408 



TYLER AND PREISENDOBFER 



[chap. 8 



and h{Z, — ) are the upwellincj ( + ) ond doivmvelling ( — ) sadar irradiances, and 

 refer to up- and downwelling flux, respectively, at depth Z. They may be 

 obtained from field-radiance measurements. Alternatively, spherical irradiance 

 collectors may be used to measure these quantities. A possible experimental 

 arrangement is shown in Fig. 7. Observe that the collectors are complete 

 spheres in each case, but the sphere that measures h{Z, — ), for example, should 

 be shielded from the upwelling flux by some device which at the same time 

 impedes as little as possible the interchange of flux across the horizontal plane 

 at depth Z. In analogy to our earlier discussion of the relation between h and 

 ^4„, we can show that the downwelling spherical irradiance, ^4„(Z, — ), actually 



t To Surface 



(o) (b) 



Fig. 7. Schematic arrangement for determining downwelling ( — ) and upwelling ( + ) 

 spherical irradiance. 



measured by the shielded sphere shown schematically in Fig. 7, is related to 

 h{Z, -)hy 



h^.{Z,-) = IHZ,-). 



(30) 



Similarly, the upwelling spherical irradiance, hi„{Z, +), measured by the other 

 shielded sphere shown schematically in Fig. 7, is related to h{Z, + ) by 



h4A^,+) = lh{Z,+). 



(3i; 



The connection between h4„ and the spherical irradiances deflned above, 

 assuming ideal shielding, is straightforward : 



h,„{Z) = hi„{Z,-) + h4AZ,+). 



(32] 



Furthermore, 



h{Z) = h{Z,-) + h{Z,+). 



(33) 



