OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 99 

 surface is 



f = ^... (VI, 16) 



where ix represents the geometric slope. Consequently the currents as 

 computed from (VI, 13) are also represented by 



10 fdD\ , 10 fdD\ ,,,. ._^ 



That is, the current is parallel to the geopotential contours and is so 

 directed that in the Northern Hemisphere, for which the above equations 

 are valid, the surface rises to the right of an observer looking in the 

 direction of flow, and in the Southern Hemisphere it rises to the left. 



The Fields of Pressure and Mass in the Ocean 



The relation between the distribution of mass and pressure is expressed 

 by the hydrostatic equation, which can be written 



dp = ps,t},pdD or dD = as,^,pdp, (VI, 18) 



where the pressure is measured in decibars and the geopotential in 

 dynamic meters. If the distribution of mass is known, the hydrostatic 

 equation can be used for computing the differences in pressure at two 

 dj^namic depths, Di and D2, or the difference in dynamic depth of two 

 pressures, pi and p2. In order to represent the pressure field completely, 

 it is necessary to know the isobars in one level surface or the topography 

 of one isobaric surface. 



In dealing with the atmosphere, complete information can be obtained, 

 because the distribution of pressure at sea level can be derived from 

 direct observations of pressure and because the decrease of pressure with 

 height can be computed from upper air observations of temperature and 

 humidity. When dealing with the oceans, however, one encounters the 

 fundamental difficulty that it is impossible to determine directly the 

 pressure in any level surface or the topography of any isobaric surface. 

 The sea surface itself can in the first approximation be taken as an isobaric 

 surface, but the topography of the sea surface cannot be ascertained, 

 although, according to oceanographic evidence, the sea surface in many 

 localities is definitely sloping. Consider the fact that in the Gulf Stream 

 off Cape Hatteras in latitude 35°N current velocities up to 150 cm/sec 

 have been observed. From equations (VI, 13) it follows that the slope 

 of the surface must be equal to 1.5 X 10~^. The current flows toward the 

 northwest, and the surface therefore rises toward the southeast, the rise 

 being 1.5 cm in 1 km. This slope is computed from observations of the 

 currents, and cannot be measured in any manner. Direct observations 

 of the pressure along the sea bottom would be of value only if the points 



