LRMS = RMS/Vl + (k ' B)2 , (7) 



where RMS is the recorded root mean square of departures between temperatures 

 on a regression line and the temperature data that the line is supposed to fit; 

 LRMS is the RMS corrected to represent departure of data points from a regression 

 line in the bathythermogram, in units of termperature; k is the constant relating 

 measures of depth and temperature (equals about 14.5 meters per degree Celsius); 



and B is equal tn ^ 1 ^ where (z] , T]) and (z2, T2) are the regression points 



bracketing the interval of interest. 



The RMS is provided as a measure of the appropriateness of fit of a regres- 

 sion line to a set of data points. It may be interpreted as an indication of profile 

 roughness over the range of the line, as an index of random scatter of data points 

 within the thickness of a smooth stylus trace, or as a combination of these factors. 

 If there is ambiguity in the choice of interpretations available there is likewise 

 ambiguity in the interpretation of digitized points that provide the lines of fit. 



COMMENTS AND CONCLUSION 



A. Room for Analytical Studies 



The profile regression problem and the method of solution described 

 here provide a rich source for extensive statistical studies, with inquiries 

 concerning: comparisons between the graphical method of solution using 

 relationships of measure taken from the standard scale bathythermograph and 

 alternative solutions; the appropriateness of fitting straight lines to a profile 

 data set, as opposed to fitting other types of curves; alternatives to selecting 

 a median regression point when regression lines on overlapping line sets do 

 not intersect in the range of overlap; possible variations of the three level 

 tolerance algorithm using different tolerance ratios, and comparisons; the 

 application of this solution algorithm to profile data sets other than those 

 afforded by mechanical BT's; the best method for selecting regression filters, 

 or "line thicknesses", to process mass quantities of profile data. 



B. The "Thr ee Level Tolerance Algorithm" 



The three level tolerance algorithm was devised to simulate a graphical 

 approach to detecting profile line sets with ruler and pencil. That is, a 

 graphical approach to digitizing significant depths on a BT would be: (1) identify 

 profile segments that obviously constitute straight lines (identify an initial set of 

 thin line sets); (2) identify points of intersection between neighboring straight 



17 



