Modeling phosphorus transport in a river under unsteady flow conditions

Phosphorus is the key nutrient for phytoplankton growth in water bodies; it has been identified as a source for the hypoxia problem in the Gulf of Mexico. The in-stream dynamics of phosphorus transport is complex and has not been understood well. In this study, a new model for phosphorus transport was developed to investigate within-channel river dynamics. This convective-dispersive model is coupled with hydrodynamics and sediment transport sub-models to simulate suspended sediment, total dissolved phosphorus, total phosphorus, and particulate phosphorus concentrations with changing flow conditions. It emphasizes sediment and phosphorus dynamics in unsteady flow conditions and differs from many previous solute transport studies conducted under steady-state flow conditions. The study also attempts to connect the structure of the bed sediment sub-model to the storage zone concept from previously conducted solute transport studies.; There exist possible problems of numerical dispersion and instability in the solutions, which may occur due to varying velocity under unsteady flow condition. To solve this problem, various numerical methods were tested and the implicit Lagrangian method was selected, which showed least numerical dispersion, given a computational grid size. The model is applied to a 55-km stretch of the River Swale in Yorkshire, UK, within the framework of the Generalized Likelihood Uncertainty Estimation (GLUE) methodology. The GLUE methodology is a Bayesian Monte Carlo simulation-based technique, in which multivariate information on the model system can be easily integrated. Utilizing this property, sequential conditioning corresponding to simulation dependency was carried out. In-stream dynamics was identified by comparing the model predicted results with the observed variables. Various forms of phosphorus flux between the flow and sediment were also simulated, showing the effect of sediment particle size on phosphorus transport. Finally, model parameter sensitivity analysis was carried out within the GLUE framework. Results indicate that the in-stream dynamics of phosphorus can be successfully investigated by the modeling approach.