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<br />19 <br /> <br />While all the terms in the previous equation are retained in the calculation of <br /> <br />UR to maintain mass continuity I it can be seen that the dominant terms that UR <br /> <br />balances are the accelerations of the vertical updraft and the decrease in air <br /> <br />- <br /> <br />density with height. This is an agreement with intuitively reasonable arguments. <br /> <br />Thermodynamic Equation <br /> <br />The thermodynamic equation for the rate of change of cloud temperature may <br /> <br />be written as: <br /> <br />de ae d ~ ~ e~ 8 Kh <br />-=-W-+- K ~--(e-e)+A(e-e) <br />at dZ dZ h Q Z R2 . e e <br /> <br />L L <br />+ CV (DQCEW) +...!... (DQCFW!) <br />C <br /> p p <br />L Lf <br />+ CS (DQCE!) +c (DQ FW) <br /> p p <br /> <br />(eq. 20) <br /> <br />L <br />+ ~ (DQFCWI) - (DQM/) - (DQH I) <br />p <br /> <br />where e = potential temperature <br />Kh = eddy conductivity for heat <br />L = latent heat of condensation <br />v <br />Lf = latent heat of fusion <br />L = latent heat of sublimation <br />s <br />C - specific heat of air at constant pressure <br />p <br />DQCFW = instantaneous mass rate of condensation on water drops <br /> <br />'0 <br /> <br />DQCFWI = instantaneous mass rate of condensation of water on ice <br /> <br />at T > T <br />o <br />