104 MALKUS [chap. 4 



climatologically prevalent cloud forms. A similar formulation by Mosby (1936) 

 was used by Sverdrup ; detailed discussion and criticism of the physics under- 

 lying these approaches is found in the work of London (1957). For our purposes, 

 it is important to note that incoming radiation has decreased to about half its 

 cloudless value as the mean cloudiness approaches eight-tenths. 



For the reduction in back radiation due to clouds, Budyko's evidence 

 suggests a faster-than-linear decrease, namely, 



Qb - ^^o(l-Cw'«)> (-5) 



with more adjustable constants than the earlier linear formulation used by 

 Mosby and Sverdrup which was 



Qb = Qboi^-O.SSn). (5a) 



In (5), m= 1.5-2.0, and C, tabulated taking into account mean frequency of 

 clouds at various heights by latitude, ranges between 0,5 at the equator and 0.8 

 at high latitudes. Since (5a) gives a sharper reduction in Qi, with n than does 

 (5), we find for average sky covers of about five-tenths that the differences 

 between Sverdruj)'s larger and Budyko's smaller Q^q are considerably com- 

 pensated in the final estimate of Qb. 



Despite the faster-than-linear decrease in (5), even here Qb is only very 

 weakly dependent on cloudiness. For a given latitude and season, therefore, 

 the mean radiation balance may be well approximated by a relation of the form 



R ^ A-Bn (6) 



where the constants A and B are obtainable from the radiation tables. Such a 

 relationship might provide a first start at modelling the interaction between 

 energy input and circulation dynamics, particularly in the tropics where mean 

 cloudiness appears to be, to a first order, directly dependent upon the low-level 

 convergence in the flow (Malkus and Ronne, 1960). For demonstration, a 

 sample calculation of i? as a function of cloudiness in tenths is presented in 

 Fig. 5 for latitude 20°, in February, using the radiation figures of Budyko's 

 Tables 1, 2, 6, 7 and 8. 



It is also now possible to assess the degree of feasibility and adequacy of 

 quantitative air-sea exchange determinations using the energy balance method 

 set forth in equation (3). For annual averages, the storage S, though probably 

 important in long-period climatic changes, is surely negligible in comparison to 

 the other terms and their accuracy. In the months of February and August, 

 when the ocean heat content reaches its minimum and maximum, respectively, 

 it is zero. The net flux divergence, Qvo, is similarly negligible for some regions, 

 and for whole oceans, and may be calculated and included for those basins, 

 such as the Caribbean-Atlantic (Colon, 1960), where measurements of current 

 transports are available. 



While the foregoing limitations, especially in the radiation evaluations, 

 greatly restrict the scope of the energy equations, particularly in time- 

 dependent, dynamic, and short-period studies, there are significant and geo- 



