Biogeosciences www.biogeosciences.net 1726-4170 1726-4189 5 1 2008 10.5194/bg-5-227-2008 http://www.biogeosciences.net/5/227/2008/ http://www.biogeosciences.net/5/227/2008/bg-5-227-2008.html http://www.biogeosciences.net/5/227/2008/bg-5-227-2008.pdf 227 251 2008-02-21 A step-by-step procedure for pH model construction in aquatic systems A. F. Hofmann a.hofmann@nioo.knaw.nl F. J. R. Meysman K. Soetaert J. J. Middelburg Netherlands Institute of Ecology (NIOO-KNAW), Centre for Estuarine and Marine Ecology, P.O. Box 140, 4400 AC Yerseke, The Netherlands We present, by means of a simple example, a comprehensive step-by-step procedure to consistently derive a pH model of aquatic systems. As pH modelling is inherently complex, we make every step of the model generation process explicit, thus ensuring conceptual, mathematical, and chemical correctness. Summed quantities, such as total inorganic carbon and total alkalinity, and the influences of modeled processes on them are consistently derived. The different time scales of processes involved in the pH problem (biological and physical reactions: days; aquatic chemical reactions: fractions of seconds) give rise to a stiff equation system. Subsequent reformulations of the system reduce its stiffness, accepting higher non-linear algebraic complexity. The model is reformulated until numerically and computationally simple dynamical solutions, like a variation of the operator splitting approach (OSA) and the direct substitution approach (DSA), are obtained. As several solution methods are pointed out, connections between previous pH modelling approaches are established. 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