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<br />17 <br /> <br />where: K = eddy viscosity <br />m <br />g = acceleration of gravity <br /> 6' = virtual potential temperature in cloud <br /> 6' = virtual potential temperature in environment <br /> e <br /> OL = liquid water content <br /> 0, = ice water content <br />R = cloud radius <br /> UR = radial advective velocity <br /> The terms on the right of equation (1) represent, from left to right, the <br /> <br />changes in vertical velocity due to advection, vertical turbulent diffusion, buoyant <br /> <br />'acceleration, turbulent entrainment, and dynamic entrainment. This formulation of <br /> <br />the turbulent entrainment term, hereafter referred to as K-entrainment, is the <br /> <br />parameterized transformation of the expression for horizontal turbulent diffusion <br /> <br />given by Priestly (1953). <br /> <br />The so-called dynamic entrainment term represents the systematic inflow or <br /> <br />outflow of air that is required to satisfy mass continuity. The dynamic entrainment <br /> <br />term is necessitated by the assumption of a constant radius cloud. If the radius of the <br /> <br />cloud were allowed to vary in accordance with the effects of mass continuity, it <br /> <br />would generally be smaller than the assumed radius below the updraft maximum and <br /> <br />larger above it. Entrainment of environmental air, below the updraft maximum <br /> <br />where UR <0, results, therefore, in a significant dilution of the per unit mass value <br /> <br />of the cloud parameters when averaged over the assumed cloud radius. Detrainment <br />