90 The Three-dimensional Temperature Distribution and its Variation in Time 



For particular parts of the sea and for short intervals of time it may also be necessary 

 to take into consideration the heat carried by ocean currents, or by mixing processes 

 into or out of the oceanic region under consideration and also the heat which causes 

 over short periods of time changes in water temperature. The above equation is, 

 however, sufficient for the ocean as a whole. The individual terms will now be dis- 

 cussed in some detail. 



(a) Direct Solar Radiation 



Of the solar constant /^ is 1-94 g-cal cm~- min"^ one horizontal cm^ at the sur- 

 face of the Earth obtains for a zenith distance z of the sun (altitude /; = 90^ — r) 

 and due to the angle of incidence and the reduction in intensity due to the atmos- 

 pheric absorption only the intensity 



/ = /q e~^" sec z cos r. 

 Sec z is the relative thickness of the air through which the radiation passes (equals 1 

 for an atmosphere pressure of 760 mm Hg with the sun at zenith; equal to 2 when 

 the sun is at an altitude of 30°). e-^« = ^ is the transmission coefficient and q has 

 under normal conditions a value between 0-6 and 0-7, a = 0-1 28-0-054 log sec z and 

 ris the "turbidity factor". If z and Tare known then the direct solar radiation inci- 

 dent per cm^ on a horizontal surface can be calculated directly for any altitude of the 

 sun. 



Part of the solar energy reaching the sea surface will be reflected there. This part 

 depends on the angle of incidence, that means from the zenith distance of the sun. 

 Schmidt (1915) has calculated that due to the compensatory effects of solar radiation, 

 which decreases with increasing zenith distance and of the simultaneously increasing 

 reflection the intensity of the reflected radiation for approximate calculations can be 

 put as ^ = O-OlO-O-013/o. By using the known total amounts of heat received by 

 1 cm^ of the Earth's surface by direct solar radiation with an average value of the 

 transmission coefficient, and by knowing the reflection loss at the sea surface, it is 

 possible to calculate the amount of energy obtained by 1 cm^ of the sea surface in 

 one day. Table 37 gives the mean daily total sum for a year for q = 0-6-0-7. The 

 figures show that even assuming a continuously clear sky the equator receives barely 

 one-half and the pole only a fifth of the solar radiation incident on the upper atmos- 

 phere. When the transmission coefficient is 0-6 the entire surface of the Earth receives 

 only 44% of the theoretical amount of heat. This value will be still further reduced 

 by the presence of clouds. If the cloudiness is w (as a fraction of the visible sky) then 

 the radiation actually reaching the surface of the sea is only 



