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<br /> <br />including the updrafts within the cloud as well as the subdoud How ,in order to capture <br />physically meaningt'ul Lagrangian time scales of pariicle trajectories. It is only at this <br />level of sophistication that the present and future modelling studies can playa lead role <br />in testing various seeding hypothesis and furthering the U11derstanding of certain physical <br />processes. <br /> <br />f'" <br />I <br />L. <br /> <br />Considering these requirements the three-dimensional, time-dependant, non- <br />hydrostatic, anelastic model developed by Clark (1977, 1979), Clark and Farley (1984) <br />and Clark and Ball (1991) which employs a terrain following coordinate transiormation <br />was chosen to conduct the modelling studies. <br /> <br />( ". <br /> <br />2.2.1 Model equations <br /> <br />r' <br />i <br /> <br />The model employs a form of the anelastic approximation with expansion of the <br />thermodynamic variables aroU11d vertical profiles of an idealized atmosphere with constant <br />stability iDltead of constant potential temperature as in the Ogura and Phillips (1962) case. <br />The idealized atmosphere is considered to be in a mean How corresponding to hydrostatic <br />and geostrophic balance. The thermodynami<: variables are separated into a basic state, <br />terms with tilde, plus perturbations from the basic state represented by a prime. The base <br />state and the sum of the base state plus perturbation are both in hydrostatic balance. <br />The double prime terms represent the three-dimensional time-dependant deviations of the <br />variables, finally giving <br /> <br />L. . <br /> <br />, <br />.1 <br /> <br />r' <br />i <br />I <br />L <br /> <br /> <br />27 <br /> <br />. <br /> <br />.. <br /> <br />. <br />