A(h) = 



1 



















1 











-3 



-2 



3 



I 



h 2 



h 



h 2 



h 



2 



1 



-2 



1 



h 3 



h 2 



u 3 



h 2 



, K :: = 



U i-i/.-i Vi,h u i-i,i Vi,j 



P S P s 



i-l,j-l i-l,j-l i-l,j i-l,j 



U. . . q. . . U. . 



P. . . s. . P. . 



'/I 



and a 



00 



30 



03 



• 'I 



a 



33 



Substituting the a elements into equation (19) produces a two-dimensional 



mn 



cubic polynomial formula representing the data within each of the R.. subareas 



covering R. The mean value of the field (C), within the R.. rectangle, is 



i| i| 



computed from equation (19) by 



Si"? / / 



h x. , y. 



■1 



-1 



3 3 



2 2 



i=0 n=0 



"mn (x-x ; _ 1 ) m (y-y t _ 1 ) n dydx. (21) 



i-1 



The bicubic spline computer program given in the appendix contains 

 the option of evaluating this integral between arbitrary limits within each 

 R.. rectangle. This feature allows computation of the mean anomalies at a 

 grid spacing either equal to that of the U.. input data, or one-half or one-third 



the spacing of the input data. Setting the (x. 



T 



y. i) origin equal to (0,0), 



13 



