454 DUNTLEY [chap. 9 



underwater telephotometer by Duntley (1949, 1950). The data provide verifica- 

 tion of the contrast reduction equations and demonstrate the practical vahdity 

 of the approximation (Duntley, 1951; Duntley and Preisendorfer, 1952; 

 Preisendorfer, 1957). 



2. Inherent Contrast 



The inherent spectral contrast, Co{zt, 9, </>), of objects under water presents a 

 far more intricate analytical problem than does the contrast reduction effect 

 discussed above. To be rigorous, all of the reflectance and gloss characteristics 

 of both the target and its background must be known, and the three-dimensional 

 configuration of target and background must be taken into account with 

 respect to the underwater radiance distribution which irradiates their surfaces. 

 No practical general procedure for meeting these requirements is available but 

 research directed toward this goal is in progress. Two common and important 

 special cases are, however, easily treated : (1) an object which appears as a dark 

 silhouette, wherein the inherent contrast is —1, and (2) a horizontal matte 

 surface of known submerged reflectance, wherein the inherent spectral contrast 

 is controlled by the downwelling and upwelling spectral irradiances H{z, — ) 

 and H{z,+) (Duntley, 1960). 



3. Sighting Range 



Most underwater sighting ranges are so short that the visual angle sub- 

 tended by ordinary objects is sufficient to make the exact angular size of the 

 object unimportant. Underwater sighting ranges are, therefore, usually con- 

 trolled by the contrast transmittance of the path of sight, i.e. by water clarity. 

 This is not true of very small objects (e.g. small pebbles, grains of sand, etc.) 

 nor is it true when semi-darkness prevails because of depth or low solar eleva- 

 tion. Nomographic charts for predicting underwater sighting ranges for objects 

 of any size from data on a{z), K{z), depth, solar altitude, target reflectance, 

 bottom reflectance, etc. have been prepared by Duntley (1960) on the basis of 

 equation (6) and visual threshold data by Taylor (1960). 



Application of the nomographic visibility charts to a wide variety of under- 

 water visibility problems in many kinds of natural water has resulted in the 

 following useful rules-of-thumb : 



1. Most objects can be sighted at 4 to 5 times the distance 



ll[a{z)-K{z) cos 6]. 



2. Large dark objects, seen as silhouettes against a water background, can 

 be sighted at the distance 4/a(z) when the path of sight is horizontal. (This 

 rule can be used by swimmers for estimating a{z).) 



3. In some natural waters a{z) = 2.1K{z); in such waters the downward 

 sighting range of most objects = | the horizontal sighting range of large, 

 dark objects. 



