the scattering coefficient is, in general, many times larger than the absorp- 

 tion coefficient (ref. 17). The irradiance at depth z includes unscattered 

 and scattered light. The effective attenuation coefficient is then less than 

 a because the scattered light is mostly forward scattered (ref. 18), and thus 

 it can also become part of the irradiance at depth z. The diffuse attenuation 

 coefficient determines the exponential attenuation of diffuse light with depth. 

 Duntley (ref. 19) empirically determined that the diffuse attenuation coeffi- 

 cient k is 



b 



k = a + - 



6 



Because of the large contribution of scattered light to the irradiance of the 

 laser light, the effective attenuation coefficient for laser penetration Y& 

 is better approximated by the diffuse attenuation coefficient kg, at the laser 

 wavelength than by the single-scattering attenuation coefficient. The limiting 

 value of Tg is ag for very large collection cone angles, that is, greater 

 than H0° (ref. 20); however, this extreme value for the effective attenuation 

 coefficient is not felt to be generally applicable for most laser irradiance 

 cases. In this analysis it is assumed that y is constant with depth. It 

 should be noted that Koeppen and Walker (ref. 15) have reported that y raav 

 change with depth; however, no generalized relationship was given for this 

 variation. 



The laser-induced fluorescence, in W/nm, emitted from the chlorophyll a 

 in vivo at 685 nm contained in the differential volume A z dz at a depth 

 of z is 



dF(Xf) AX f = H z AXg anA z dz (2) 



where 



AXf fluorescence bandwidth at 685 nm, nm 



0" cross section for fluorescence at 685 nm per chlorophyll a molecule 

 contained in the algae when excited by laser wavelength Xg,, 

 m^/molecule 



n concentration of chlorophyll a contained in the algae, molecule/m3 



The fluorescence cross section per chlorophyll a molecule is equal to the 

 fluorescence energy emitted per chlorophyll a molecule at 685 nm divided by 

 the incident excitation energy per unit area. 



The fluorescence which is emitted from the volume A z dz in the direction 

 of the laser fluorosensor system is refracted at the water surface. Thus, the 

 criterion for fluorescence to be collected by the telescope receiver system is 



