A procedure for the calculation of pH in fresh and salt waters has bee
n developed. The method is based on a fourth-order polynomial relation
ship between hydrogen ion concentration and other (conservative) water
quality parameters. The method avoids trial and error estimations and
results in a direct calculation procedure that can be implemented in
models developed in various modeling environments, such as spreadsheet
s, conventional programming languages (BASIC, C, FORTRAN, PASCAL, etc.
) or specialized modeling languages (ExtendTM, StellaTM). The method d
eveloped is based on the solution of the full alkalinity-pH equation.
Because of the need for simplification of the equations to yield expli
citly solvable polynomial equations, the accuracy of the solutions dep
ends on the simplification made and varies with water properties. Thre
e simplifications are tested based on a second-, a third- and a fourth
-order polynomial equation for hydrogen ion concentrations. The equati
ons have been tested for salinities ranging from 0 to 35 parts per tho
usand (fresh to sea water), for temperatures ranging from 0 to 35 degr
ees C, for total carbonate carbon concentrations of 0.1 and 5.0 mmol/l
iter, and for total ammonia nitrogen concentrations of 0 and 10 mg/lit
er. Approximations are most accurate in waters of high total carbonate
carbon and low ammonia concentrations, where the fourth-order approxi
mation yields results that are within 0.05 pH units for the full range
of pH values tested (5-10).