NO. 10 WATER TRANSPARENCY — WILLIAMS, JOHNSON, DYER 7 



B b = Brightness of the surrounding water at the hydroscope depth. (This 



is the background against which the Secchi Disc is seen.) 

 B D = Actual brightness of the disc at the disc. 



BbD = Actual brightness of the surrounding water at the disc depth. 

 R, = Reflectance of the sea surface. 

 Rd = Reflectance of the Secchi Disc. 



Uv, = Relative amount of light going in an upward direction compared to 

 that going in a downward direction at the hydroscope depth. 

 D = Length of attenuating medium interposed between the eye and the 



object. 

 d = Depth of the glass-bottom bucket or hydroscope. 

 k = Extinction coefficient. 



When the Secchi Disc is observed, it can be seen as long as the 

 brightness of the disc is greater than that of its surroundings. In 

 other words, the contrast produced by the disc against its background 

 allows the disc to be seen as long as this contrast is above the thresh- 

 old value for human visibility. 



Contrast is usually defined in the following manner : 



^ . , [ Object brightness — Background brightness 



Background brightness 



where the absolute value signs are used to keep the quantity positive 

 when contrast is produced by a dark object on a light background. 



In this particular case, there are two distinct contrasts to be dealt 

 with — the apparent contrast, or that which the eye sees, and the actual 

 contrast, or that which actually exists at the disc level. 



Using the symbols defined above, the apparent contrast Ca may be 



expressed as : 



, x „ Bo — Bb 

 (0 Ca — —b 



Db 



and the actual contrast, Cn, by : 



/ \ ^ BoD BbD 



(2) Crz 



BbD 



It turns out that diminutions of contrast through an attenuating 

 medium follow this relationship : 



(3) CA=Cne-" D 



or, substituting the values for C A and C R from (i) and (2) in (3) 

 we get : 



/ v Bo Bb BoD BbD _fcn 



(4) — o = 5 e 



Db BbD 



Since B is the brightness of the disc at the eye, this means that only 

 the amount of sunlight reaching the eye from the disc is involved. 



