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<br />o. <br /> <br />r.' <br /> <br />,. <br /> <br />r~ <br /> <br />lor' <br /> <br />i, <br />, <br />I , <br /> <br />. ' <br /> <br />!.-- <br />I. <br /> <br />". <br /> <br />: . <br />L.., <br /> <br />. <br /> <br />8 = S(Z) + 8'(z) + 8"(x,t) = S(1 + ,.) <br /> <br />T = T(z) + T'(z) + T"(x,t) <br /> <br />p = ji(z) + p'(z) + p"(x,t) <br /> <br />(1) <br /> <br />. p = p(z) + p'(z) + p"(x,t) <br /> <br />q" = q~(z) + q:(x, t) <br />where , is the potential temperature, T the absolute temperature and p, p and q", <br />respectively are the pressure, density and the water vapor mixing ratio. <br /> <br />The momentum equation~ which includes the drag forces of the water and ice <br />substances can be written as, <br /> <br />~V +plk x V =- Vp" <br />Dt <br /> <br />(2) <br /> <br />[LJ"" ] _ <br />_ u "p UTi; <br />+ kpg -=- + eoq - -:. - qc - qa - qiA - qiB +-. <br />, "7P 8z; <br /> <br />The second term on the left of (2) is the Coriolis force where k is the unit vertical vector, <br />Jthe constant coriolis parameter and V the three-Qi"3'"T'slonal velocity vector. The second <br />term on the right is the buoyancy and water and precipitation loading terms. qc, CUl, qiA, <br />and qiB are the eloud- and rain-water, and the ice and graupel mixing ratios respectively. <br />The parameters ~ = (R,,/R,,)-1, with R" and R", being the gas constants for dry air and <br />water vapor and ..., = Cp/C" represents the ratio of the specific heats of air at constant <br />pressure and constant volume. The third term OD the right is the stress tensor T, due <br />to sub-grid scale turbulence and mixing processes. The .tress tensor i. parameterized <br />according to the nrst-order theory SmagoziDsky (1903) and Lilly (19'02). Clark (1979) <br />gives a description of this scheme in terms of an eddy viscosity term K",. Finally, the mass <br />continuity equation. for air is apprnrimated in the anelastic form by <br /> <br />28 <br />