SECT. 2] LARGE-SCALE INTERACTIONS 127 



over precipitation rate at the ocean surface, or as the flux divergence, Qvw, of 

 water- vapor transport in the atmosphere. Qvo is the flux divergence of horizontal 

 ocean-heat transport in cal per cm 2 per sec and Qva is the flux divergence of 

 horizontal heat and potential energy transport in the atmosphere in cal per cm^ 

 per sec, or very nearly the flux divergence of the transport of Cp6 {Cpd'^CpT + 

 Agz), where 6 is potential temperature, Cp the specific heat of air at constant 

 pressure, A the heat equivalent of work, g the acceleration of gravity and z 

 the elevation above the ground. The compressibility of air necessitates this 

 formulation for the heat-energy transport in the atmosphere, since vertical 

 ascent within a column may convert sensible heat into potential energy, and 

 conversely, depending upon the prevailing lapse rate. 



Rs is the radiation balance of the entire column, or the difference between 

 the short-wave radiation absorbed and the net long- wave radiation emitted. 

 Methods and results of evaluating it have been described in the earlier literature 

 by Simpson (1928), Kimbafl (1930) and Baur and Phillips (1934, 1935). More 

 recent evaluations with better and more extensive data have been presented by 

 Houghton (1954), London (1957) and Budyko (1956), who reports the work of 

 Bagrov (1954). Again, the greatest difficulty in these calculations resides in 

 ascertaining the amounts of various cloud types and their radiative, reflective 

 and absorptive properties, particularly in assessing the absorption of short- 

 wave radiation in the atmosphere. Nevertheless, the agreement between the 

 last three authors is apparently relatively good concerning the annual average 

 magnitude of Rs and its dependence on latitude, particularly that between 

 Houghton and Bagrov, as demonstrated in Fig. 13. 



As stated earlier (page 92ff.), all evaluations of Rs show that the ocean-air 

 system as a whole gains radiation heat equatorward of about latitudes 38° and 

 loses heat by radiation poleward. If the high latitudes are not to cool progres- 

 sively with time and the low latitudes to warm up (precluded by the closely 

 reahzed steady-state assumption (6), Introduction, page 92), specified transports 

 in the earth's movable parts, namely sea and air, must take place. Thus equa- 

 tion (25) states physically that in regions of positive radiation balance the 

 excess heat energy may be carried away by sensible heat transport in the ocean 

 and by a combination of sensible heat, latent heat and potential energy export 

 in the atmosphere, while regions of negative radiation balance must make up 

 the deficit by corresponding imports. Therefore, computation of Rs as a function 

 of latitude immediately permits assessment of the total heat-energy flux 

 divergences in sea and air together (sum of terms on right side of (25)), and by 

 integration, enables the total heat-energy flux across latitude circles to be 

 obtained. 



In the first three columns of Table I we performed this integration for the 

 Rs figures of Bagrov (reported by Budyko) and compared them with similar 

 computations by Houghton and London. The Russian figures and Houghton's 

 are in nearly perfect agreement, while those of London are about 50% lower, 

 illustrating the magnification of fairly small flux-divergence discrepancies 

 when integrated. Houghton's and Budyko's fluxes are about 60% larger than 



