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<br />DECEMBER 1978 <br /> <br />R. E. CARBONE AND LOREN D. NELSON <br /> <br />2309 <br /> <br /> <br />10-1 <br /> <br />(a) Spontaneous <br /> <br />MODEL <br /> <br /> 10-2 <br /><t <br />I <br />E <br />u 10-3 <br />0 <br />Z <br /> 10-4 <br /> <br />~~ <br /> <br />v <br />, v <br />"" "vv <br />.... ''Zv <br />, ." '~ "' <br />.:-'- '''-.. '-. <br />" '~_.... ~" <br />~""'-~ <~ <br />"':-~"~~ <br />~':"~ '-, ' <br />"'-0'... l..''- <br />'..P ~'""'''''' '- <br />"O..:,~~,:.::..~ <br />....,',g-... <br />'",,- ' <br />.... ~~~"'" <br />v , "~~"" <br /> <br />, ~' <br />, , <br />.... .... <br />v ......::::"'~......... <br />:---....:...~D <br />v ' "-.:: <br />'" <br /> <br />Growth 0 0 0 <br /> <br />Dissipation " " ". <br /> <br />10-5 <br />o <br /> <br /> <br />0.8 <br /> <br />1.'6 2.4 . 3.2 <br />D (mm) <br /> <br />4.0 4.8/0 <br /> <br />(b) Collision Breakup <br /> <br />,.<~ <br /> <br />"'... <br /> <br /> <br />COLLISION <br />,'-. 8 SPONT. <br />'..'-. Growth - <br />'''~ Dissipation -.-. <br />'.\:--, <br />',,, <br />'\, <br />"~ <br /> <br />~~ <br /> <br />SPONTANEOUS <br /> <br />0.8 <br /> <br />1.6 2.4 3.2 <br />D (mm) <br /> <br />4.0 <br /> <br />4.8 <br /> <br />FIG. 6. (a) Average drop spectra for the model and observations at R=27.S mm h-l during growth and dissipation <br />stages. IT = 1 limits are shown for observations and Marshall-Palmer spectrum for R = 30 mm h-l is also shown. Model <br />results do not incorporate the collision breakup process. (b) Model results as in Fig. 6a together with model results in- <br />cluding the collision breakup process. <br /> <br />drops >3 mm. The model spectrum for the dissipation <br />stage approaches the MP solution which is shown for <br />R=30 mm h-I.4 The observations show evolution in <br />this direction but do not reach the MP extreme. <br />Fig. 6b shows the model spectra for all processes <br />including collision breakup as formulated by Young <br />(1975). In this case it is clear that both growth- and <br />dissipation-stage results change negligibly at cloud base <br />compared to the pure spontaneous breakup case. These <br />results strongly suggest that collision breakup is not an <br />important process at and below cloud base; however, <br />the absence of change is not in itself conclusive. The <br />only significant change (microphysical or thermo- <br />dynamic) which resulted from introduction of collision <br />breakup was a sharp increase in the number concentra- <br />tion of large hydrometeors 3-4 km above cloud base. <br />Apparently the fragment distribution generated by <br />collision breakup facilitates the rime growth of ice and <br />the coalescence growth of rain aloft. Increases from 50 <br />to 60 dBZ occurred for ice particles and from 25 to 40 <br />dBZ for water drops. There was no significant change <br />either in ice content or liquid water content in these <br />reglOns. <br />Another way to illustrate temporal evolution of the <br />spectra is shown in Fig. 7. Here the exponential spec- <br />trum parameters No and ^ are shown as a function of <br />rainfall rate and time. Time is indicated on each figure <br />in minutes from the initiation of moist convection in <br /> <br />4 The MP distribution is given for MSL terminal fallspeeds. <br />Observations and model results are density adjusted to ~3 km <br />MSL. <br /> <br /> <br />the model. The marching of each parameter in time from <br />low values to high ones is apparent in Fig. 7. MP values <br />are indicated by solid lines, and it can be seen that the <br />model closely approaches these values in the dissipa- <br />tion stage of storm evolution. Also shown in Fig. 7 <br />are the regressions from all observations, stratified by <br />growth and dissipation stages. There is substantial <br />quantitative agreement between the model and observa- <br />tions in the growth stage when No ranges from two to <br />three orders of magnitude below the MP value of 0.08 <br />cm-4. The model shows ^ as essentially constant in the <br />growth phase (~8 ,em-I) whereas the observations <br />indicate a gradual increase (trom 5 to 8 em-I) in the <br />1-20 mm h-I range. There is qualitative agreement <br />betweeJl the model and observations in the dissipation <br />stage in that both parameters are larger (for equivalent <br />rainfall rate) than in the growth stage. As previously <br />shown in Fig. 6, the observations do not approach MP <br />values as the model does. <br />The Srivastava (1971) solution in Fig. 5 appears to <br />bracket the observations in the sense opposite to MP- <br />apparently representing a limiting case of spectral form <br />in growth stage echoes. Although Srivastava did not <br />include vertical air motion and sedimentation in his <br />model, the similarity of spectral form with measured <br />spectra is considered to be physically meaningful <br />provided certain initial conditions are satisfied. <br />Srivastava permitted stochastic coalescence and spon- <br />taneous breakup to reach an equilibrium condition. <br />The preponderance of numerical and experimental <br />evidence, which was reviewed in Section 1, indicates <br /> <br />