132 BACASTOW AND KEELING 



The equations for total boron and alkalinity are 



SB - [B(OH) 3 ] + [B(OH) 4 ] = (l + Y^j [B(OH) 4 ] (D.12) 



A= [HCO" 3 ] +2[C0 2 3 "] + [B(OH) 4 ] + [OH] -- [H + ] (D.13) 



Consequently 



K,/[H'l : 2K,K 3 /[Hr ^B_^_ 



1 + Ki/[H + ] +K 1 K 2 /[H + ] 2 l + [H + ]/K B [H ] 



To calculate the evasion factor 



(Pm — Pmo)/PmO 



% = 



constant A 



_(2C-2C )/2C _ 

 Eq. D.14 for A is rearranged as a polynomial in [H + ] , 



5 



L D n [H + ] n = 

 n=0 



where 



(D.15) 



D - — KjK^KbKw 



D, = [(A - 2SC - 2B)K 2 K B - (K 2 + K B )K W ]K, 



D 2 = [(A - 22C + K B )K 2 + (A- 2C - SB)K B ] Kj - (Kj + K B )K W 



D 3 = (A- SB + K,)K B + (A - 2C + K 2 )K, - K w 



D 4 = A + Kj + K B 



D 5 =1 



The polynomial was iteratively solved by Newton's method for a new value of 

 [H ] corresponding to the new total inorganic carbon concentration 

 2C + A2C. The iteration step, 



i D n [H + ]P 

 [H + ] i+1 = [H + ];--^ (D.16) 



2 nD n [H + ]p-' 

 n=l 



