A Reaction-Based, Diagonalization Approach to Water Quality Modeling

There are many water quality models (e.g., WASP, QAUL2E/QUAL2K, CE-QUAL-ICM, etc.) that have been employed by practitioners in surface water quality modeling. All of these models are similar to each other. The major differences among them are the number of water quality parameters included and the number of biogeochemical processes considered. There is a need to develop a model that would allow the inclusion of any number of water quality parameters and enable the hypothesis of any number of biogeochemical processes. This paper presents the development of a numerical water quality model using a general paradigm of diagonalizing reaction networks. In a reaction-based approach, all conceptualized biogoechemical processes are transformed into a reaction network. Through the decomposition of species governing equations via Gauss-Jordan column reduction of the reaction network, fast reactions and slow reactions are decoupled, which enables robust modeling of fast/equilibrium reactions. For example, the model alleviates the needs of using simple partitions for fast reactions. The system of species governing equations is transformed into three sets: algebraic equations (either mass action equations or users' specified) of equilibrium-variables, differential equations of kinetic-variables and differential equations of component-variables. With the diagonalization strategy, it makes the inclusion of arbitrary number of fast and kinetic reactions relatively easy, and, more importantly, it enables the formulation and parameterization of kinetic reactions one by one. To demonstrate the flexibility and generality, the eutrophication model in WASP5, QUAL2E, and CE-QUAL-ICM are recast in the mode of reaction networks. This illustrates that the model embeds the most widely used water quality models as specific examples. Based on these three examples, the deficiencies of current practices in water quality modeling are discussed and the actions that must be taken to improve these practices are addressed.