0.53 dB km *. These results show that cumulative attenuation and non-Rayleigh scattering effects on Z^^ can result in significant differences between Z ^ q and Z ^ 1, especially near the core of the storm when Z ^ q > 40 dBZ. The method outlined here estimates these effects using ( Z^g, Z ^ ) measurements. Figs. 5.16 and 5.17 show Z ^ q compared to predicted and measured Z^,.' for CP-4 rays with azimuth angles 35° and 40° CCW from north, respec tively. The leading edge of the cell is at the range of 16 km for both rays which extends to around 28 km. corrected for the bias of 3.5 dBZ. The measured Z^ 1 is The results indicate accurate prediction of the apparent Z^,.' using this correction technique. The discrepancies in the trailing edges of Fig. 5.17 are most likely due to ice contamination in the CP-4 CAPPI's which are derived primarily from a PPI scan at 4° (see Fig. 5.1). for the lower measured Z ^ ' This ice would readily account °f around 2-4 dB between 24-27 km. Fig. 5.18 shows the simulated results for Z^,.' had the CP-4 radar been co-located with CP-2. Since the core of the storm cell is elon gated in the CP-2 direction resulting in a longer path of high Z ^ through the cell, the maximum accummulated two-way attenuation at an azimuth angle of 38.2° CCW from north is 3.3 dB, higher than the earlier predictions for the current CP-4 location. For a peak (Zj^g, Zpp) of (54.5 dBZ, 2.96 dB), the peak A^^ is 0.94 dB/km. The shape G O - t- t-HIO -------------- Z H3 (pred) + + + + Z HS (CP-4 1 Reflectivity (dBZ) 50 40 — 3 0 - 20 -- 16 20 (a) 24 22 Range from CP-4 26 26 (Km) 00 - r - Z hio --------------Z H5 (pred) 4- + + + Z hs ( C P - 4 ) Reflectivity (dBZ) 5 0 --- 40- DO - 20 - 10 14 16 (b) Figure 5.3 16 20 Range 6 . from 26 24 22 CP-4 20 30 (km) Spatial variation of reflectivity factors at S-band measured by CP-2 compared with the predicted and the measured reflectivity factors at C-band along the CP-4 rays with azimuth angles (a) 35° and (b) 40° CCW from north. GO " " ^H5 + + + + ZH5 (pred) Reflectivity (dBZ) 50 - 40 30 20 - 22 24 26 28 30 Range from CP-2 32 34 36 (km) 181 Figure 5.17. Spatial variation of reflectivity factors at S-band measured by CP-2 and the simulated reflectivity factors at C-band along the same ray originating from CP-2 at an azimuth angle of 38.2° CCW from north. C-band reflectivity values without accounting for attenuation (Zjjs) are also shown. 182 non-Rayleigh scattering effects of the raindrops result in values of Zjjg (dashed curve in the figure) being somewhat less than and The scatter plot of the 35° and 40° rays are shown in Figs. 5.19 5.20, respectively. Since the attenuation effects are more pronounced for higher reflectivities, an equal or better match of the predicted Z ^ ' with the measurements at these levels compared with the lower reflectivities indicates that the prediction procedure works satisfactorily. A scatter plot of the data from all the rays within the storm's core (Zj^ q > 40 dBZ), corresponding to the 7 rays between azimuth angles 30°- 45°, is shown in Fig. 5.21. An error analysis of these rays resulted in 2.4 dBZ in NSED with a mean Z^^ of 36.4 dBZ for values of Z ^ ' Z^' > 20 dBZ. The error analyses for Z^^' > 30 dBZ and > 40 dBZ gave similar results demonstrating that the attenuation effects were accounted for satisfactorily. 5 .6 Summary In this chapter, the apparent reflectivity profiles of a radar operating at C-band were predicted using S-band (Zjj^q , Z ^ ) measurements at S-band at a different location. relationships between (Zj^ q The scheme used , Z^^) and (Zj^, A ^ ) obtained from simulations derived from disdrometer data. The comparisons resulted in good agreement between the measured and predicted apparent reflectivity profiles at C-band for rainfall. This was demonstrated by a standard error of 2.4 dBZ for reflectivities in the range between 20 dBZ-55 dBZ. The results support the use of the dual polarization (ZfliQ* Zpjj) technique to predict scattering and attenuation effects of o 20 40 60 ZH5(pred) (dBZ) Figure 5.18. Scatter plot of the predicted and measured reflectivity factors for the CP-4 radar at C-band for the ray with the azimuth angle 35° CCW from north. 0 20 40 60 Z H5 (pred) (dBZ) Figure 5.19. Scatter plot of the predicted and measured reflectivity factors for the CP-4 radar at C-band for the ray with the azimuth angle 40° CCW from north. 00 u> 184 60 Z H5<CP-4) (dBZ) + -h 40 20 20 Z H5 (pred) Figure 5.20. 40 60 (dBZ) Scatter plot of the predicted and actual reflectivity factors for the CP-4 radar at C-band for even rays with the azimuth angles between 30°-45° CCW from north. 185 narrow beam microwaves propagating through rain-filled media along paths originating from other possible radar locations. CHAPTER 6 OTHER APPLICATIONS In this chapter the potential use of tions is considered. in two other applica These are the determination of the scavenging rates of aerosols by precipitation and the possible role of (Z„, radar observations in the measurement of vertical air velocities. 6.1 Aerosol Scavenging Rates Precipitation scavenging dominates the aerosol removal processes from the atmosphere and has been estimated to be responsible for as much as 80% of total aerosol removal (Junge, 1963; Robinson and Robbins, 1971; Reiter, 1971). Although many studies have been done to identify pollutant sources and their dispersal in the atmosphere, limited research has been directed towards obtaining realistic removal rates by precipitation. Accurate estimation of the interaction of aerosols and rainfall is becoming more important for their effects on visibility, material damage to property, human health and welfare and in climatic studies for their effect on the Earth's radiation balance. Precipitation scavenging consists of two major processes (Semonin and Beadle, 1974). "Washout" occurs during the fall of hydrometeors whose growth has substantially terminated whereas "rainout" refers to the removal process within clouds that occursduring the formation and growth of cloud particles. The aerosol particles affected by 186 precipitation scavenging range from 0.001 ym to 10 ym in radius, and, at different size categories, the effective scavenging mechanisms also differ. For aerosols less than 0.1 y m in radius, Brownian diffusion causes the aerosol particles to coagulate with hydrometeors. range of aerosols between 0.1 and 1 For the ym, there is a significant minimum in scavenging effects which is referred to as the "Greenfield gap" (Greenfield, 1957; Pruppacher and Klett, 1978), although field measurements by Graedel and Frany (1974) indicated larger than expected scavenging in this range which was attributed to electro static attraction. Radke et al. (1980) also reported on airborne measurements that scavenging effects were an order higher for submicron particles. Interestingly, the largest mass of aerosols reside in this region, coinciding with a relative maximum in the retention efficiency of the human lung (Beard, 1974a). Phoretic forces (thermo- and diffusio-phoresis, motion of particles arising from non-uniform heating and by concentration gradients, respectively) are more effective in this region. Aerosol particles in this size category also serve as cloud condensation and ice nuclei and may subsequently be removed through precipitation of the raindrops and ice particles they formed. Raindrops containing these nuclei are also efficient by Brownian diffusion, phoretic forces, inertial impaction and electrical forces (Grover et al., 1977). 1 For particles larger than ym in radius, removal caused by inertial impaction with hydrometeors dominates the scavenging process. External electric fields also cause the aerosols to collide with the hydrometeors resulting in their removal from the atmosphere at these size ranges. 188 An overall scavenging coefficient for the below-cloud processes or washout rate, A(r) (s *) has been defined to incorporate different mechanisms of removal of aerosol particles of radius r by rainfall from the atmosphere to compute the fractional decrease in time of the particle concentration (Chamberlain, 1953; Engelmann, 1970). fDmax A(r) = A(D) N(D) vfc(D) E(r,D) dD (s -i ) (6-1) 0 where E(r, D) is the dimensionless scavenging efficiency of raindrops of equivolume diameter D for particles of radius r and A(D) is the horizontal cross-sectional area of raindrops. A(D) vfc(D) E(r, D) is the volume swept out per second by a raindrop of diameter D falling with the terminal velocity vfc. Hence, for a raindrop size distribution N(D), A(r) is the fractional number of particles of size r removed in one second. The particle mass concentration remaining in the air at a particular time t after initiation of the washout process is given by M = Mq exp(- A(t - tQ )) (g m 3) where Mq is the initial mass concentration at time tg. (6-2) Eq. (6-2) shows that removal of aerosol particles from the atmosphere is an exponential decay process where the scavenging rate, A determines the half-life of the scavenged particles, (t - tg) = 0.693 A *(r). Eq. (6 -1 ) shows the dependence of the scavenging rate, A on the drop size distribution (DSD). 189 While determining A, Dana and Hales (1974) and Hill and Adamowicz (1977) employed the DSD given by Best (1950) in their scavenging models. Slinn (1974) reviewed the various empirical DSD's used in the scavenging studies and evaluated Eq. (6-1) as a function of mean volume drop diameter D through an assumed empirical relationship between R and D. In all of these, as in most scavenging studies, A is given as a function of R and the aerosol particle size. DSD effects are often ignored even though they can cause large discrepancies in aerosol precipitation scavenging rates as pointed out by Slinn (1974). 6.1.1 Scavenging Rates Since the method estimates N(D) from (Z^, it can conveniently be employed to obtain the scavenging rate of aerosols under different rain storm conditions. Eq. (6-1) shows that for a monodisperse aerosol size distribution, A ■ A(r, D) is a function of DSD only. For a particular N(D) and particle radius r, A should then be related to the radar parameters as A * A(Z„ , Zj^) similar to the estimation of the rainfall parameters R and M (Chapter 2). The first step in computing A for different DSD's is to obtain the scavenging efficiency E(r, D) for a range of particle radii and drop diameters. Scavenging efficiencies are often taken to be equal to numerical collision efficiencies of aerosols collected by water drops. This relationship assumes an adhesion efficiency of unity which indicates that water drops retain all the particles colliding with them as shown by the experimental findings of Weber (1969). Determination of the numerical collision efficiencies have been 190 studied by various authors (Beard, 1974a,b; Beard and Grover (1974); Grover et al., 1977; Wang and Pruppacher, 1977; Wang et al., 1978; Radke et al., 1980). In this section, scavenging efficiencies are computed for the 20 drop size categories of the Joss-Waldvogel type disdrometer and for particle radii of 0.2, 0.5, 1.0 and 2.0 y m based on the tabulated numerical collision efficiencies of Beard (1974b). Values for the necessary drop and particle sizes were found by interpolation. The drops and the particles were both assumed to be unchanged, although computations are also possible for a moderately charged case. The simulated two-parameter relationships A■A(v w -W l V 2 <6-3) were determined employing the computed E(r, D) for each drop and aerosol size from the central Illinois disdrometer measurements of October 1982 (Seliga et al., 1986). 6 Results of a multiple regression analysis, derived from the linear relationships of the logarithm to the base 10 of the parameters, are given in Table 6.1 for four different aerosol radii. Similar relationships, employing the actual rainfall parameters R and Dq as A = A(R, Dq), are also shown in the same table, although they are not directly observable by radar. The high correlation coefficients (p = 0.90-0.99) presented in the table indicate a very good fit for A using two parameters. Since in other scavenging studies, A is usually determined using a single estimator and an assumed DSD, the regression analyses for A were also performed using Zjj and R as the only estimators. Table 6.2 summarizes the 191 Table 6.1 Empirical formulas to estimate precipitation scavenging rates A from both (Zjj, Zqr) and (R, D q ) . Relationships were derived from multiple regression analyses using disdrometer data and for different aerosol radii. Correlation coefficients (p) for the regression rela tion relating the logarithms of the parameters are also shown. R is the rainfall rate, Do is the median volume diameter, is the reflectivity factor and Zdr is the differential reflectivity. A - a Z ai Z 3 2 A a0 H DR Aerosol Radius, a(pm) /N A ao ai 0.2 1.51x1O'9 0.5 2 *2 P 0.886 -2.69 0.91 .2 2 xl 0 " 1 0 0.941 -2 . 1 1 0.98 1.0 2.72xlO~10 0.938 -1.87 0.99 2.0 7.85xl0~8 0.884 -2 . 2 1 0.97 A ■ bo Rbl D ob 2 Aerosol Radius, a (pm) £ 0 A A bl b 2 P 0.2 1.46xl0"6 0.969 -2.46 0.98 0.5 1.74xl0- 7 0.982 -1.24 0.99 1.0 1.71xlO-7 0.978 -0.820 0.99 2.0 4.93xl0" 5 0.935 -1.53 0.99 192 Table 6.2 Empirical formulas to estimate precipitation scavenging rates A from both Zjj and R. Relationships were derived from regression analyses using disdrometer data and for different aerosol radii. Correlation coefficients (p) for the regression relationship relating the logarithms of the parameters are also shown. R is the rainfall rate and Zh is the reflectivity factor. A - ‘0 *HC1 A Aerosol Radius, r (vim) so C 1 P 0.2 8.07xl0“8 0.392 0.81 0.5 5.01xl0“ 9 0.554 0.94 1.0 4.33xl0~ 9 0.594 0.96 2.0 2.07xl0~6 0.478 0.91 A - d„ r “1 A Aerosol Radius, r(ym) P do 0.2 7.10xl0" 7 0.602 0.90 0.5 1 .2 1 xl 0 “ 7 0.807 0.98 1.0 1.34xl0~ 7 0.855 0.99 2.0 3.15xl0~5 0.707 0.97 193 results of these analyses. The lower correlation coefficients (recall that these are for the logarithmic relationships, and therefore small changes are significant) when Z^ is used as the only estimator of A indicate that using (Z^, Z ™ ) provides an improved estimation for A. Although using R as the only estimator of A results in better estimations than when using only Z^, Fig. 6.1 illustrates the disdrometer-derived dispersion between R and A in a correlation diagram for the aerosol size r ■ 0.2 pm. mm h From the figure, for R < 10 the difference in A for the same R can exceed a factor of 30. This illustrates the need to account for DSD 6.1.2 when estimating A. Simulation The relationships described in Table 6.1 and 6.2 can be used to estimate the scavenging rates for natural rainfall to determine the applicability of the (Zjj, Z_^) method. of A for four different aerosol radii Fig. 6.2 shows the variability between (0.2-2 Pm). The solid lines indicate the scavenging rates computed directly from Eq. (6 .1 ) for actual disdrometer measurements. The crosses indicate the radar estimates of A computed using the (Z^, Z_j^) relationships of Table 6 .1 , whereas the x's denote the estimates using Z^ as the estimator using the regression formulas in Table 6.2. Estimates of A using R and/or Dq are not shown since they are not radar observables, although these relationships may be useful for future applications. The results of Fig. 6.2 indicate a very good agreement for the empirical (Z„, Z^^) estimation for all aerosol sizes. largest The discrepancy is seen at the aerosol radius r = 0.2 p m for A < 10 ^ s 194 SCAVENGING RATE, A (s'1) r = 0 .2 /x R(mmh’ ') Figure 6.1. Computed scavenging rate A and rainfall rate R scatter plot for aerosols of radius 0 . 2 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982. SCAVENGING RA T E , A (s' r * 0.2 /X 1-6 N w — re 0 20 40 60 80 I 00 I20 I40 I60 I 80 TIME(min) Figure 6.2(a). Computed and simulated time history of A for aerosols of radius 0.2 Urn corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. VO Ln R A T E , A ( s ' 1) SCAVENGING r6 >-7 .-8 o 20 40 60 80 100 I20 I40 I60 I 80 TIME(min) Figure 6.2(b). Computed and simulated time history of A for aerosols of radius 0.5 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. 196 R A T E , A ( s ' 1) SCAVENGING I Cf 6 *7 O 20 60 80 I 00 I20 I40 I60 I80 TIME(min) Figure 6.2(c). Computed and simulated time history of A for aerosols of radius 1.0 ym corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. 197 SCAVENGING RATE, A (s' r3 .-4 1-6 r7 0 20 40 60 80 I00 I20 I40 I60 I80 TIME(min) Figure 6.2(d). 198 Computed and simulated time history of A for aerosols of radius 2.0 pm corresponding to disdrometer measurements from the rainfall event of 6 October 1982 where A is the scavenging rate. 199 The Z„ estimates greatly overestimate the actual A for smaller A and H underestimate s for large A. For example, for r = 0.2 P m and A > 10 ^ the 2L, method underestimates A by as much as a factor of A, for A < 10 ^ s * the maximum overestimation is around a factor of 10. Fig. 6.3 shows the superimposed scavenging rate time plots for the same aerosol sizes (0.2-2.0 Pm). This figure illustrates dependence of A on size as well as the marked decrease in the large A for aerosol sizes in the submicron range in agreement with the "Greenfield gap." The overall A differs by around a factor of 10 for aerosol radii r * 2 pm and r * 0.5 pm and a factor of A between r * 0 . 2 pm. rates occur at r = 2.0 pm. The largest scavenging * 2 pm and r The results of these simulations demonstrate that the (Z method should serve as a useful tool to estimate A, similar to its utility for estimating rainfall characteristics and specific attenuation. The method provides an improvement over the current practices of approximating distribution employing R. DSD with an empirical, single parameter Therefore, using scavenging rates should improve our knowledge of how storms cleanse the atmosphere of aerosols via the washout process. An additional improvement in studying the scavenging processes may also be achieved by considering the aerosol size distribution N(r) and its effects on the empirical relationships derived in this chapter. 6.2 Vertical Air Velocities Several methods of employing a vertically pointing pulsed-Doppler radar for determining vertical air velocities within the radar beam RATE, A ( s ' 1) SCAVENGING IO ' 6 20 40 60 80 1 0 0 I 20 140 I60 80 TIME(min) Figure 6.3. Computed scavenging rates A showing their variability with aerosol size in the range < r < 2 ym. 0.2 200 201 have been proposed (see Section 6.2.1). Pulsed-Doppler radar provides the Doppler velocity spectrum of particles within the scattering volume. During a rainfall event, this spectrum includes the effects of different terminal fall velocities of raindrops as well as vertical air motions in the column. using This section examines the possibility of as an estimator for the terminal velocity contribution to the mean Doppler velocity seen by a vertically pointing radar and the subsequent estimation of vertical air velocities. 6.2.1 Previous Studies In earlier studies, several components of the Doppler velocity spectrum have been utilized for vertical air velocity determination. Particularly emphasized in early work were the mean Doppler velocity <v> and the minimum and the maximum velocities in the spectrum, v ^ vma x ’ and ^ore recently, the complete Doppler spectrum in multiple wavelengths are under consideration. The first study to determine vertical air velocities in the rain region employed maximum downward velocity. vmt>y (Probert-Jones and Harper, 1961).They concluded changes in vmav as a function of height were due that to changes in vertical air velocity assuming that static fall velocities of the largest drops do not change. Battan (196A) and Battan and Theiss (196-6) extended this technique by employing the lower end of the velocity spectrum (indicating upward velocity). They added 1 ms this bound to account for the fall velocity of the smallest *to drops. They also indicated that turbulence broadens the edges of the spectrum and drop size sorting would complicate the results. Rogers (196A) 202 assumed a Marshall-Palmer (M-P) exponential distribution form of the DSD and derived an empirical relationship between the reflectivityweighted fall velocity and (Eq. 6-10). Atlas et al. (1973) concluded that the methods of Battan and Rogers are subject to significant errors. Hauser and Amayenc (1981) assumed an exponential DSD in their three parameter (3P) method which does a linear least squares fit to the relation linking the DSD parameters and the vertical air velocity to the Doppler spectrum. This method also shows a large variability due to spectral broadening and the particular DSD assumption. Grosh (1983) suggested using to estimate terminal fall velocities and improve multiple Doppler wind measurements. His <vfc- ZDR> relationship was based on the vfc(D) and D q (ZjjR ) expressions by Rogers (1964) and Seliga et al. (1981), respectively, and is not considered to be a satisfactory relationship for <vt> * Sangren et al. (1984) reported on the comparison of the dual-wavelength or ratio method (Rayleigh versus Mie scattering) proposed by Walker and Ray (1974) and the previous methods. They concluded that this method, while in theory being the most accurate one with no a priori assumptions on air motions or DSD,is extremely sensitive to poor data quality such as mismatched pulse volumes and spectral artifacts. More recently, Wakasugi et al. (1986) proposed a direct method employing VHF Doppler radars using a least-squares fit of six parameters of the Doppler spectrum assuming an exponential form for N(D) and a Gaussian form for turbulence. 203 6.2.2 Doppler Velocity Components Measured Doppler velocity is weighted with the power backscattered from the particles moving in the radar volume (Battan, 1973). 00 | v S(v) dv (6-4) <v> = Zf!----------00 I S(v) dv where S(v) is the Doppler velocity spectrum obtained from the Doppler frequency spectrum (v ■ Xf/2 ) and is related to the total average power by, 00 Pr =J S(v) dv (6-5) •00 In this analysis, for simplification all velocities including vertical air motion and fall velocity which would represent motion toward a ground-based radar, are taken as being positive. Neglecting turbulence effects, the Doppler velocity (v) in S(v) has two main components, the fall velocity of raindrops v and the mean vertical velocity w of the air containing the same raindrops. Since a unique relationship between the equivalent drop size and the fall velocity exists, the components of the normalized Doppler 204 spectrum (Sn (v) * S(v)/Pr ) are related to DSD through (Doviak and Zrnid, 1984), S (w + v ) dv = au (D)N(D)dD/n n t C n (6 - 6 ) where r| is the reflectivity or scattering cross-section density. From Eqs. (6-4) and (6 -6 ), the mean Doppler velocity in still air, which is the reflectivity weighted fall velocity r can be found from D max <v > . t r D v tCfH (D)N(D)dD (6-7) max aR (D)N(D)dD For Rayleigh scattering and spherical raindrops, <vfc> can be expressed as rDmax <v > = t , v tN(D)D dD -2— -----------fDmax (6 - 8 ) N(D)D dD Conceptually, the vertical air motion can then be estimated from the mean Doppler velocity <v> and the reflectivity weighted fall velocity <vt> * w = <v> - <vt> (6-9) To estimate <vfc>, Rogers (1964) employed an empirical expression for vfc(D) and the M-P DSD to arrive at 205 <vt> = 3.8 z0,071 (6-10) Sekhon and Srivestava (1971), assuming a different DSD for a thunderstorm, derived a similar expression, <vt> = 4 . 3 Z0 (6-11) '0 5 2 Joss and Waldvogel (1970b) for various types of rainfall, found <vt> = 2 . 6 Z 0 , 1 0 7 (6-12) Rogers (1967) expanded his results to a two-parameter DSD and arrived at <vt> = 0.46 (Z/M) 1 / 3 (6-13) where M is liquid water content in g m -3 . Since fall velocity of raindrops is a unique function of the raindrop size, ZjjR is expected to be a good estimator of <vt> in that it also is a unique function of the raindrop size for good estimator of Dq. radar which scans X J> 3 cm and a To determine <vt> using ZpR , a dual polarization in n e a r l y horizontal planes would be required. Combining these measurements w i t h Doppler spectrum from a pointing radarcould thenconceivably lead When the vertical air motion inmeasurements to a measure of w. w is known, the DSD can be estimated from o„(D) J* n 6 = JL (6-14) z Sn (w + v t) dvt = D 6 N(D)dD/z (6-15) where Eq. (6-15) Indicates that, given w, N(D) can be obtained from Zjj and Sr (v ) without any a priori assumptions about the form of N(D). The difficulty in employing Eq. (6-15) is its sensitivity to small uncertainities in w. Atlas et al. (1973) indicated that errors of ±0.25 m s * can cause errors of 100% in N(D). The estimation of w from Eq. (6-9) by the use of empirical <vt>-Zjj relationships such as Eqs.(6-10), (6-11), (6-12) and (6-13) is also subject to large errors and therefore limits further the quantitative estimation of N(D) (Rogers, 1967, 198A). The next section shows that a very good estimation of <vt> from ZnD measurements appears feasible which in turn should lead to more DK reliable estimations of w from vertical Doppler spectrum measurements. 6.2.3 Model Computations In order to obtain an empirical relationship that enables Z ^ to be used as an estimator of <vfc> , simulations were performed using the 6 October 1982 central Illinois disdrometer measurements. shows a plot of the reflectivity weighted fall velocity Zpj^ for all the DSD's during this 3-h rainfall event. Fig. 6 .A <vfc> versus The plot indicates a very strong correlation between <vt> and Z ^ for all drop sizes and suggests a power law relationships of the form (6-16) The results of the regression analysis based on the linear relationships between the base 10 parameters are shown in Table 6.3. logarithm's values of these Similar < V t > z (ms-1) 207 Z DR (dB) Figure 6.4. Reflectivity weighted fall velocity dependence on ZD£ derived from disdrometer simulations where Zjjr is the differential reflectivity. 208 Table 6.3. Constants of the <vt>“ZDR relationship derived from a linear regression analysis of the relationship expressed in base 10 logarithms. Corresponding 95% confidence limits and correlation coefficients (p) are also given. <vt> is the reflectivity weighted fall velocity and Zq R is the differential reflectivity. <V Data Range A a bv " 3v Z]DR A avli *v 2 6.72 6.71 6.73 6.92 6.90 6.94 V 6V A A vl bv 2 P 0.367 0.364 0.369 0.999 0.249 0.244 0.254 0.992 0.2 < ZDR (dB) < 1.3 1.3 < ZDR (dB) < 2.6 209 relationships in Chapter 3, the table gives the estimated value of the coefficients (av , bv ) and their 95% confidence limits for the two regions, 0.2 <. Z DR < 1.3 dB >. and Z DR >. 1.3 dB. This two-section piecewise linear approach is preferred, since it helps reduce the variation between the measured and estimated parameters over the entire range of Z^R . A similar analysis was also performed for between Dq , but the correlation <vt> and Dq was not found to be as strong as <vt>- indicating that Z^R is a better estimator of <vt> than Dq. A relationship similar to Eqs. (6-10), (6-11) and (6-12) was also obtained for the same data, using Z^ as the estimator for <vt> . 6.5 shows the scatter plot of <vfc> with respect to Z^. Fig. Although <vt> and Zjj are well correlated, the spread in <vt> for a given Zjj is excessive compared to Z^R (Fig. 6 similar to the one performed for <v > .A). A regression analysis for Z^, resulted in A.O Zjj0 , 0 6 1 (6-17) the coefficients of which are within the range of the empirical relationships obtained by Rogers (196A) and Sekhon and Srivastava (1971) (Eq. 6-10) and (Eq. 6.11). These three > -Z^ relationships as well as the relationship of Joss-Waldvogel (1970b) (Eq. 6-12) are also plotted in Fig. 6.5. None of these relationships produce results as good as <vt>-Zjjp relationship. 6 .2.A Proposed Experiment The above findings regarding potential use of Z^R as an estimator 210 9 JW 8 7 in 5 SR 4 JW 3 0 I0 20 30 40 50 60 ZH(dBZ) Figure 6.5. Reflectivity weighted fall velocity dependence on Z^j derived from disdrometer simulations, including empirical <vt> - Z relationships due to Rogers (1964), Sakhan and Srivastava (1971), Joss and Waldvogel (1970) and this work, indicated as R, SR, JW and D, respectively. Z is the reflectivity factor. 211 for <v^> suggests several possibilities for testing its utility, especially in conjunction with vertical Doppler velocity spectrum measurements for estimating of N(D) and w. One such possible experiment is described here. - A vertically-pointing radar performs Doppler spectrum measurements continuously at one or more range gates to determine S(f) from which S(v) is derived. performed with Simultaneous a second radar, narrow sector scanning in the horizontal plane at different elevation angles over the verticalpointing radar or in the vertical plane containing the vertical-pointing radar. Attempts should be made to match the resolution volumes of the radars through siting of the radar, choice of antenna patterns and spatial averaging. Also, the elevation angle of the Zp^ radar should not exceed 1 0 ° in order to minimize any errors due to aspect angle complications. - Having chosen common scattering volumes for analysis, Z ^ is used to estimate <vt >. - w is then obtained from w « <v>-<vt> where <v> is the reflectivity weighted mean Doppler velocity seen by the vertically-pointing radar. - N(D) is approximated from S(v) and w from N(D) - ZD ' 6 - g £ Sn (i + vt ) where S (w + v.) = S (v). n t n 212 - From N(D), various rainfall parameters such as R, M, D q are estimated and can be compared with the corresponding method - Disdrometer arrays on the ground at the vertically-pointing radar site can provide ground truth data to compare with the radar estimates. This combined experiment should be performed as soon as possible in order to test the ZDR“<vt> hypothesis developed in this section. CHAPTER 7 SUMMARY AND CONCLUSIONS 7.1 Review of the Problem Radar has the ability to provide information about the atmospheric medium and scatterers over large geographical areas from a single location in real time. This capability represents an important improvement over ground and aircraft-based systems, thereby reducing costs and delays in information transmission and analysis. Conven tional radar remote sensing techniques employ the backscattered return power at a single linear polarization to estimate rainfall parameters such as rainfall rate (R), liquid water content (M) and drop size as well as the propagation-related parameters, specific attenuation (A) and relative phase shift (A<J>) of rain-filled media. Extensive studies using this technique of employing a single radar observable indicated that the natural variability in raindrop size distributions (DSD) often results in unsatisfactory estimations of these parameters. For example, rain-parameter diagrams, based on exponential or gamma model distributions, show that errors of one to three orders of magnitude in radar estimates of these parameters are possible. Current radar remote sensing techniques are beginning to employ multi-parameter radar measurements to obtain additional information 213 214 about various characteristics of the atmospheric medium and scatterers. One of the most promising techniques is the differential reflectivity or method, introduced by Seliga and Bringi (1976), which utilizes the backscattered returns at two orthogonal, linear polarizations: horizontal and vertical. technique is based on three properties: As applied to rainfall, this (1 ) raindrops deform into nearly oblate spheroidal shapes as they fall, and this deformation increases with increasing drop size; (2 ) their symmetry axes are mutually aligned along the vertical direction, and the deviation of raindrops from these axes is negligible; and (3) the size distribution of raindrops is reasonably dependent on two parameters. Based on these properties, a dual linear polarization radar measuring the difference between the reflectivity factors at horizontal and vertical polarizations (in dB), introduces a second radar observable in addition to Z^ to provide improved estimates of the rainfall parameters R, M and Dq as well as the specific attenuation and relative phase shift at either polarization. (Chapter 6 Simulated results ) indicate that the Z^^ method also has the potential of improving estimation of other parameters which are dependent on DSD variations such as the scavenging rate of aerosols and reflectivity weighted fall velocities of hydrometeors. This study examined the application of the Z ^ method in the estimation of rainfall parameters by comparing radar-derived estimates with estimates of the same parameters obtained from ground-based measurements using disdrometers and raingages. The comparisons accounted for the differences in resolution volumes and physical locations of the radar- and ground-based systems. The temporal evolution of the rainfall parameters were then compared to verify the validity of the Z ^ method. To achieve these results, empirical relationships describing the dependence of the rainfall parameters on outlined based on simulations derived from disdrometer measurements obtained during a field experiment on 6 October 1982 in central Illinois. The method to estimate rainfall parameters was applied for three case studies taken from the 1982 Ohio-State Precipitation Experiments (OSPE) and the MAYPOLE '83 and '84 projects. This work also described the application of the Z ^ method to predict C-band reflectivity profiles from S-band measurements and compared the results with actual C-band measurements. This task included the estimation of C-band specific attenuation and measurements. Potential applications of the Z ^ method to scavenging of aerosols and estimation of vertical air velocities were also considered, based on simulations derived from an existing disdrometer data base. 7.2 7.2.1 Simulations and Experimental Results Disdrometer Simulations In Chapter 3 the relationships linking rainfall parameters R, M simulations of Seliga, Aydin and Direskeneli (1986). These simulations produced empirical, power-law relationships between the 216 radar and rainfall parameters. Error analyses, based on these and other (Zj. , Zjjr) rainfall relationships derived from exponential and gamma model DSD's, are also presented. The results for R are also given for three Z-R relationships, including an empirically derived relationship. The errors for these relationships were computed in terms of the normalized bias (NB) and normalized standard error of the difference (NSED) in addition to two other commonly used error measures, average difference AD and absolute average difference AAD. The error values obtained from these simulations form the lower bound for any estimate derived from these relationships for a typical rainfall event, since no experimental error due to radar observations are involved. The error analyses indicated that the empirical relationships, obtained from the simulations employing (Z^, result in the lowest error estimates for the rainfall parameters considered. 7.2.2 Case Studies In Chapter 4 three case studies were undertaken applying the (Z^, method of estimating rainfall parameters under diverse field conditions. The estimation of radar-derived parameters utilize the empirical relationships obtained from the simulated results of Chapter 3. The results pointed out significant improvements in R and M estimation using (Z^, Zq „) radar observables compared to using Z^ alone. Estimating D q from Z ^ also resulted in a satisfactory comparison with disdrometer ground-based measurements. 217 7.2.2.1 OSPE Disdrometer Comparisons The two-parameter estimation method employing (Zjj, Z ^ ) was tested in the 29 October 1982 central Illinois case study. The results of radar-derived parameters obtained from 179 radar scans at a constant elevation angle of 0.9° were compared with the disdrometer which was located 47.1 km away from the radar. A systematic approach to select the appropriate radar volume to be compared with the disdrometer is outlined. This included a cross-correlation analysis between the (Z^, Z^^) pairs obtained from the radar swath and disdrometer-derived values. This approach led to a definition of the radar spatial averaging needed to match the temporal averaging of the disdrometer. Results of various (Z^, Z ^ ) averaging schemes for deriving the radar rainfall parameters are also compared. empirical (Z^, NSED. The relationship for R produced 9.1% NB and 24.4% These values were compared to a 30.8% NB and 35.8% NSED for the best Z-R relationship, indicating that a significant improvement in R was obtained with the Z ^ method. This approach for making radar and ground-based samples is also considered useful for future rainfall parameter comparisons where significant distances between radar and ground-based measurements are involved. Several possible explanations for the larger error estimates over the simulated results presented in Chapter 3 are also outlined. 7.2.2.2 MAYPOLE *83 Disdrometer Comparisons This field experiment on 4 June 1983 involved the CP-2 radar and disdrometer measurements obtained from a site located a short distance 218 away from the radar (6.35 km), resulting therefore in a narrow radar beamwidth. Since the effects of different fall velocities for different size drops become important in such a case, transformation of the disdrometer measurements to the radar altitudes was employed. By accounting for the horizontal wind transport effects, the regions where the radar measurements were most representative of the ground-based observations were estimated for each radar elevation angle. The time diagrams and the statistical analyses of radar- and disdrometer-derived radar and rainfall parameters were in very good agreement. The results also pointed out the importance of accounting for drop size sorting in similar studies in order to obtain satisfactory results. 7.2.2.3 MAYPOLE '84 Raingage Comparisons This field experiment involved considerably higher rainfall rates (R >120 mm h *). max The radar estimates were obtained from different CAPPI's (Constant Altitude Plan Position Indicator) by transforming the data from radar space to three-dimensional Cartesian coordinates using successive bilinear interpolations. This was done with the CEDRIC computer code, developed by the National Center for Atmospheric Research. The fall time and wind transport of the raindrops were accounted for in the comparisons with the ground observations. Error analysis, using the raingages as the reference, resulted in a 6.8% NB for the empirical (Z„ , Zpg) relationship compared to 14.8% and 16.6% for two Z-R relationships. Similarly, NSED of the (Z^, Z^^) estimation was 30.6% which was considerably better than the NSED's of 45.4% and 53.9% for the same two Z-R relationships. 219 7.2.3 C-Band Profiles In Chapter 5 the predicted and measured reflectivity profiles of a C-band (5.A5 cm) radar (CP-4) are compared using S-band ( Z ^ q , Zj^) measurements (CP-2) obtained at a different site. The comparison scheme involved the determination of the relationships linking (Z^g, Zg^) to (Zjjg, Ay,.). Prediction of the observed C-band reflectivity factors Zjj,.1 from ( Z^g, Z ^ ) to be compared with simultaneous CP-4 radar measurements involved first estimating ( Z ^ , ) and then accounting for the accumulated attenuation along rays originating from CP-4. Predicted contours were then obtained by combining the individual ray results. These comparisons resulted in a good agreement between the predicted and apparent reflectivity profiles at C-band for the rainfall event. The standard error for the comparisons was 2.4 dBZ for Zjj,.1 in the range of 20-55 dBZ. This study demon strated that (Zg, Z^jj) rainfall measurements by a radar operating at a non-attenuating S-band wavelength can be used to estimate the attenuation and scattering of microwaves originating from a radar which operates at an attenuating wavelength and is located at a different site. 7.2.4 Other Applications The potential use of Z ^ discussed in Chapter 6. in two other applications have also been Precipitation scavenging is responsible for most of the total aerosol removed from the atmosphere, and the scavenging rate A of the aerosols by the washout process is strongly dependent on the size distribution of the raindrops. The question of whether the Z ^ method may serve as a useful tool to estimate A and 220 provide improvements over the current practice of relating A with R is examined. Conceptually, the scavenging rates for aerosol size similar to its use for distributions can be computed rainfall parameter estimation, since the Z^R method accounts for changes in DSD. disdrometer Simulated results from a rainfall event measured by indicate that A can v a r y for the same R. by as much as a factor of 30 Empirical relationships linking (R, D q ) as well as using a single parameter R or D q were obtained. Results of the regression analyses for these simulations show significant improvements for using (ZR , ZDR) over R, indicating an excellent potential of the Z^R method for remotely inferring aerosol washout scavenging rates. Estimation of vertical air velocities may also benefit from improved estimates of raindrop characteristics. Vertically pointing Doppler radars measure the reflectivity weighted mean Doppler velocities which include the weighted mean fall velocity component <v^> of hydrometeors. Simulations indicate that these fall velocities can be estimated from Z^R which, when combined with Doppler measurements, can yield the remaining vertical air motion component. A possible experiment which involves a dual polarization radar scanning the volume over the vertically-pointing Doppler radar is described for this purpose. Simulation results relating ZpR and <vfc> are also given along with a - relationships. Z^R provides a significant improvement for fall <vt > relationship for comparison with existing velocity determination over the standard method. This implies that the DSD can also be obtained more accurately from the spectrum, since the vertical air velocities would be known more accurately. 221 7.3 Recommendations for Future Research 7.3.1 Rainfall Studies The improvements obtained by the method in estimating rainfall parameters suggest that additional research in this area employing dual polarization radar would provide detailed information about the statistical nature as well as the spatial and temporal variability of rainfall. By employing dense disdrometer and raingage networks, coupled with radar observations, higher resolution varia tions in R can be identified. Longer periods of observation of rainfall events will also be required to obtain statistical information on R within an area. These data would be important for reliability studies of communication links, especially along groundbased and earth-satellite paths. Additional comparisons of radar and disdrometer. and/or raingage measurements, especially at high R's, should also be performed at different locations throughout the world in order to test the methodology more completely. Such measurements would also provide important information about the DSD characteristics of these storms. 7.3.2 Hydrology, Flash Flood Forecasting and Weather Modification The method should be an important tool in hydrology for estimating water resources over large areas; in flash flood forecasting for more timely warnings and in weather modification by providing accurate, quantitative estimates of rainfall parameters over both short and long time durations. The Z_.p method should also 222 contribute to these topics through improved characterization of rainfall events by supplying measurements in areas without groundbased measurement systems or additional information in the presence of such other observations. 7.3.3 Attenuating Wavelengths Prediction The scheme describing the estimation of reflectivity profiles in Chapter 5 can also be extended to other attenuating wavelengths such as X- or Ka -bands. In addition, the prediction scheme allows for the estimation of Z ^ profiles by a similar procedure involving profiles. and Zy This has possibly important applications in attenuation studies involving radars operating at attenuating wavelengths. Characterization of storm cells and the presence of different hydrometeor phases may also be possible by comparing the predicted and measured profiles of apparent reflectivities at attenuating wavelengths. In studies involving more than a single radar, such as in multiple-Doppler systems, accurate absolute and relative measure ments of radar observables should be achieved by intercomparing predictions and measurements. 7.3.A Cloud Physics. Scavenging. Earth Energy and Radiation Budget Since Z ^ is an estimator of the drop size, processes involving the evolution of hydrometeors can benefit from improved estimates of size distributions at any stage during cloud formation. Similarly, scavenging processes involving the removal of aerosols and other 223 pollutants are expected to benefit from the improved estimation of DSD's during precipitation. This latter finding suggests that studies aimed at estimating the scavenging rates for different types of rainfall events should be undertaken. Another important area of application is the effect of liquid water contained within clouds and its ramifications for the energy and radiation budget of the Earth. Studies examining the effects of DSD and liquid water content variations on the albedo characteristics of storm systems should provide improved understanding of ecological balance and climate modeling studies. APPENDIX Radar Specifications 224 225 Specifications of the CP-2 and CP-4 Radar Systems Radars Parameters CP-2 CP-4 Doppler Capability Yes Yes Antenna Shape Parabolic Parabolic Diameter 8.5 3.67 Half-Power Beamwidth (deg) .96 1.06 43.9 41.2 System Gain (dB) Radome on 43.8 Radome off First Side Lobe Level (one way) (dB) -23 to -30 Radome on -16 to -22 -22 to -25 Radome off Polarization dual single Rotation Rate (deg/sec) 0-15 0-25 Wavelength (cm) 10.67 5.45 Frequency (MHz) 2809 5500 Peak Power (kW) 1200 200-400 .2 to 1.5 1 Transmitter Pulse Width (y sec) Pulse Repetition Frequency (Hz) 480-1500 500-2000 600-700 (4.2) 750 (5.5) 1. 8 1. 8 Receiver Noise temperature (Noise figure dB) K Log video bandwidth (MHz) 226 Radars Parameters_________ Linear channel bandwidth (MHz) CP-2______ CP-A 1 0.9 (Adjustable) Transfer Function Doppler Linear, Limited Linear, Limited Intensity Log, Linear Log, Linear 90 90 ■116 -109 -18 -6 Dynamic Range Log Channel (dB) Sensitivity Minimum detectable signal (dBm) Equivalent reflectivity factor at 25 km (dBz) (Rain) 227 CHILL Radar System Specifications (Seliga and Mueller, 1982) 10 cm Radar Transmitter: Peak Power Frequency Pulse Width Pulse Repetition Frequency 600 kw 2700-2800 MHz 1.0 ys 950 Hz Antenna: Size Gain Beamwidth Polarization 8.5 m parabolic reflector A3.3 dB l.(P E- and H-planes H or V Coherent Receiver: Linearity Noise Figure Dynamic Range Minimum Detectable Signal ±0.5 dB 11 dB 60 dB -103 dBm Incoherent Receiver: Type Noise Figure Dynamic Range Minimum Detectable Signal Logarithmic 11 dB 60 dB -103 dBm REFERENCES Al-Khatib, H. 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