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<br />- 55 - <br /> <br />relationship can be calculated. which is Z = 296 . R1.47. <br /> <br />'E <br />E <br />~ <br />o <br />Z <br /> <br /> <br />!=ig. 9: Measured drop-size distributions (dot- <br />ted lines) compared with best-fit e~ponential <br />curves (straight lines) and distributions re- <br />ported by others (dashed lines). (From Marshall <br />and Palmer. 1948.) <br /> <br />10- <br />~ <br /> <br />4 <br /> <br />0, mm <br /> <br />It is obvious from Fig. 10 that not all drop size distributions have the simple expo- <br />.nential fonn. Yet measurements from many diffBrent regions have shown that an exponential <br />tends to be the limiting form as individual samples are averaged. In Fig. 11 size distribu- <br />tions summed over the entire precipitation occurrence are shown for drizzle. widespread <br />rain and thunderstonn rain together with the typical height dependence of ::the radar re- <br />flectivity factor Z in these situations. It is seen in Figs. 10. 11 and Table 2. which con- <br />tains the relations between the parameters for the distributions in Fig. 11. that No varies <br />widely from one rain to another. <br /> <br />Table 2: Parameters of tne drop size distributions of Fig. 11. <br /> <br />type of precipi- No A-R Z-R Bright Band <br /> tat ion m-3mm-1 [A in mm-1 [Z in mm6m-3 <br /> R in mm/h] R in mm/h] <br />drizzle 30000 A = 5.7 R-O .21 Z = 140 R1.5 weak or none <br />wide spread rain 8000 A = 4.1 R-O.21 Z = 250 R1.5 heavy <br />thunder stonn 1400 A = 3.0 R-O.21 Z = 500 R1.5 none <br /> <br />Indeed. Waldvogel (1974) has demonstrated that No is not constant even during a particular <br />precipitation episode and has tenned this phenomenon "No-jump". The exponential approxima- <br />tion. however. is seen to be reliable in most cases. We therefore use No and A to represent <br />a raindrop spectrum. Instead of determining these two parameters from a least square fit of <br />the data points in a log N vs. 0 plot. which can lead to erroneous results due to a merely <br />qualitative interpretation of the spectrum. we calculate the two quantities W(mm3m-3). the <br />water content and Z(mm6m-3). From these. reprl:lsentative values of No and A can be calculated <br />using the transformation equations (Waldvogel, 1974): <br /> <br />No = .H~94/3lir/3w = 446 {it/3W; A = (~: f/3(it/3 = 6.12 (~r/3 . (9) <br /> <br /> <br />A very interesting feature of equation (9) is the possibility to determine microphysical <br />parameters (No. A) by directly measurable bulk quantities (W. Z). The procedure to deter- <br />mine all the relevant rain parameters (W, R. Z, No. A) from measured drop size distributions <br />will be given below. <br />