336 FOFONOFF [SECT. 3 



The equations defining geostrophic velocity are 



ciP 



These equations can be expressed in terms of geopotential by the transformation 



dxjp 



(35) 



[dxj^ \dxjp/\8PJ:,,y ^1 



/8P\ _ /80\ l/80\ _ /80\ 



\<^yfpl VPJx,y ' \8y 

 so that the equations become 



The derivatives in (36) are taken along isobaric surfaces so that we can 

 subtract an arbitrary function of pressure from 0{P) without affecting the 

 values of the derivatives. Therefore, putting (32) in the form 



0(P) = 0(0)- f aQdP-[ hdP, (37) 



jo jo 



where ao is specific volume of sea-water at a reference temperature and salinity, 

 but a function of pressure, and 8 is the anomaly of specific volume, we can 

 express the geostrophic equations as 



. ,p, g^(0) , 8 ADjP) ^^^^ 



JUg{P) = + , 



By cy 



where the anomaly of geopotential, or "dynamic height", AD, is defined by 



At the ocean surface, the geostrophic equations reduce to 



a0(O) 



AD{P) = r hdP 

 )phic equa 



-MO) = 



/%(0) 



8x 

 80(0) 



(39) 



(40) 



8y 

 so that equations (38) can be written 



dAD{P) 



-f[vy{0)-Vg{P)] = - 

 /[%(0)-%(P)] = - 



8x 



8AD{P) 



8y 



(41) 



