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<br />16 <br /> <br />The model combines the vertical equation of motion, the first law of <br /> <br />thermodynamics, and equations of mass continuity of air, water vapor, liquid, <br /> <br />and solid hyclrometeors. All quantities represent average values of the parameters <br /> <br />over the cross section of the air column per unit mass of air and are understood <br /> <br />to be functions of both the spatial location in the vertical column and time. All <br /> <br />parameters in the model are, whenever possible, expressed in terms of quantities <br /> <br />quasi-conservative upon vertical transport to simplify model equations. Thus, we <br /> <br />will deal with potential temperature in preference to temperature, gm/kg rCJther <br /> <br />than gm/m 3, number/gm instead of numbe'i"m 3, and so on when expressing parameters <br /> <br />within the model. <br /> <br />Equations of Motion <br /> <br />Following Silverman and Glass (1973), the equation for the vertical component <br /> <br />of velocity can be written as: <br /> <br />~~- -W ~~ + a~z (Km ~~] <br /> <br />[8 I - 8 I ] <br />+g e _ Q _ Q _ <br />e I L I <br />e <br /> <br />8K W <br />m <br />R2 <br /> <br />+ AW <br /> <br />(eq. 14) <br /> <br />where: A = 0 <br /> A 2 UR <br /> = <br /> R <br /> <br />when UR ~ 0 <br /> <br />when UR < 0 <br />