The Three-dimensional Temperature Distribution and its Variation in Time 91 



Since the radiation on the surface of the ocean is difficult to measure and only few 

 determinations have been made, Mosby (1936) has given an empirical equation for the 

 mean monthly and annual values of the radiation incident per cm^ on a horizontal 

 surface for given values of the mean altitude of the sun and of the mean cloudiness 



Qs == kh{\ - 0-07 liv); g cal cm-^ min-^. 



The bars indicate mean values and k is a factor which depends on the turbidity of the 

 atmosphere; at the equator it is 0-023, at 40^" latitude 0-024 and at 70° latitude 0-027. 



{h) Diffuse Sky Radiation 



During the day the surface of the Earth also receives general scattered short-wave 

 radiation from the atmosphere and also direct solar radiation reflected from clouds. 

 Estimates based on the direct measurement of total radiation (direct + diffuse radia- 

 tion) show that in general the average value of the diffuse sky radiation for the whole 

 Earth and for a cloudless sky amounts to about 56% of the total radiation on the 

 upper limit of the atmosphere. If we take this value as an average for all latitudes, for 

 a cloudiness u-, the direct radiation S2 will be increased by diffuse radiation amounting 

 to 0-56vr • Si. At the surface of the water this more or less generally scattered radiation 

 will suffer a reflection loss of 6-6%. The fraction of diffuse radiation from the sky 

 entering the water is thus given by D = 0-52h' • S^. 



(c) Long-wave Radiation of the Atmosphere 



The effective back-radiation R^ is the difference between the radiation according to 

 the Stefan-Bo I tzmatm law (E = err*) and the long-wave radiation of the atmosphere 

 and depends, for a cloudless sky, on the absolute temperature T of the lowest layer of 

 the atmosphere and on the water-vapour pressure in this layer (e in mm Hg) (Ang- 

 strom, 1936). The effect of clouds is shown in a reduction of the effective back-radia- 

 tion and can be calculated if the cloudiness is given. With this equation it is possible 

 to calculate numerically the longwave radiation of the atmosphere for a given tem- 

 perature, water-vapour pressure and mean cloudiness. The effective back-radiation 

 can be measured directly, but such measurements have only seldom been made over 

 the sea. Angstrom has derived an empirical formula which has been given by Moller 

 in the following form 



^eff = oT^[l - (0-210 + 0-174 X 10-»-»55eo)(l - 0-675vv)], 



where a is the Stefan-Boltzmann radiation constant, T is the absolute temperature, 

 Re^ is the vapour pressure above the surface of the sea and w — as before — is the mean 

 cloudiness. 



For the surface of the sea it can be rearranged to give 



Q^ = 0-954ar4 - (7r[(0-210 + 0-174 x lO-oo^^e^^^i _ o-765m-)]. 



Since, as shown by Lauscher (1944), the radiation from a plane water surface is 

 decreased by 6-6% by back-reflection (see p. 60). The effective radiation is the first 

 loss in the heat balance (see Table 36, item 1 (heat loss)). 



