part in 100, for all depths (0 to 500 fm.) and for all 

 surveys and nautical charts used in the compilation. 

 Because of lack of data on bias in the soundings, 

 I assumed unbiased work; hence, e^ was taken to 

 be zero. The variance of the observational errors 

 was estimated by assummg that the errors are 

 normally distributed and that the value, 1 part 

 in 100, represents 99 percent of the total distri- 

 bution (this assumption implies that systematic 

 and personal errors have been removed from the 

 data and that any reduction errors have a ran- 

 dom distribution). Therefore, 



±c?/100= ±2.576 VK7; ^^"^® K„=0.000015c?2 



where the variable d equals the maximum depth, 

 in fathoms, within each 5-minute unit area. 



To account for round-off errors, I added a con- 

 stant factor to eacli variance value. This factor was 

 0.083 fm. when the soundings were recorded to the 

 nearest fathom and 0.0023 fm. wlicn recorded to 

 the nearest foot. I assmued a rectangular, or uni- 

 form, distribution of these errors ; hence, the vari- 

 ance equals E~/Z (see Weatherburn, 1961, p. 14), 

 where E equals one half of the round-off interval. 



Positional' errors (cp). — Veatch and Smith 

 (1939) discussed the accuracy of positioning for 

 the radio-acoustic ranging methods used in the sur- 

 veys of the 1930's (see also Adams, 1942). They 

 concluded (p. 65) that the accuracy was 1 part in 

 200 for distances less than 100 nautical miles from 

 the control (reference) points used in a sm^vey. 

 To approximate a maximum estimate of positional 

 errors, I used 1 part in 100 for all of the surveys 

 (except for a few recent ones which cover a large 

 part of Nantucket Shoals) and all the nautical 

 charts. 



Again, because, of lack of data, I assumed un- 

 biased work; hence ij, was taken to be zero. The 

 variance of the positional errors was determined 

 in the same way as described above for observa- 

 tional errors; hence Fep=0.000015Z>% where the 

 variable D equals the maximum distance in nauti- 

 cal miles between each 5-minute unit area and the 

 nearest control point (sonobuoy or station vessel) 

 used in a survey. For nearshore nautical charts 

 the distance D was measured to the nearest promi- 

 nent shore feature. 



To each vai'iance value 1 added a constant fac- 

 tor — 0.0045 nautical mile, to account for such car- 

 tographic errors as paper distortion and misalign- 



ments in tracing and printing. Tliis factor was cal- 

 culated by assuming a normal distribution of car- 

 tographic errors with a 99 percent limit of ±0.1 

 inch or ±0.17 nautical mile at a scale of 1 : 125,000. 



For the recent sui'veys on Nantucket Shoals 

 (1959-61), during which electronic positioning 

 systems were used, I assumed a 99 percent error 

 of ±0.066 nautical mile (±400 feet) and a normal 

 error distribution; hence F(3;, = 0.0007 nautical 

 mile. To this was added the cartographic error 

 variance of 0.0045 nautical mile giving a constant 

 total error variance of 0.0052 nautical mile for 

 these surveys. 



Ivferpolatioii errors (ei and e/). — If we were 

 concerned with maps showing only the depths of 

 soundings, the total error would be a simple com- 

 bination of the positional and observational errors 

 discussed above. Because, however, we are dealing 

 with isobatli maps, interpolation erroi's must also 

 be considered. These errors are of two kinds: (1) 

 those associated with depths interpolated along 

 axes between actual soundings (primary interpola- 

 tion error, ei) and (2) those associated witii depths 

 interpolated between the primary interpolation 

 axes (secondary interpolation error, e/). 



The equations for computing these interpolation 

 errors are (Stearns, 1968) : 



e,= er = Q 



(3) 

 (4) 

 (5) 



These are based on a simple two-point linear 

 interpolation scheme. 



The evaluation of F,, and F,,, depends on the 

 particular survey pattern used. The quantity 

 (F|-|-7^) in equation 4 is the mean sum of the 

 squares of the distances between the soundings. 

 For a rectangular array of discrete soundings 

 along more or less parallel track lines, as is the 

 situation for most of the hydrographic surveys 

 of the Middle Atlantic Continental Shelf, this 

 quantity equals }i(a^+b-), where a is the distance 

 between track lines and b is the distance between 

 soundings on each line. By taking the mean of five 

 systematic samples of the two distances, I esti- 

 mated the quantities a and b for each 5-minute 

 unit area. 



42 



U.S. FISH AND WILDLIFE SERVICE 



