Js, 



O'tJo 



Figure 2.— Standard deviatiou of the isobath depth error. (1) Less than 0.25 fm. (2) 0.25-0.49 fm. (3) 0.50-0.99 fm. 

 (4) 1.00-1.99 fm. (5) 2.00-3.99 fm. (6) 4.00-7.99 fm. (7) 8.0O-15.99 fm. (8) 16.00-31.99 fm. (9) 32.00-63.99 fm. 

 (10) 64.00-127.99 fm. (11) 128.00 fm. and more. 



The figures in the diagram may be used to esti- 

 mate the expected correspondence between the 

 mapped depths and the true depths. This expected 

 correspondence is expressed as a probability that 

 the true depth falls between certain limits. For 

 example, if we assume a normal distribution of 

 depth errors in an area where the standard devia- 

 tion of the depth error is 1 fm., then the probabil- 

 ity is 99 percent that the indicated depth is correct 

 to within ±2.6 fm., 90 percent tliat the dei)th is 

 correct to within ±1.6 fm., or 50 percent tliat tlie 

 depth is correct to within ±0.7 fm. Tlie depth of 

 any isobath as shown on tlie maps should be 



thought of as representing a probable range of 

 depths rather than as a single exact depth. 



The above limits were computed by the formula 

 r=Zi(T, where r is the expected range of depths, 

 0- is the standard deviation taken from the depth 

 error diagram (fig. 2), and Z, is a number that 

 depends upon the probability i and upon the kind 

 of error distribution (see Dixon and Massey, 1957, 

 or other statistics textbooks). 



The above formula gives the expected range 

 due only to errors in the map. To find the expected 

 range when the maps are being used aboard a ship 

 to search for a given bathyraetric feature, the 



M 



U.S. FISH AND WILDLIFE SERVICE 



