Development of a mathematical model considering nutrients kinetics for assessing uMgeni river water quality.
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Surface water is an essential component of the natural environment which needs to be sheltered from all sources of contamination because human and aquatic animals depend on it for their survival. However, the discharge of organic wastes into water bodies has deteriorated its quality and placed economic restrictions on water use. Anthropogenic inputs of nutrients into the water column has become one of the vast water quality problems around the world. This result in the reduction of dissolved oxygen level and promotes algae growth in the water body. Therefore, there is a need for the development of an effective nutrient management strategy which is essential in protecting the water body. Standard practice is to use water quality models as an important part of environmental valuation tools for modeling and controlling the surface water pollution. Water quality models have been a useful tool in maintaining the water quality status and evaluating the fate of pollutants in different water bodies. Numerous methods are available for solving solute transport in natural streams and rivers. However, existing methods are flawed either because of their limitation in application to a natural water body due to their inaccurate in estimating model parameters or their failure to simulate the advection component of solute transport. The Hybrid cell in series (HCIS) model which is a conceptualized model serves as an alternative method to solve solute transport in a natural river. It overcomes the difficulties associated with the existing approaches such as Fickian based models by converting its second � order partial differential equation to a first - order ordinary differential equation which could be solved analytically. Additionally, the conceptual hybrid model was able to include advection component to its process which overcomes the difficulty associated with mixing cells model. In this study, additional components to the conceptualized hybrid cells in series model have developed for the first order kinetic reaction of Ammonia (NH3), Nitrite (NO2) and Nitrate (NO3) along with advection and dispersion processes using mass balance concept. A basic hybrid model which consist of a plug flow cell and two different thoroughly mixed cells all connected in series is developed to predict nutrients solute transport in a river from a point source of pollution. Analytical solutions of the HCIS model along with the nutrients kinetics were obtained using Laplace transformation. A C-Sharp programming language was then used to implement the analytical solutions obtained for these models where a user-friendly software package was developed. The developed models were used to predict the temporal and spatial variation of the nutrients concentration in the water body v The potential of the developed model has been tested using hypothetical data and a field data obtained from uMgeni River to predict the effect of ammonia, nitrite, and nitrate nutrients concentration along the selected river reach. The data collected from several sampling locations along the study area from January 2014 to December 2014 were used to verify the model�s efficiency. The prediction of ammonia, nitrite and nitrate concentration using the developed HCIS models have shown excellent agreement with field data of the uMgeni River, South Africa. Thus, the analytical solutions obtained can accurately predict the nutrients solute transport in uMgeni River. Further, the study has shown that the response of hybrid models matched satisfactorily with the numerical solution of Fickian based Advection-Dispersion Equation model which was solved with explicit finite difference method. The performance of the model was validated using statistical tools based on the coefficient of determination (R2) which was carried out at a 95 percent level of confidence between the observed and simulated data. It was observed from the correlation that the observed and simulated values of the nutrients concentration in the river demonstrated a high correlation coefficient (R2) and the standard error (SE) was low for all components of the model (NH3, NO2, and NO3). Hence, the results show that the developed model has demonstrated high accuracy and provide a novel tool for predicting ammonia, nitrite, and nitrate concentration distributions in the River. This research work presents the development and application of HCIS model for predicting the concentration of nutrients, i.e., NH3, NO2, and NO3 in water bodies. Based on the study, the hybrid model is effective in predicting the spatiotemporal concentration of ammonia, nitrite, and nitrate nutrients in the natural water body. However, the influence of high rainfall event significantly increases the nutrient concentrations of the river which was not considered in the current model. Thus, this gives a prospect for the consideration of non�point source pollution component in the hybrid model formulation.