Evaporation from the Surface of the Sea and the Water Budget of the Earth 231 



50° N 30° 20° 10° 0° ICP 20° 30° S 50° 



Fig. 104. Calculated and observed values of evaporation in successive latitudinal zones of 

 the Atlantic (according to Wiist). 



The formula given above for E can be changed into a more practical form. Ex- 

 pressing e in mm and u in m/sec and putting p = 1000 mb and z = 10 m then E 

 in mm/24 h vi'ill be given by 



E = K^oi^s - ^lo) "lo- 



Kio lies between 0-12 and 0-19. This simple formula is quite remarkable since it is 

 based solely on theoretical considerations. The theory of evaporation discussed above 

 involves a hydrodynamically smooth surface with a laminar boundary layer (molecular 

 diffusion of water vapour) with a turbulent layer of air above it. The evaporation 

 from the water surface can also be calculated for other different stratifications of the 

 layer of air above the water and there can be obtained the general equation 



E = pKoyF^^es — e^) Ua, 



where kq is the Karman constant, y is the frictional coefRcient and F is the Mont- 

 gomery evaporation factor. The latter depends on the structure of the lowermost 

 layer of air, on the wind velocity and on the stability and nature of the boundary 

 layer. The observations of Montgomery seem to indicate a sharp increase in F at 

 u = 6-5 m/sec for a = 6 m, while lower values for F are found for lower wind veloci- 

 ties. In this case, the water surface is smooth and has a laminar boundary layer above 

 it. Turbulence only becomes effective with higher wind velocities and increases the 

 evaporation rate. Only further observation can show whether this transition is 

 gradual or sudden. On this subject see Vol. I, Pt. 2, and especially Munk (1947). 



5. The Water Budget of the Earth 



The source of atmospheric water vapour is to be found in the first place in the 

 evaporation of water at the surface of the ocean ; the evaporation of water from the 

 continents taking only a secondary place. In so far as the water vapour formed over 

 the surface of the ocean remains there, condenses to clouds and returns as precipita- 

 tion, it is referred to as a minor water cycle. Part of the oceanic water vapour is, 

 however, carried by air currents inland over the continents and together with water 

 vapour originating from the land gives rise to precipitation over the land. If this water 

 is not evaporated again and returned directly to the atmosphere, it will be returned 

 to the sea by streams, rivers and ground water (run off), and closes in that way the 

 major water cycle. 



