A reaction-based river/stream water quality model: Reaction network decomposition and model application

Fan Zhang, Gour Tsyh Yeh, Jack C. Parker, Hongbo Zhang, Xiaonan Shi, Cheng Wang, Ruochuan Gu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper describes details of an automatic matrix decomposition approach for a reaction-based stream water quality model. The method yields a set of equilibrium equations, a set of kinetic-variable transport equations involving kinetic reactions only, and a set of component transport equations involving no reactions. Partial decomposition of the system of water quality constituent transport equations is performed via Gauss-Jordan column reduction of the reaction network by pivoting on equilibrium reactions to decouple equilibrium and kinetic reactions. This approach minimizes the number of partial differential advective-dispersive transport equations and enables robust numerical integration. Complete matrix decomposition by further pivoting on linearly independent kinetic reactions allows some rate equations to be formulated individually and explicitly enforces conservation of component species when component transport equations are solved. The methodology is demonstrated for a case study involving eutrophication reactions in the Des Moines River in Iowa, USA and for two hypothetical examples to illustrate the ability of the model to simulate sediment and chemical transport with both mobile and immobile water phases and with complex reaction networks involving both kinetic and equilibrium reactions.

Original languageEnglish
Pages (from-to)605-620
Number of pages16
JournalTerrestrial, Atmospheric and Oceanic Sciences
Issue number5
StatePublished - Oct 2012


  • Chemical equilibrium/kinetics
  • Chemical reactions
  • Eutrophication
  • Rivers/streams
  • Sediment transport
  • Water quality models


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