SECT. 4] LIOHT 407 



There exists another way of obtaining a. This method requires no previous 

 knowledge of a or s. It appHes to horizontally stratified media like the ocean, 

 and is exact, completely general, and particularly simple to use in natural 

 hydrosols. This is the method which makes use of the divergence relation of the 

 light field (Preisendorfer, 1957) and yields the equation : 



''"^^^^^ ^a(Z)HZ). (27) 



H{Z, +) is the net upwelling irradiance measured at depth Z, i.e. H{Z, +) = 

 H{Z, +) — H{Z, —). Here H{Z,+) is the irradiance at depth Z on a cosine 

 collector which receives the upward moving flux. H{Z, — ) is the irradiance at 

 depth Z due to downward moving flux. h{Z) is the scalar irradiance at depth 

 Z, and a{Z) is the value of the volume absorption function at depth Z. Accord- 

 ing to (27), to obtain a{Z) one performs the following operation: 



1 dH{Z,+) 

 ^(^) = h{Z) dZ ^^^^ 



on the measurable quantities H{Z, +) and h{Z). In the determination_of a{Z) 

 by this method, it is clear that in order to evaluate the derivative oi H{Z, +), 

 measurements of H{Z,+) and H{Z,-) must be made in some interval of 

 depths about the depth Z. 



The volume absorption coefficient is an* inherent optical property of the 

 medium, and has the dimension of reciprocal length. 



E. Apparent Optical Properties 



The apparent optical properties of natural waters consist at present of a set 

 of seven quantities whose numerical values depend on the angular structure 

 of the light field as well as on the physical composition of the water. 



The apparent optical properties can be obtained from four basic measure- 

 ments ; a pair of irradiances and a pair of scalar irradiances. In each of these 

 pairs, one member is assigned to upwelling flux, the other to down welling flux. 

 The reason that there are precisely four such quantities stems from the con- 

 ceptual decomposition of the flow of radiant energy in any natural hydrosol 

 (stratified or not) into two streams — an upward flowing stream and a dow^n- 

 ward flowing stream across each horizontal plane in the medium. 



The four basic irradiances are: 



H{Z,+) h{Z,+) 



(29) 

 H{Z,-) h{Z,-). 



H{Z, +) and H{Z, -) are the upwelling { + ) and doivnwelling { — ) irradiance, 

 respectively. They are induced by the up- and downwelling flux streams at 

 depth Z. These quantities may be obtained from field-radiance measurements, 

 or they may be measured by flat irradiance collectors. In like manner, h{Z, + ) 



