Evaporation from the Surface of the Sea and the Water Budget of the Earth 227 



pressure corresponding to temperature and salinity of water, Ca is the vapour pressure 

 in the air. Different expressions have been chosen for the functions /i, /g and/3 ^nd a 

 formula of this type is given on p. 220 which shows the dependence of observed 

 evaporation on the prevailing meteorological conditions and with a suitable choice of 

 constants gives satisfactory values. However, it can hardly be assumed that such an 

 evaporation formula which is a product of different functions could give a correct and 

 causative description of the actual physical process of evaporation ; it is rather to be 

 expected that such a formula would be of the form 



fh = fiP, T, u) {e, — e^, 



where the function/is probably a complicated function of the meteorological factors. 

 According to the results of research in turbulence, the transport of the water vapour 

 continuously formed at the sea surface into the air immediately above it proceeds by 

 turbulent exchange; the magnitude of this exchange depends on the roughness of the 

 evaporating surface which in turn also depends on the velocity of the air over the water. 

 SvERDRUP (1936, 1937-8, 1951) was the first to attempt to clarify the problem as to 

 how the evaporation process operates at the surface of the sea with a well-defined 

 roughness under the influence of the turbulent exchange. His ideas are based on two 

 circumstances which aie essential for a solution of this problem: 



(1) Immediately above the water surface a thin boundary layer exists in which the 

 water vapour transport proceeds only by ordinary (molecular) diffusion. 



(2) Above this boundary layer the water vapour transport proceeds through the 

 turbulent exchange A in form of random movements of the air particles (turbulence). 



The exchange A (according to laboratory experiments) is a linear function of the 

 height above the water surface and depends on the roughness of the water surface. 

 The latter is described by the roughness parameter Zq, and according to the results of 

 Rossby about the increase of wind velocity with height Zq is considered constant im- 

 mediately above the sea surface (zq = 0-6 cm). This is valid for weak to moderately 

 strong winds. Correspondingly, 



A = pk^iz — Zo) J- , 



where r is the tangential force (stress) of the wind, p is the density of the air and kg 

 is the Karman constant with a value of 0-38-0-40 (see Vol. I, Pt. 2). 



The thickness of the boundary layer immediately above the water surface depends on 

 the wind velocity. The layer itself can hardly be regarded as invariably composed of 

 the same air particles. Since the turbulent eddies will sometimes penetrate down to and 

 into the boundary layer, it must clearly be understood that this layer occasionally 

 disappears completely; however, after some time it will always be re-formed so that 

 a mean thickness of this layer can be introduced. 



In addition to the theoretical case built up on the basis of these ideas Sverdrup 

 also discussed a second possibility where the water surface was assumed to be "smooth" 

 and the transport of water vapour away from the sea, due to turbulence, starts from the 

 sea surface itself. Observations seem to favour the first case with a diffusion layer and 

 turbulent transport above, and therefore only this case will now be dealt with. 



For the exchange coefficient A we may write 



A = pko(z — Zo) u^. 



