Evaporation from the Surface of the Sea and the Water Budget of the Earth 229 



where k is the diffusion coefficient in cm^/sec then the thickness of the diffusion layer 

 is given by 



'e. 



and for a roughness parameter Zq 



In 



d + 



•] 



Vp 



A-o 



0-165 



u^. = 



Uz, 



hl{(z + Zo)/Zo} "^ log{(z + zo)/zo} 



where «, is the wind velocity at a height z. Finally, the evaporation E is thus obtained 

 from the above formula 



E = 



8u, 





(es - e^). 



If the thickness of the diffusion layer is known then the evaporation E can be calcu- 

 lated, if we observe: (1) the wind velocity at a height above the surface of the water, 

 by means of which u^ is found; (2) the temperature and the relative humidity at this 

 height, wherewith e^ is known; (3) the salinity, from which e, can be determined. Only 

 observations can give information on the thickness of the layer d. For this Sverdrup 

 used the values determined by Montgomery (1940) on board the research vessel 

 "Atlantis", wheieby Zq = 0-6 cm was assumed. Table 88 contains this calculation. 



Table 88. Values of the friction velocity u^, the evaporation E and 



the thickness of the diffusion layer d for a rough water surface 



(zq = 0-6 cm) 



(According to observations of the research vessel "Atlantis") 



The value of d decreases with increasing wind velocity, and Fig. 103a shows that as a 

 rough approximation d increases linearly with 1/w^. With suitable weighting of each 

 group Sverdrup obtained d = 4-12/z/^. 



Unfortunately, there are no simultaneous measurements of evaporation available 

 to allow a close test of the theory. Sverdrup with these values of <y and using the meri- 

 dional distribution of temperature, relative humidity and wind velocity at the surface 

 of the Atlantic, calculated the meridional distribution of evaporation and compared 

 this theoretical distribution with the zonal values obtained by Wiist, applying the 



