Subroutine MINCON is called in to calculate the starting 

 point for the profile within MSQLOC in minutes from the lower 

 left corner. MINCON uses the function AMP to calculate the 

 meridional parts for the latitude component. The mathematical 

 foundation for AMP is given in Thomas (1964) and in U.S. Naval 

 Oceanographic Office (1962) . 



Subroutine RHUMB is called in to calculate, using AMP, the 

 rhumb line bearing through the MSQLOC area. A rhumb line is 

 used here because the subroutine BATHY can only interpolate 

 along a straight line. The rhumb line approximates a chord of 

 the great-circle path on a Mercator chart with the maximum deviation 

 from the great circle at the approximate midpoint of that chord 

 in the MSQLOC area. This deviation varies from zero to a 

 maximum of about two nautical miles depending upon the great- 

 circle path orientation. Maximum deviations occur in east-west 

 paths in high latitudes, but are considered a necessary trade- 

 off for the system's overall speed of operation. 



The random-access storage device is queried by the subroutine 

 LOOKUP, which passes through the SYNTABLE to find the file key 

 and the relative address of the MSQLOC area, then extracts the 

 actual block size and the column and row information. These 

 parameters are used by the subroutine BATHY to extract gridded 

 bathymetric data for the MSQLOC area. 



From subroutine BATHY the subroutine GRIDBLK calls in the 

 gridded data. Subroutine BATHY determines which quadrant the 

 rhumb line will pass through so as to maximize the number of 

 intersections for interpolation. This quadrant will determine 

 whether or not the columns or the rows will be the independent 

 variable for the cubic spline. The quadrant arrangement is 

 shown in figure 15. 



If the rhumb line falls in quadrants 2 or 4 , the direction 

 of the first interpolation is along a column and the independent 

 variable is the distance from the origin along the column to the 

 intersection of the rhumb line. If the rhumb line falls in 

 quadrants 1 or 3 , the interpolation will be along a row and the 

 independent variable then is the distance from the origin along 

 the row to the intersection with the rhumb line. At the inter- 

 section a value is interpolated by the cubic spline using the 

 gridded data values along that column (or row) as the dependent 

 variable. 



When all the values have been interpolated at each inter- 

 section, the values now become the dependent variable v/hile the 

 distance along the rhumb line from the start of the profile 

 becomes the independent variable. The cubic spline is used once 

 more to interpolate the final profile values at distances 



27 



