by pantograph to dimensionally stable plastic 

 compilation sheets at a uniform scale of 1 : 125,000 

 (Mercator projection, scale of 1 : 125,000 at lat. 40° 

 X.) ; each sheet covered 1° of latitude and longi- 

 tude. Transfer was done in stages for each piece 

 of source material ; small quadrangles were trans- 

 ferred independently to minimize distortion of 

 scale and paper. Adjustment and matching be- 

 tween surveys, corrections, and final smoothing 

 of the isobaths were done on the compilation 

 sheets. The USCGS made the final map layout 

 and design. 



RELIABILITY OF THE MAPS 



Present technology makes it impractical to ob- 

 serve large areas of the sea floor directly; thus, 

 bathymetric maps are necessarily interpretive 

 drawings of an invisible surface (for discussions 

 of this subjective element in bathymetric mapping 

 see Veatch and Smith, 1939; Jones, 1941; and 

 Shepard, 1943) . Such maps are usually made from 

 discrete soundings, between which assumed depths 

 must be interpolated before contour lines of con- 

 stant depth (isobaths) can be drawn. The uncer- 

 tainty of these assumed dejjths, j^lus observational 

 and positional errors in the original soundings, 

 makes exact correspondence between a bathymetric 

 map and the real sea floor an impossibility. The 

 user of a map, however, should know what accu- 

 racy to expect. 



The following paragraphs of this section discuss 

 the evaluation of the reliability of the maps, the 

 reliability diagrams which appear on each map, 

 and the spatial distribution of the map errors. 



A general method for quantitative estunate of 

 the reliability of isoline maps has been presented 

 by Stearns (1968). In this general method the 

 reliability of isolines (expressed as a variance) is 

 related to (1) observational errors, (2) positional 

 errors, (3) interpolation errors, (4) errors in the 

 time of an observation, (5) synopticity errors (er- 

 rors due to lack of simultaneity in the observa- 

 tions), and (6) the space-time rates-of-change and 

 the directions of the gradients of the mapped 

 variable. 



In applying the method to the present bathy- 

 metric maps, I considered all the above factors, 

 with the exception of time and synopticity errors. 

 I omitted the time-dependent errors, first, because 

 little exact information is available on the rates- 

 of-change of bottom topography, and, second, be- 



cause such clianges, except in limited areas, are 

 likely to be very small during the period of useful 

 life of the maps. 



The reliability equations (Stearns, 1968), witli 

 the time-dependent terms omitted, are as follows : 



e3 = io+epPp Cos yp+eiQi Cos yi+^i'g,' Cos 7/ 



(1) 



which expresses the expected bias of the values of 

 the isobaths at any point on the map or within 

 any subarea of the map, and 



T%=T/„-f F,^(T/,^+^|) (Fc„. .,+C^^7; 



+ Ve,{V,^ + gl) (Fcoa .,+ C^=T,) (2) 



+ e?C^^.,[1^Cos 7, + C^= 7,]+^?Fcos y,) 



+V,;{V,/+gr-)(Vcosy,'+C^"-y,') 



+ '^ :HV,^'[Vaosy/ + C^' y/] + 9r-Vc.,sy/) 



which expresses the variance of the values of the 

 isobaths at any point, or within any subarea, on 

 the map. 



These equations may be evaluated for a map as a 

 whole (in which case a single average reliability 

 value would be obtained), or for any arbitrarily 

 selected small portion of a map. For the present 

 maps, the equations were evaluated for each ad- 

 jacent unit area of 5 geographical minutes to a 

 side. This unit area was selected as a compromise 

 between the geogi'aphic divei"sity of the map's reli- 

 ability and the time available for manual compu- 

 tation. Over 1,600 unit areas were involved in the 

 evaluation. 



Evaluation of the Reliability 



The evaluation of the terms in equations 1 and 2 

 are discussed in this section. 



Ohsermtional errors (e„). — The echosoundings 

 made during the sm-veys of the 1930's and used 

 as the basis for constructing most areas of the 

 present maps were evaluated by Veatch and 

 Smith (1939)— see also Adams (1942). They con- 

 cluded (p. 60) that the accuracy of these sound- 

 ings was within 1 part in 100 for areas deeper than 

 100 fm. and witliin 1 part in 200 for areas shallower 

 than 100 fm. To approximate maximum errors on 

 the shelf proper, I used their larger estimate, 1 



BATHYMETRIC MAPS AND GEOMORPHOLOGY OP MIDDLE ATLANTIC CONTINENTAL SHELF 



41 



