214 MALKus [chap. 4 



(~ 100 m/day or 10-^ cm/sec) and the 0.5-2% density variations between cloud 

 and clear air are neglected, so that we may write 



Flpm = {Wa Aa-Wc Ac)qs-Wd AdQ, (47) 



where pm is the mean air density at the level, the bars denote mean values, qs 

 is the saturation specific humidity at the average air temperature and q is its 

 clear air value. The equation of continuity is 



Wa Aa-Wc Ac = Wd Ad. (48) 



Substituting (48) into (47) we have 



Wd = F/pmiqs-q) Ad. (49) 



All quantities for evaluation of (49) are known. i^=1.5xl0i2 g/sec, pm = 

 1.1 X 10-3, while Fig. 52 shows that at 1400 m the air temperature is about 

 16°C, so that (from tables) qs^ 13.6 g/kg and (from the right-hand curve) q is 

 8 g/kg. With a mean cloud cover of 35% at this level (see Table XI, line 6), 

 MJd= 1.2 cm/sec, a value well supported by the Woods Hole measurements and 

 deductions therefrom (Malkus, 1958; Bunker, 1959). 

 From equation (48) 



Wa = {WcAc + WdAd)IAa. (50) 



If 94% of the cloudy matter is iliactive and descending at an average rate of 

 10 cm/sec, so that only 2% of the area (6% of the cloudy matter) is actively 

 rising, Wa comes out as 2 m/sec, in conservative agreement with Fig. 54 and the 

 other Woods Hole observations. Thus, despite their appearance, the ordinary 

 trade cumuli are easily adequate fuel pumps ; they are raising energy more than 

 a hundred times as fast as its rate of dissipation by all air and sea motions 

 combined. 



When first photographed (Fig. 55a), the topmost tower of the cloud shown 

 in Fig. 54 had penetrated nearly 200 m above the inversion base into the dry 

 air. Shortly after, the tower was observed to cut off and evaporate, like the one 

 schematically shown in Fig. 24, making its contribution to the raising and 

 destruction of the inversion. The beginning of this process is seen in Fig. 55b, 

 taken about 2 min after Fig. 55a. The tower has risen about 350 m and shrunk 

 in diameter from about 670 to about 450 m, imparting its evaporated moisture 

 to the dry surroundings. In poking through the inversion base, this cloud 

 proved itself an exceptional trade cumulus. In a detailed study of the mechan- 

 isms in the moist layer, Malkus (1958) showed that its observed deepening 

 downstream is achieved if only one-tenth of the cloud matter active in mid- 

 layer is left above the inversion base in the process of tower dissipation. 



In the verification of this prediction lies the key feature of trade-wind clouds. 

 The important question to ask of them is not "Why do they grow?" but "Why 

 do they not grow taller and more vigorously?" As Fig. 52 typifies, temperature 

 lapse rates are statically unstable to saturated motions at least to the inversion 

 and commonly throughout the troposphere ; air parcels rising wet adiabatically 



