Q(E) = 3.767 Cd (0.98 e„ - ej W 

 Q(C)= 2,488 Cd (T. - T.) W 

 To = P Co WK 



(4) 

 (5) 

 (6) 



To obtain the radiation entering the water, the incident 

 radiation reaching a unit surface of ocean must be reduced 

 by the amount reflected. The reflection was calculated from 

 the formula given by Andersen (1952): 



R = aa'' 



(7) 



where a and b are the proportions of the month when clouds 

 of cumulus and stratus type, respectively, are predomi- 

 nant, a + b = 1; 



C, the cloudiness in tenths of sky covered; 



e,, the vapor pressure of the air in millibars computed by 

 using the formulae of Murray (1967); 



e, , the saturation vapor pressure over pure water at the 

 seawater temperature, in millibars; 



T, , the temperature of the air in degrees Celsius; 



T„ , the temperature of the water in degrees Celsius; 



W, the wind speed in meters per second; 



Qo, radiation from sun and cloudless sky in calories per 

 square centimeter per day; 



R, reflectivity of the sea surface; 



a, noon altitude of the sun in degrees; and 



Cp , the nondimensional drag coefficient. 



Heat Exchange Computations 



Q(S), radiation from sun and sky.— The direct and 

 diffuse radiation from a cloudless sky, Q i, was obtained 

 from the Smithsonian Meteorological Table (Smithsonian 

 Institution 1949) using an atmospheric transmission coeffi- 

 cient of 0.7. These values were then corrected to correspond 

 to the atmospheric transmission that gave the radiation 

 values observed at Ocean Weather Station "P" (OWS-P) 

 (Tabata 1964a) with the formula Qo = 33.2 + 1.011 QV The 

 cloudless sky radiation was then corrected for cloud cover 

 and reflection from the sea surface, to give Q(S), the 

 radiation passing into the water. 



Uncertainty in the computed radiation from sun and 

 sky, Q(S), is caused primarily by the cloud cover 

 correction. The difficulties are caused by the variability of 

 cloudiness as well as the primitive nature of observation 

 from ships at sea. Observations at sea include an estimate 

 of the total cloud cover regardless of type. Thus the 

 presence of cirroform clouds with a high transmittance 

 cause an underestimate of the calculated radiation using 

 total cloudiness. Quinn and Burt (1968) found this to be a 

 problem in the tropical Pacific where cumulus and 

 tTroform clouds predominate. 



Using a large number of observations from OWS-P, 

 Tabata (1964b) derived a formula that gave the transmit- 

 tance as a linear function of cloudiness and mid-month noon 

 altitude of the sun. This formula gives Q(S) within 5% of 

 the observed radiation when mean monthly cloud values 

 are used. OWS-P lies at lat. 50°N where stratus type 

 clouds predominate. In low latitudes cumulus types of 

 clouds predominate (U.S. Weather Bureau 1938). Seckel 

 and Beaudry (1973) showed that the cloud correction 

 formula with a transmittance as a function of the cube of 

 the cloudiness (Laevastu 1960) gave radiation values 

 agreeing beter with Wake Island observations than values 

 obtained with other correction formulae. They suggested 

 the use of the two formulae, one for cumulus type clouds 

 and the other for stratus type clouds. In the calculation of 

 this report the two correction formulae were used in 

 proportion to the occurrence during a month of cumulus 

 and stratus type clouds. 



where a is the mid-month solar altitude and a and b are 

 empirical constants adapted from Tabata (1964a). For a 

 cloud cover of 0.5 or less, a = 0.33 and b = -0.42. For a 

 cloud cover of more than 0.5, a = 0.21 and b = -0.29. 



Q(B), the effective back radiation.— The effective back 

 radiation. Q(B). consists of the long-wave radiation from the 

 sea surface, which is proportional to the 4th power of the 

 absolute sea-surface temperature, minus the downward 

 long-wave radiation from the sky. The latter depends on 

 the water vapor content of the atmosphere as well as the 

 type, density, and height of clouds. Because of the 

 variability in time and space of these properties, the 

 downward long-wave radiation is difficult to determine. A 

 number of empirical formulae exist for the computation of 

 Q(B), most of which were derived for overland conditions. 

 Uncertainties are primarily introduced by the cloud factor 

 in the empirical equations (Kraus 1972) that is given both 

 as a linear and quadratic function of cloudiness. Because of 

 its common application for the computation of large-scale 

 air-sea interactions, we have used Equation (3), the 

 modified Brunt equation (Brunt 1932) with the empirical 

 constants of Budyko (1956). 



Q(E), heat used for evaporation.— The turbulent flux of 

 water vapor between the ocean and atmosphere, besides 

 Q(S). is the most important process affecting Q(N). It has 

 been estimated (Jacobs 1951) that of the total solar energy 

 absorbed at the sea surface during the course of a year, 

 approximately 50% is used for the evaporation of seawater 

 that becomes available to the atmosphere in the form of 

 energy latent in water vapor. 



Absolute magnitudes of the rate of evaporation at the 

 sea surface are still in doubt. The trouble lies, in part, with 

 the uncertainties of the transfer coefficients — C e . C h . and 

 Cd— used to calculate the turbulent fluxes of water vapor, 

 heat, and momentum. Results of experiments over a 

 Kansas plain (Businger et al. 1971) indicate that for 

 neutral conditions the drag coefficient, Cd , is not equal to 

 the sensible heat transfer coefficient, C h • Other results 

 (Paulson, Leavitt, and Fleagle 1972) from the Barbados 

 Oceanographic and Meteorological Experiment (BOMEX) 

 indicate that Ch and Ce> the evaporation coefficient, are 

 equal but differ from Cd, the drag coefficient. Additionally, 

 the transfer coefficients are dependent on the atmospheric 

 stability and the ocean- wave spectrum. Deardorff (1968) 

 derived stability corrections for the transfer coefficients 

 at neutral stability as a function f the bulk Richardson's 

 number. Davidson (1974) and DeLeonibus (1971) have both 

 shown the separate influences of stability and ocean-wave 

 spectrum on C □ . 



The magrnitude of the transfer coefficients and their 

 dependence on stability and the ocean-wave spectrum is 

 still under investigation. For this reason and despite the 

 results quoted above, we follow Malkus (1962) in using a 

 constant Cd in the computation of each of the turbulent 

 fluxes (Equations (4), (5), (6)). The value used in this paper, 

 Cd = 0.0013 referred to the 10-m level, has been suggested 



