The vertical distribution of algae can change dramatically in the first 

 5 m and the ratio of fluorescence to chlorophyll a concentration changes with 

 depth because of different amounts of solar irradiance reaching different 

 depths (ref. 26). In terms of the present analysis, only average values of 

 chlorophyll a concentrations and fluorescence cross sections can be used. The 

 errors involved in these assumptions are difficult to quantify in terms of 

 their impact on the accuracy of chlorophyll a in vivo concentration because 

 each measurement condition is different. The horizontal variation of algae 

 can be very large over only a few meters, especially during bloom conditions; 

 and with large changes in algal concentrations, large changes in the attenua- 

 tion coefficients occur. For these reasons it is imperative that all measure- 

 ments be made over the same sampling volume. 



Discussion of Error Analysis Results 



For single-wavelength laser fluorosensor systems, it can be seen from 

 table 1 that increased measurement accuracy of output and received power from 

 5 to 2.5 percent does not significantly decrease the error in the chlorophyll a 

 concentration when the error in the effective attenuation coefficient is 

 greater than 10 percent. Without remote measurement capability for the atten- 

 uation coefficient, the error in its estimation can be large, greater than 

 50 percent. If the standard deviation of the effective attenuation coefficient 

 is small, the uncertainty in the chlorophyll a concentration is nearly the same 

 as it is for fluorescence cross section. Thus, the resulting standard devia- 

 tion for chlorophyll a concentration depends primarily upon both Sk/k and 

 6a /a. 



From the fluorescence cross section data presented in reference 14, an 

 excitation wavelength can be selected for which the fluorescence cross sections 

 for all four algal color groups are nearly equal. The approximate wavelength 

 is 6 1 8 nm. The average fluorescence cross section information at this wave- 

 length for the color groups is given in table 2. If an average fluorescence 

 cross section of 0.15 x 10~21 m^ is assumed for any algal composition encoun- 

 tered with the single-wavelength laser fluorosensor system, the maximum error 

 in the fluorescence cross section is 40 percent, and thus the standard devia- 

 tion 5n/n would be less than 40 percent. Uncertainties in effective atten- 

 uation coefficients and fluorescence cross section due to factors listed in 

 previous sections also influence the error in the chlorophyll a concentration, 

 as shown in table 1 . With a supplemental remote measurement of attenuation 

 coefficients, it is felt that the concentration of chlorophyll a can be deter- 

 mined within 100-percent accuracy, which is sufficient for many applications. 



For the multiple-wavelength laser fluorosensor to be able to determine the 

 chlorophyll a concentration in each algal color group, the uncertainties of the 

 fluorescence cross sections must be reduced so that the normalized standard 

 deviation for the chlorophyll a concentration in all color groups is less 

 than 1.0. Under these conditions, matrix equation (11) can be solved without 

 difficulty for the concentration matrix. If 6n/n is greater than 1.0 for any 

 color group due to an uncertainty in a , £ is an ill-conditioned matrix, which 

 can produce completely unrealistic values for the chlorophyll a concentrations 

 (e.g., negative concentrations). The error analysis for multiple-wavelength 



22 



