176 MALKUS [chap. 4 



quantitative photography (Ronne, 1!)59; Riehl et al., 1959; Malkiis, Roniie 

 and Chaffee, 1961) show that penetrative chimneys indeed exist in disturbed 

 areas with the right sizes and numbers to effect the necessary transports. In a 

 dynamic hurricane model, Malkus and Riehl (1960) have shown how the 

 condensation heat released and spewed skyward by "hot towers" creates the 

 storm-driving pressure heads. Here we shall use the hypothesis in its original 

 equatorial trough context to complete the energy balance in Fig. 35. 



From the second law of thermodynamics, heat gained in the sub-cloud layer 

 can penetrate to a maximum altitude where the heat content again equals the 

 extreme value of CpT + Lq observed near the ocean surface, which cannot 

 exceed about 85 cal/g (corresponding to T = 29''C; g = 20.8 g/kg at a relative 

 humidity of 80%). In Fig. 36, the upper 85 cal/g level has been denoted by a 

 heavy line. Located near 125 mb (about 50,000 ft) in the trough zone, this 

 upper limit of the tropospheric mass circulation is in fair agreement with the 

 average observed height of the tropical tropopause. Actually, protected 

 buoyant cumulonimbus cores will rise with values of Qo = {CpT + Lq)o depending 

 on surface conditions in their region of ascent. Having different diameters, 

 they will come into equilibrium with their surroundings at varying altitudes of 

 the upper troposphere and there begin outflow to middle latitudes. We shall 

 assume a mean value of Qo corresponding to the mean surface properties at the 

 equatorial trough over the ocean: T = 28°C; g=18.9 g/kg (relative humidity 

 80%); ^0 = 83.4 cal/g. If the entire mass-circulation import from the trades 

 were to assume this value through contact with the sea surface and ascend in 

 buoyant towers, we get an upward energy flux through 500 mb of 1.50 units, 

 15% short of the 1.73 units required in Fig. 35 for balance. 



This small discrepancy could arise from the same neglect of Qvo or calcula- 

 tional uncertainty in radiation which led to a high Qs and consequently the 

 large lateral export above 500 mb. With a Qs of 19 units (one-half that shown ; 

 Bowen ratio 20%) an exact balance is readily achieved, with an 18% diminished 

 h export and only slightly altered c„ profile. Riehl and Malkus, however, 

 tentatively treated the discrepancy as real and hypothesized internal vertical 

 recycling of the air. Using the results of cumulonimbus studies, they showed 

 that an increase in undilute ascent of 60% over mass-circulation requirements, 

 with compensatory descent, can complete the energy balance as shown in 

 Fig. 35. Chilled thunderstorm downdrafts penetrating to the sea surface could 

 enhance the production rate of sub-cloud air by sea-air exchange and, in 

 particular, explain an abnormally high Qs. Evidence exists (Garstang, 1958) 

 that in tropical storms the ratio QsjQe jumps to much higher values than 

 characteristic of the undisturbed trade regime. Further developments in any 

 of the four areas of radiation, tropical mean mass flow, oceanic advection or 

 exchange dynamics in disturbances could contribute to resolving this un- 

 certainty, which fortunately overstates rather than minimizes the transport 

 requirements to be met by the towers. 



We see here an outstanding example of the streakiness of geophysical fluids. 

 The fact that the key transports and conversions are localized to restricted, 



