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



upper limit of the atmosphere, it follows, according to the Gaussian integral law,* 

 that for the total column of air over the land 



(p^rt) + Q)dB -\\ (B,dL- I ^,dL = 0, 



where dL is an element of the land surface L ; the two terms of the first integral vanish 

 for the land surface and the upper limit of the atmosphere since at these extreme 

 limiting surfaces either p„ or it) will be equal to or .4 will be 0; for the two other 

 integrals the amounts passing through the control surface B disappear. Now, the mean 

 precipitation amount per unit time on the continent is 



^,dL 



P dL, 



L 



and the mean evaporation amount over the continent is 



Finally, the water vapour flux through the surface B towards the land is 



S,dL. 



JL 



W.- Wr 



(Pu,^ + S)„ dB. 



B 



The condition of a stationary state thus gives one of the basic Bruckner equations as 



Ec~Pc + {W^ - W,) - 0. 



If, on the other hand, the integration is taken over the total ocean, one obtains 

 in the same way [the inwards (oceanwards) directed horizontal normal of dB is now 

 —n] the second basic Bruckner equation 



P, + E, + {W^ - W,) = 0. 



Integration of the continuity equation over the entire atmosphere above the surface 

 (C + O) gives 



Pe i Pq ^^ Ee Eg, 



which can, of course, also be obtained by subtraction of the first two equations. 



The basic equations for the water budget of the Earth involve five quantities; a 

 knowledge of three is sufficient to evaluate the others numerically. In general, it does 

 not matter which of them we presume as known and which we want to obtain. How- 

 ever, the accuracy with which the different quantities can be determined from the 

 available observations is not the same for each. The precipitation over the sea can be 

 estimated only with difficulty. For that purpose in wide regions of the oceans only the 

 rain density (the mean precipitation amount for a single rain day) and the rain fre- 

 quency (the average number of days with precipitation) are available from ships' 



* The Gaussian integral law states that the volume integral of a volume Kwith a surface A taken 

 over div a is equal to the negative surface integral of r„ taken over the entire surface A, where // 

 is the normal to A directed towards the interior, so that 



III 1.va</^'=-||».,/^. 



