R = 100 m 



AXd = 5 nm 



AXf = 20 nm 



P (Xi) = 5000 W (peak power at each laser excitation wavelength X^) 



The normalized standard deviation for the chlorophyll a concentration for 

 cases I and II was determined from equations (16) and (17) for various values 



of the normalized standard deviations of 

 are shown in table 4. 



r > 



o> 



k, and a. These results 



Second approach .- In the second approach to the error analysis of the 

 chlorophyll a concentration, it is assumed that the ratios between the fluores- 

 cence cross sections at the four excitation wavelengths for each algal color 

 group are constant and only the absolute magnitude of the fluorescence cross 

 sections can change. With these assumptions, equation (9) can be reduced to 



£ a iJ b JJ n J 

 j=1 



where Oij = ^ijbjj and a^j are constants, 

 written 



In matrix form this may be 



X = A B N 



where B is a diagonal matrix and A is a matrix of constants. Taking a 

 derivative of both sides and using the chain rule results in the following 

 equation: 



X 1 = A B' N + A B N* 



By using matrix algebra, N' can be determined from 



N' = B" 1 A" 1 X' - B~ 1 B' N 



(18) 



where A -1 and B~^ are the inverse matrices for A and B. 

 shown that B"" 1 A -1 = Z~ 1 where Z~ 1 was previously defined, 

 matrix elements equation (18) can be written 



It can also be 

 In terms of 



17 



