dynamic depth anomaly field. The latitude and longitude are used as the independent variables 

 because this is the most convenient form in which to obtain the data from NODC and thus no 

 coordinate transformations are necessary. The north-south and east-west geostrophic velocities 

 can now be obtained by differentiating equation (1): 



TJQ = 10 Sdp (2) 



f R sin 30 



10 dd n 



Vrf, = - 



iR dd 



where 



Vq = north-south velocity 



V0 = east- west velocity 



f = CorioUs Parameter 



R = Radius of the earth 

 The dynamic depth anomaly field frequently, however, displays so much structure that to 

 replicate it accurately with a single function of the form given in equation (1) would require a 

 polynomial of prohibitively high order. This difficulty can be overcome through the use of two- 

 dimensional spline fits of the data. In this case the area of interest is divided into rectangles 

 and the data in each rectangle is still fit by the method of least squares with a polynomial of the 

 form expressed in equation (1), but with the constraints that the different polynomials and their 

 first and, if necessary, higher derivative match on the boundaries of the rectangles. The order of 

 the polynomial is selected to yield whatever goodness of fit is desired. The advantage of spline 

 fitting is that the data which was previously fitted by one polynomial is now fitted by several 

 polynomials, allowing much more structure to be represented. Equations (2) can still be used to 



evaluate the components of geostrophic velocity. 



2 



