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<br />5 <br /> <br />numerically simulate cumulus convection as a series of discrete but interacting <br /> <br />Lagrangian "parcels. II While such a scheme retains the past "history" of each <br /> <br />parcel, great difficulties arise in allowing realistic interactions between parcels. <br /> <br />Unless all state parameters in a parcel vary together during a parcel-parcel <br /> <br />interaction,a new and discrete parcel will be formed to continue further inter- <br /> <br />action and parcel multiplication. Unless drastic simplifications are made, soon <br /> <br />there are too many "parcels" for cost-effective numerical simulation to continue. <br /> <br />This lack of realism in continued inter-parcel interactions is the basic fault of the <br /> <br />Lagrangian system. <br /> <br />Virtually all multi-space-dimensional convection flow field models (Ogura <br /> <br />[1971], Orville [1970], etc.) use the Eulerian approach, sacrificing knowledge of <br /> <br /> <br />the past time history of a particular cloud entity in return for knowing the in- <br /> <br /> <br />stantaneous values and fluxes of relevant parameters at a large number of regularly <br /> <br />spaced points within the cloud. <br /> <br />Detailed one-space-dimensional microphysical models of cloud structure <br /> <br />are also overwhelmingly Eulerian. This has occurred predominantly due to the in- <br /> <br />clusion of stochastic coalescence in such detailed microphysics. Were the frame- <br /> <br />work anything but Eulerian, then each 2-particle collision would create a previously <br /> <br />nonexistent particle ("parcel") leading to almost immediate numerical breakdown. <br /> <br />The Eulerian method has been carried over from the coalescence terms <br /> <br />and applied to spatial transport terms as well, resulting in a much more realistic <br /> <br />simulation of interactions and transport between and among the different regions <br /> <br />..,; <br /> <br />~ <br />