An elementary parcel model with explicit condensation and supersaturation |
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| Authors: | RR Rogers |
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| Institution: | Department of Meteorology , McGill University , Montreal |
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| Abstract: | The development of droplet size, supersaturation, and temperature in an ascending, unmixed parcel of cloudy air was investigated using a numerical model in which condensation and supersaturation are explicitly calculated. Of particular interest was the steady‐state value which the super‐saturation attains, and the time required to reach this value. The results were found to be in reasonable agreement with an approximate analytical solution of the equations that predicts a steady‐state supersaturation equal to G(p, T)U/vr, where G(p, T) is a known thermodynamic function of temperature and pressure, U is the updraft speed (assumed constant), v is the number of droplets per unit mass of air (assumed constant), and r is the droplet radius. The approach to this limiting value is very nearly exponential, with a time constant equal to G(p, T)/Q 1 vr, where Q 1 is a function of temperature. Without giving up the possibility of approximate analytical solutions, the equations can be elaborated to allow an accelerating updraft or to simulate the effects of rapid droplet coalescence. |
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