SECT. 2] LARGE-SCALE INTERACTIONS 103 



The net back radiation under cloudless conditions is the difference between 

 long-wave radiation emitted by the surface, which radiates very nearly like a 

 black body, and that received from the atmosphere, due mainly to its water- 

 vapor content, ^^o thus increases with temperature and decreases with vapor 

 pressure ; within the common range of these parameters the variation is, in fact, 

 a rather slow decrease with rising temperature, due to the warmer air's higher 

 capacity to hold water vapor. Sverdrup (1942, p. Ill) has published a con- 

 venient graph from which Q^q may be read as a function of sea-surface tempera- 

 ture and the relative humidity at ship's deck level. Budyko's table {loc. cit., 

 Table 7), worked out in terms of low-level air temperature and vapor pressure 

 over soil, gives values about one-third lower in the region of overlap. 



The important departures from these tabulations, causing the actual surface 

 radiation balance to be altered by effects of the circulation lie first in the 

 rather strong reduction in Q + q by clouds and secondly in the much weaker 

 reduction of Qb thereby. Until recently the radiation hterature has asserted 

 that, to the first order, satisfactory corrections for cloudiness to the cloudless 

 tabulations are obtainable from knowledge of the average fractional cloudiness 

 alone, ignoring types, heights, and the exact nature and distribution of the 

 clouds. These correction formulas are based on the assumption that cloud 

 albedo is constant and independent of thickness ; uncomfortable doubts have 

 been creeping into the literature as a result of more measurements (see Budyko, 

 loc. cit., and review by Charnock, 1951). 



It is at this point that determinations of energetic relations depending on 

 radiation balance, as do all terrestrial energy budgets, lose their resolution. 

 Worse yet, by being forced to assume and introduce mean cloudiness as given, 

 the feedback between source and circulation is removed, and such studies 

 thereby lose their ability to treat dynamics and causality with predictive 

 ability or rigor. Furthermore, even mean cloudiness over wide portions of the 

 oceans can hardly be said to be well known observationally, while temporal 

 and regional variations therein are presently j)ure conjecture. However, 

 satellite measurements may shortly relieve the latter situation and radiation 

 work in progress offers hope that the radiative properties of different cloud 

 forms may be treated. 



Meanwhile, we must proceed to study ocean-atmosphere energy relations 

 using the best methods available. An important clue to the interaction between 

 heat sources and motions may be provided by the demonstration that the 

 average monthly radiation balance over wide portions of the oceans decreases 

 approximately linearly with mean cloudiness. Budyko shows that the incoming 

 short-wave radiation obeys a relationship of the form 



(Q + q) = {Q + q)o[l-{l-k)n]. (4) 



which he calls the Saviiio-Angstrom formula. Here n is the mean fractional 

 cloudiness and k is an empirically determined constant ranging from 0.35 to 

 0.50 in its weak increase with latitude. This empirical variation of k is an 

 attempt to include the effects of different altitudes and thicknesses of the 



