9. UNDERWATER VISIBILITY 



S. Q. DUNTLEY 



Nowhere in nature are the principles of protective coloration and camouflage 

 better displayed than in the feeding-grounds of the sea, where predators and 

 prey alike depend for survival upon their ability to see. When man invades the 

 underwater world and peers through his face-plate at the new surroundings his 

 success and his safety depends in large measure upon his visual capability. 



1. Image Transmission 



Visibility underwater is restricted in a manner somewhat analogous to the 

 obscuration produced by dense haze or fog in the atmosphere, but the nature 

 of image transmission by water differs importantly from that by the atmosphere 

 because of the vastly greater space-rate of thermodynamically non-reversible 

 energy transformation, i.e. the transformation of light into heat, chemical 

 potential energy (as in photosynthesis), etc. This major effect, called absorption, 

 causes all aspects of daylight in the sea to decrease so rapidly with depth that 

 visual ranges along paths of sight inclined either upward or downward are 

 profoundly affected in a manner quite different from the atmospheric case, 

 where absorption is negligible except in clouds of dark smoke or dust. 



Natural waters are usually composed of horizontal strata each of which is 

 nearly uniform in its optical properties. When the path of sight is entirely 

 within a uniform stratum, the spectral radiance, N{zi, 9, <f>), measured at depth 

 2i by a radiance photometer pointed in a direction having zenith angle d and 

 azimuth angle ^ is found to be related to the corresponding spectral radiance 

 N{z2, d, (J)) at depth Z2 by the approximation 



N{z2,d,cf>) = N{zi, d, cl>) exj) {-[K{z, d, <j^)]{zi-Z2)}, (1) 



where the 2-axis is vertical and positive from the mean sea-surface upward and 

 K{z, 6, <j)) is the attenuation coefficient for spectral radiance in the direction 

 6, (f) at all depths between zi and 22. This mathematical model introduces the 

 justifiable approximation that the radiance ^-function, K{z, 6, <j)), is the same 

 at all points throughout the path of sight. 



If equation (1) is represented by the differential equation 



dN{z, 6, (f>)ldr = -K{z, 6, cf>) cos d N{z, d, (j)), (2) 



where r cos 6 = zi — zi, and if the equation of transfer for spectral field radiance 

 is written 



dN{z, d, cf>)ldr = N^ {z, d, ■<j>) - a{z)N{z, d, cf)), (3) 



and if the equation of transfer for the apparent spectral radiance, t^i^t, d, (f>), 

 of the visual target is written 



dtN{z, e, cf>)ldr = N^ {z, 6, <f>) - a{z)tN{z, 6, <j>), (4) 



[MS received July, 1960] 452 



