102 MALKUS [chap. 4 



the latter is estimated as not above 0.1% or 0.3 cal/cm^ per day. These are well 

 within the accuracy of presently possible evaluations of the larger terms and 

 surely negligible for the annual and seasonal budget studies to be presented 

 here; for long ])eriods and the consideration of climatic change their omission 

 may not be so readily justified. 



R is the radiation balance of the surface, and, under certain restrictions, 

 may be independently calculated using the following form of the energy 

 conservation law, namely : 



where Q is the sum of direct short-wave radiation, q is the sum of diffuse short- 

 wave radiation, a is the albedo of the surface, and Qb the "back" or "effective 

 outgoing" radiation, which is determined by the difference between "green- 

 house" radiation of the atmosphere and outgoing radiation from the surface. 



Thus the total exchange, Qs plus Qe, may be computed as a function of space 

 and time by combining (1) and (2) to give 



Q^ + Qe = {Q + q){l-a)-Qo-S-Qro. (3) 



Equation (3) and its solution are the essence of exchange determination using 

 the energy budget method. Aside from problems raised by ocean storage S 

 and heat flux divergence Qvo, the range of validity and resolution (space- and 

 time-wise) of the method depend upon the adequacy and resolution of deter- 

 minations of JR. The latter has been discussed extensively in the radiation 

 literature (London, 1957; Houghton, 1954; Budyko, 1956). The critical 

 variable entering E, from the meteorological-oceanographic standpoint, is 

 atmospheric cloudiness, which affects both (Q + q) and Qf,. Under cloudless 

 conditions, Budyko among others has presented tables for both {Q + q)Q and 

 Qbo (subscript denotes "cloudless"). The constants in his formulas have been 

 evaluated from extensive actinometric measurements at varying latitudes, 

 mainly in the U.S.S.R. Similar tabulations have been evolved recently by 

 London (1957), who compares his results with those of the earlier workers used 

 by Sverdrup (1942) in his pioneer endeavors to construct heat budgets of the 

 oceans. To obtain {Q + q)o we need to know the solar radiation impinging at the 

 top of the atmosphere and subtract that depleted by the air column due to 

 absorption, scattering, and reflection by the atmospheric constituents. The fact 

 that Budyko's (and other workers') tables give {Q + q)Q as a function of latitude 

 and month alone implies an assumed longitudinal constancy and temporal 

 reproducibility in the air's transmissivity. 



The albedo of a water surface to direct solar radiation has been generally 

 found less than 10% except for extremely low solar angles ; the reflectivity for 

 diffuse sky radiation is somewhat larger. Equation (1) ignores this diff"erence, 

 as do most radiation tabulations, which commonly also neglect effects of 

 surface roughness and present a as a function of latitude and month, thus in- 

 cluding variations in integrated sun angle only. Under these restrictions, all 

 agree that oceanic albedo ranges from about 6-11% between 40°N and S. 



