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



Since the total amount of water on the Earth from a more general view-point can 

 be considered a constant, seven items enter into the total water budget, which for a 

 stationary state must be related with each other according to a strict principle of 

 dependence. 



These seven items are the following: 



Eq the mean annual evaporation amount from the oceans ; 



Ec the mean annual evaporation amount from the continents; 



Pq the mean annual precipitation amount over the oceans; 



Pc the mean annual precipitation over the continents; 



Wq the annual amount of water vapour in the atmosphere above the sea passing 

 over to the continents ; 



Wc the annual amount of water vapour in the atmosphere above the land passing 

 over to the sea ; 



R The annual outflow of water in rivers, etc., into the sea (run off). 

 The constancy of total water in all oceans requires that the total mean annual inflow 

 of water into the oceans Pq -\- R must be balanced by the total amount of water re- 

 moved £"0; the constancy of the water on the land requires that the water gained by the 

 land Pc must be equal to the water lost E^ + R; and finally the constancy of the at- 

 mospheric water vapour over the oceans and over the continents requires that 



E^-W,+ W, = Po, 



and 



E,+ W,-W,^ P,. 



From this it follows that the annual outflow of river water and other water into the 

 ocean (total run off) must be exactly equal to the difference between the amount of 

 water vapour in the atmosphere passing from the sea into the land and that passing 

 from the land out over the sea. Thus, the following formulation for the balance of 

 the budget of the water cycle on the Earth is obtained, which are known as the basic 

 "Bruckner" equations for the water balance of the Earth (Bruckner, 1905; Fischer. 

 1925). 



These basic equations can also be derived, as has been shown by Defant and 

 Ertel (1943), from the continuity considerations of the total water content of the 

 atmosphere in a closed and more general form. The amount of water contained in a 

 unit volume of atmospheric air consists, on the one hand, of the dry air (density: 

 Pa g/cm^) and of the amount of water vapour (density: p^), and on the other hand, of 

 the amount k (g/cm^) of the condensed water vapour in liquid or solid form. Changes 

 in the amount (p^) of water vapour in unit volume and unit time can occur locally: 



(1) By the convergence (negative divergence) — div {pw'm) of the convectional 

 flow p^tt) of water vapour. 



(2) By the convergence of the turbulent flux — div S. The turbulent flux is given 

 by (5 = —A grad q, where A is the exchange coefficient (g cm~^ sec~^) of the 

 specific humidity q = {0-623lp)e. 



(3) By evaporation of a definite amount of condensate or by condensation of a 

 definite amount of water vapour, respectively: 



±m [g cm~^sec"^]. 



