The narrow band absorption ratio RN relationship to pH is shown below.

pH = equConstant + log10 (( RN – e1)/(1-RN*e23) )

Figure 1. RN to PH

The photometer takes advantage of a direct relationship of RB and RN. Rn can be estimated from RB once a calibration procedure produces enough data to compute the equation of the line shown in Figure 2. Bo Yang et.al. found this empirical relationship which was used as their “one time” calibration of their broadband photometer.

RN = (1.1892) RB – 0.3079

Figure 2. Rn as a function of Rb

Below, the relevant equations from the Bo Yang paper translated into C++ :

double pH, equConstant,R, e1,e2,e3, e23;

double T, S; // temp and salinity

// set default values for S and T

// for salinity S values from 20 to 40

// for temperatures T from 278.15 K to 308.15 K

S = 30;

T = 303;

// eq 5

e1 = -0.007762 + (4.5174 / pow(10.0,5.0)) * T;

(10.0,4.0) *(S-35);

e23 = -0.020813 + (2.60262 / pow (10.0,4.0))*T + (1.0436 / pow (10.0,4.0)) * (S-35) ;

// eq 7 equilibrium constant equConstant

double a,b,c,d;

a = -246.64209 + 0.315971 * S + (2.8855/pow (10.0,4.0)) * S * S ;

b= 7229.23864 – 7.098137* S – 0.057034 * S * S;

c = 44.493382-0.052711 * S;

d = 0.0781344;

equConstant = a + b / T + c * log(T) – d*T; // log is the natural log ln

// eq 2

pH = equConstant + log10 (( RN – e1)/(1-RN*e23) );

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