ASnA 2 



f&Xm\ 2 



4 4 



— = — Z (ejmXm)^ + — : E E termini) 



/6a mi \2 



n j 2 m=1 



v m 



n j m=1 i=1 



'mi 1 



'mi 



(14) 



The definition of x^ (eq. (10)) and the general variance equation (12) can 

 be readily used to show 



6P r (Xi) 



-|2 



_P r (Xi) J |_ P o( x i) _ 



6P (Xi) 



-|2 



V k i / 



(15) 



where k^ = Yf + Yi- F° r the present discussions the subscripts are dropped 

 from the normalized variances (e.g., 5o m i/a m i = 6a /a for m = 1,2,3»4 and 

 i = 1,2,3,4). Equations (14) and (15) then become 



1 4 

 — r E ( £ jm x m) 

 n j m=1 



'6x > 



— E E (e jnPmi"i) 2 

 n j m=1 i=1 



(16) 



and 



'Sx\2 /6P r ^ 



'«SPo\ 2 



'6k' 



(17) 



These equations were evaluated for two cases. In case I, the calculated 

 normalized variance for the chlorophyll a concentration was based upon the 

 laser excitation wavelengths and fluorescence cross sections which are used in 

 the ALOPE system (ref. 14) and are shown in table 2. In case II, a set of 

 optimized laser wavelengths were visually chosen from figure 5 so that the dif- 

 ference between each algal color group and the other three would be maximized. 

 The fluorescence cross sections for each algal color group at each laser wave- 

 length were obtained from the data presented for representative algal species 

 in figure 5 of reference 14. Table 3 lists these parameters. No consideration 

 was given to the practicality of using lasers which operate at these wave- 

 lengths; however, all wavelengths throughout the visible spectrum can be 

 obtained with high gain dye lasers. For both cases I and II it was assumed 

 that there was a mean concentration of 20 ug/liter of chlorophyll a in vivo in 

 all algal color groups present in the water, and the power received for each 

 excitation wavelength was calculated from equation (8) using the following 

 laser fluorosensor system parameters from reference 14: 



5 = 0.25 



A r = 0.05 m 2 



16 



