systems was separated into two parts as a result of different statistics 

 applied to the fluorescence cross sections. The variance relationship between 

 P , P r , k, and n is the same in both cases. In table 4 the results are 

 presented for the normalized standard deviation of the chlorophyll a concentra- 

 tion when the fluorescence cross section is considered independent of excita- 

 tion wavelength. Even if the same sample volume is used for all excitation 

 wavelengths, at least a 10-percent uncertainty in the relative excitation spec- 

 tra for each of the color groups is anticipated. If different sample volumes 

 are used during a measurement cycle, the uncertainty in the fluorescence cross 

 section increases because of the possibility of changing algal concentrations 

 and composition. In table 4 it can be seen that even for <5a/a =0.1, case I 

 had a value of 6n/n > 1.0. Not until 6a /a was greater than 0.3 did case II 

 produce 6n/n > 1.0. It was explained previously that case I represented the 

 ALOPE parameters (table 2) and case II represented the set of optimized excita- 

 tion wavelengths given in table 3- Optimistic power measurement accuracies 

 (2.5 percent), knowledge of relative effective attenuation coefficients at all 

 excitation wavelengths to 5 percent, and a modest 10-percent standard deviation 

 of fluorescence cross section produce 177-percent uncertainty in the concentra- 

 tion of chlorophyll a contained in the golden-brown algae when ALOPE parameters 

 are used and only 53 percent when the optimized excitation wavelengths of 

 case II are used. (Measurements for golden-brown algae have the most uncer- 

 tainty in 5n/n.) In general, use of the optimized excitation wavelengths 

 reduce the uncertainty in chlorophyll a concentration by a factor of 3 from 

 the ALOPE parameters. 



When the spectral variation in the fluorescence cross sections for a color 

 group is assumed to be in a constant ratio, even though the absolute magnitude 

 may change due to light, age, and chemical factors, the chlorophyll a concen- 

 tration standard deviations given in table 5 result. As was discussed previ- 

 ously, the magnitude of the fluorescence cross section can vary over 100 per- 

 cent by chemical stress. The ALOPE system parameters, which were used in 

 case I, produce unacceptably high uncertainties for all the input parameters 

 shown in the table. The optimized excitation wavelengths used in case II yield 

 values for 6n/n which are less than 100 percent even for large uncertainties 

 in the fluorescence cross sections. 



The data presented in tables 4 and 5 are a result of different statistical 

 approaches which attempt to evaluate extreme values for the uncertainties in 

 chlorophyll a concentrations. In both approaches, the ALOPE system parameters 

 produced standard deviations in n greater than 3 times those produced in 

 case II, which assumed more optimized excitation wavelengths. 



CONCLUDING REMARKS 



Accuracy in the remote determination of chlorophyll a in vivo concentra- 

 tion depends upon the use of the correct equation for the power received by a 

 laser fluorosensor system. The appropriate form of this relationship is 

 derived in this paper (eq. (6)). Similar equations have been reported in the 

 literature; however, they differ from the present equation by as much as a 

 factor of 10. 



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