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Data-Based Mechanistic Modeling of Flow-Concentration Dynamics of Non-Point Source Pollution: A Case of Upper Vaal Water Management Area

George M. Ochieng’
Frederick A.O. Otieno
Julius, M. Ndambuki


This study aimed at applying the Data Based Mechanistic (DBM) modelling approach to develop a simple, parsimonious and discernable Flow-Concentration (F-C) model that can be partitioned into the various identifiable pathways associated with the pollutant at the catchment scale. An attempt was made to model the occurrence of acid mine drainage (AMD) in the Vaal River by using an indicator water quality parameter (sulphate concentration). The optimal Instrumental Variable (IV) methods of identifying and estimating discrete and continuous-time transfer function models as implemented in the CAPTAIN MATLAB® Toolbox were applied to the time series data in order to identify the appropriate model. A discernable F-C model was developed of three parallel pathways: the “quick-route” depletion pathway with a residence time months; a “slow-route” build-up pathway with a residence time months and a direct term component pathway regressed in 9 months. The resulting model showed that it is possible to use the DBM modelling approach to address the problem of representing the potential lag between polluting activity and its effect as well as provide more salient information about the system dynamics. This kind of information (i.e. the residence times and the advective time delays in the system) could prove useful for the catchment managers in making informed decisions including laying out remediation measures.


Keywords: Flow-Concentration Modelling, Non-Point Source Pollution, Data Based Mechanistic Modelling, Transfer Function models, Water Quality, Flow Pathways