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2312 2.0 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 35 A vs 8 (2 = ARB) 1.8 + o Growth + Dissipation 1.6 + + + ++ + 0 0 0 0 0 0 + 0 0 0 500,0 1000.0 1500.0 CD 1.4 1.2 1.00'0 A FIG. 10. Coefficient (A) versus exponent (B) resulting from Z-R regressions. Growth stage regressions (squares) are sharply separated from dissipation stage regressions (plus signs). southwest flank of the precipitation regions correspond- ing to points Ag. It is suggested once again that size sorting due to updraft in growth stage storms is indi- cated by extension of the parametric cycle to particu- larly low values of No and A. 7. Implications for radar estimation of rainfall One of the most important factors in conventional radar estimation of rainfall is the variability of drop spectra. The most common technique is to empirically or theoretically determine suitable power law rela- tionships between reflectivity factor and rainfall rate of the form Z=ARB, where Z is in mm6m-3 and R in mm h-1. Fig. 10 shows the results of regressions per- formed on the observed storms for parameters A and B. Growth stage values are indicated by squares and dissipation stage data by plus signs. Each point on the plot represents one aircraft penetration through 5-12 km pathlength of rainfall. Maximum rainfall rates within each pass range between 20 and 70 mm h-1 and minimum rates extend to 0.1 mm h-1. Growth and dissipation stage regressions are clearly separated. Growth stage relationships generally have coefficients > 500 and exponents < 1.45, whereas the reverse inequalities are evident for dissipation stage rain. Average Z-R relationships for all data from these storms are as follows: Z = 763R1.365 Z = 400R1.56 (growth stage) (dissipation stage). Fig. 11 shows these mean relationships together with the extreme regressions obtained for growth and dis- sipation stage samples. Extreme relations are defined as those which deviated most from the growth-stage and dissipation-stage averages for any single rainshaft penetration. Also shown are the model Z-R points as a function of time. The largest errors in rainfall rate estimation occur at low reflectivity values and all relationships converge at approximately 47 dBZ and 20 mm h-1. For Z=30 dBZ the extreme regressions yield rainfall rates of 0.7 and 2 mm h-1 in growth and dissipation stage echoes, respectively. If some mean relationship were utilized, rainfall would be over- estimated initially and then underestimated at later times. The predominance of updraft in the early stages of echo development and downdrafts in the late stages will further increase radar estimate bias, since the regressions are based on liquid water flux in still air. Similar arguments pertain to spatial variability where overestimates will result on the southwest (updraft) flank of the echoes and underestimates on the northeast flank. It is evident from these data that radar estimation of rainfall may be elaborated to include variable parameters Z = A (x,y,z,t)RB(x,y,z,t) such that anticipated size distribution variability as a function of position within an echo and age of the echo may be accommodated. While somewhat cumbersome, this approach is clearly within existing computational capabilities. A limiting factor, however, is the probable lack of generality over a wide range of convective storm situations, since the drop spectrum emanating from cloud base is wholly deterIIlined by the particular dynamic and microphysical structure. While similarities no doubt exist for certain environmental conditions and geographic locations, the matrix of possibilities is quite 60 50 '" E "- <D 40 E E N CD "0 2 vs R Relationships - 763 RI.36 (mean, growth stage) -- 400 R1.56{mean, dissipation) Extremes + + + Model (min) 29 + + + + 37 + + 39 20 + 49 10 R (mm/h{l) 100 FIG. 11. Plots of mean and extreme Z-R relations including model results as a function of time. Note convergence of all regressions near 47 dBZ, 20 mm h-1.