SECT. 4] LIGHT 411 



H{Z, + ) and h{Z) also exhibit noticeable departures from linearity, especially 

 in near-surface regions. These departures from linearity were detected in the 

 early measurements but were not always attributed to changes in flux distribu- 

 tion in the field surrounding the collector. 



The current views in hydrologic optics are such that the departures from 

 linearity by semi-log plots of H{Z,-), H{Z,+) and h{Z) are a source of 

 extremely useful insight into the intricate structure of light fields in natural 

 hydrosols. The logarithmic slopes of the H{Z, - ), H{Z, + ) and h{Z) plots are 

 defined in general as follows : 



K(7 +)- 1 dHjZ, ± ) 



1 dH{Z) 



^^^^ = -m ~d^' ^^^^ 



F. Some Relations Between Inherent and Apparent Optical Properties 



Certain relations between the inherent and apparent optical properties 

 discussed above have been found helpful in collating the data of basic experi- 

 mental research and have provided, in some instances, deeper insight into the 

 "whys" and "hows" of the fine structure of the depth dependence of the 

 apparent optical properties. The derivations of these relations may be found 

 elsewhere (Preisendorfer, 1958). 



The most important of these connecting relations is the following : 



K(Z,-)-a(Z,-) 

 ^<^'-> = Z(Z,+) + a(Z,+)' (*«) 



where 



a{Z, ±) = D{Z, ±)a{Z). (41) 



Thus (40) links together the ^-functions for irradiance, the i?-functions and 

 the i)-functions, i.e. the main apparent optical properties, with the inherent 

 optical property a. 



There are also available the following useful inequalities : 



a[Z,-) ^ K{Z,-) < a(Z, -) (42) 



or, equivalently, 



Similarly, 



or, equivalently, 



where 



a{Z) ^ K{Z,-)ID{Z,-) ^ a{Z). (43) 



a(Z, 4-) ^ K{Z,-^) ^ a{Z,+) (44) 



a{Z) ^ K{Z,+)ID{Z,+) < a{Z), (45) 



a(Z, ± ) = D{Z, ± )a{Z). (46) 



