Evaporation from the Surface of the Sea and the Water Budget of the Earth 233 



This quantity m represents the internal turnover of water in unit volume per unit time 

 and is positive if more condensate evaporates than water vapour condenses, but 

 negative if more water vapour condenses than condensate evaporates. 

 The continuity equation for water vapour is thus 



-^ + div (pu>^) + div S = +m. 

 ot 



Local changes in the condensate k in a unit volume in unit time can occur in two ways : 



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

 definite amount of water vapour respectively. If more condenses than evaporates, 

 then according to the above argument this change is -\-m; however, in the opposite 

 case, —m. 



(2) The water content in a unit volume (liquid or solid) can also change if, for 

 instance, part of it is removed as precipitation or is advected by air currents to other 

 levels. For each point in space this movement of condensate can be considered a 

 condensate flow which can be described by a vector 51, The absolute value |Sl| is the 

 amount of condensate which passes in unit time through a unit area of a surface 

 perpendicular to the direction of movement of the condensate. At the point where 

 there is no condensate or if the condensate shows no movement then 1^| =0. The 

 flux of condensate through a unit surface along the normal /m is 5l„ = 51^, and in par- 

 ticular, for z = 



gives the precipitation amount per unit area and unit time at the surface of the Earth 

 (z = 0). The change of k due to such processes of condensate movement is then given 

 simply by the convergence —div £ of the condensate flux. 



The condensate continuity equation is then 



— = —div ^ — m. 



dt 



Adding the two continuity equations for water vapour and condensate gives the 

 continuity equation for the total water content finally in the form 



^'''""' + "^ + div (p„tt, + S + S) = 0. 



Ot 



For a stationary, average state in the atmosphere this equation reduces to 



div (p^lt) + S + SI) = 0. 



Imagine now a vertical surface of control B, which parallels the coasts of a (not neces- 

 sarily continuous) continent and reaches upwards to the upper limit of the atmos- 

 phere. Considering a surface element dB with a horizontal normal n directed towards 

 the interior of the continent (landwards). Then, integrating the above equation over 

 the total volume between the surface of control B, the surface of the Earth and the 



