TABLE 81 325 



RATE OF CONDENSATION IN ASCENDING MOIST AIR 1 



The rate of condensation per unit cross-section area in an adiabatically ascending shallow 

 layer of saturated air may be expressed by 



R*=P*te4£ (1) 



at 



where 



pa = partial density of dry air, 



As = vertical thickness of the layer under consideration, 



r« = saturation mixing ratio over water (g./g.)» 



t = time, 



R w = rate of condensation (rain stage). 



A similar equation can be obtained for the snow stage by replacing r« by ri, the saturation 

 mixing ratio over ice. 



Fulks has shown that for a layer of air 100 meters thick (through which the density 

 may be considered uniform) and ascending at a vertical velocity w, the rate of condensation 

 Rv, expressed in millimeters depth of water per hour can be written 



|?. = ( l +r .)[^^ 7 .-266S^] W + r.^i^7- W (2) 



where 



ew = saturation vapor pressure over water (mb.), 



T = temperature, (°K.), 

 7„ = saturated pseudoadiabatic lapse rate, rain stage, (°C./100 gpm.), 



w = vertical velocity (m. sec." 1 ). 



Since r„ is ordinarily small in comparison with unity, equation (2) for a vertical velocity 

 of 1 meter per second is approximately 



tf„ = .|0j^ 7w _266S£^ (3) 



Corresponding equations for Rt, the rate of condensation in millimeters depth of water 

 for the snow stage, are obtained by replacing e v by d, the saturated vapor pressure over 

 ice ; 7» by 7<, the pseudoadiabatic lapse rate for the snow stage ; r« by r«. 



Table 81 contains values of R v computed from equation (2) for a layer 100 meters 

 thick having an upward motion of 1 meter per second. Values of Ri are shown in 

 parentheses. When the rate of condensation in layers of other thickness or having dif- 

 ferent vertical speeds is desired, select a mean value of Rv, (or Ri) for each 100-meter 

 layer, multiply by the appropriate vertical velocity in meters per second, and sum the 

 results for the various layers. Or an approximate result may be obtained by selecting a 

 mean Rv, (or Ri) for the whole layer and multiplying by the thickness in hundreds of 

 meters and the upward speed in meters per second. 



It should be noted that modifications introduced by turbulent mixing, radiation and 

 other nonadiabatic processes, and the effect of the air in sustaining the condensate, have 

 been neglected. These effects must be considered in determining the rate of precipitation 

 as actually observed at the ground. 



1 Fulks, J. R., Month. Weath. Rev., vol. 63, p. 291, 1935. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



