actions has been discussed in detail by Malkus 

 (1962). The empirical formulas are still the 

 subject of intensive research and may change. 

 Should changes be made, the derived results of 

 this paper can be adjusted, since the original 

 meteorological properties are also given. 



Two criteria are important in the computation 

 of the heat exchange processes presented in ta- 

 ble B. First, the results must satisfy the needs 

 of the TWZO investigation, in which relative 

 changes from month to month and season to sea- 

 son are of primary interest. Secondly, there 

 must be a basis for comparison with the results 

 in the North Pacific such as were obtained by 

 Wyrtlci (1966). 



The net heat gain or loss to the sea water 

 as a result of the exchange processes at the sea 

 surface is of interest to the oceanographer and 

 is expressed in the budget equation 



Q(N)= Q(S)- Q(B)- Q(E)- Q(C). 



The net heat exchange across the sea surface, 

 Q(N), is positive when the sea water gains heat. 

 The terms on the right side of the equation are: 

 Q(S), the radiation from sun and sky; Q(B), the 

 effective back radiation; Q(E), the heat of evap- 

 oration; and Q(C), the conduction of sensible 

 heat. 



The following formulas have been used to 

 compute the heat exchange processes in table B: 



Q(S) = 0.98 Q^ (1 - 0.30C - 0.38C^) 



Q(B) = 1.14 (10)-^ (273.16 + T,^)'' (0.39 - 0.05/e^) 

 (1- 0.6C^) + 4.58 (10)"'^ (273.16 + T„)^ 

 (T„-Ta) 



Q(E)= 3767 C (0,98e„-eg)W 



Q(C)= 4(T^-Ta)W. 



The heat exchange components are expressed in 

 cal. cm7^day~' and the symbols are: 



C , the cloudiness in tenths of sky cov- 

 ered; 



Cg , the vapor pressure of the air in 

 millibars; 



e^, , the saturation vapor pressure over 

 pure water at the sea-water temper- 

 ature, in millibars; 



T(j , the temperature of the air in degrees 



Celsius; 



T^ , the temperature of the water in de- 

 grees Celsius; 



W 



'D ' 



the wind speed in meters per second; 



the radiation from sun and cloudless 

 sky in calories per square centi- 

 meter per day; 



the nondimensional drag coefficient. 



The values of e^ and e„ were computed from 

 formulas given by List (1951: p. 366) and Mur- 

 ray (1967). The methods of computing Qo and 

 Crj are given below in the discussion for each 

 formula. In the computation of Q(B), Q(E), 

 (e), and Q(C), the sea surface temperature 

 based on surface marine observations was re- 

 duced by 0.7° C. (Saur, 1963). 



Although different workers agree about the 

 meteorological properties that affect the heat 

 exchange processes, the coefficients used in the 

 empirical formulas vary. To allow compari- 

 sons of the results in this paper with those of 

 other workers, each of the heat exchange proc- 

 esses and the choice of coefficient used here 

 are discussed below. 



Q(S), Radiation from Sun and Sky 



Departures from the formulas used by Wyrtki 

 (1966), Roden (1959), and Laevastu (1960, 1965) 

 are based on direct pyranometer measurements 

 of radiation from sun and sky during the cruises 

 of the TWZO Pilot Study. It was possible to 

 integrate the analog traces for clear sky and 

 solid overcast conditions by means of a polar 

 planimeter. The clear sky direct and diffuse 

 radiation values for a transmission coefficient 

 of 0.6 given in the Smithsonian tables (List, 

 1951: tables 132 and 136), when multiplied by 

 1.03, corresponded to the measured values. 

 These results agree with the values given by 

 Bolsenga (1964). The albedo factor, 0.95, when 

 multiplied by 1.03 gives the coefficient, 0.98, 

 used in the equation. 



To facilitate the calculation of Q„ by compu- 

 ter, the harmonic analysis of the clear sky di- 

 rect and diffuse radiation values of the Smith- 

 sonian tables gives 



Qo - ^o'^ A| cose + B| sine +A2 cos 2e + Bj sin2e 



2TT 

 where & = -y-(t - 21), t is the time in days begin- 

 ning with January 1, T the number of days in a 

 year, and the A's and B's are coefficients in the 

 harmonic series. Table 1 lists the coefficients 

 for lat. 0°, 10°, 20°, 30°, and 40° N. Coefficients 

 applicable for the computation of Q^ at inter- 

 mediate latitudes were obtained by linear inter- 

 polation. 



