A mathematical model development for simulating in-stream processes of non-point source pollutants.

Abstract

In coming years, chronic water stress is inevitable owing to the unavailability of fresh water. This situation is occasioned by rapid urbanisation, climate change, rising food demand, and production. The increasing rate of water scarcity associated with water pollution problems, makes water quality management an issue of great concern. Rivers owe their existence to the relationship of rainfalls, soil properties and land use within a catchment. The entire hydrological processes that occur in the catchment area has a direct effect on occurrences and quality of the rivers there-in. A principal part of the hydrological cycle is runoff generation. Runoff characterises soil erosion, sediment transport, pollutants and chemicals all otherwise referred to as non-point source pollutants and released into water bodies. Most non-point source pollutants are generated from agricultural fields, informal settlements, mining fields, industrial areas, and roads. These sources produce increased nutrient concentrates (sewage effluent from informal settlements and fertilisers from agricultural fields) and toxic substances which alter the water quality in uncertain quantities. This affects aquatic biota and ultimately human health negatively. Non-point source pollution is a major source of water quality degradation globally and is the single most significant threat to subsurface and surface sources of usable water. Developed countries, unlike many developing countries, have long sought ways to stop the release of non-point source pollution directly into natural rivers through the establishment of best management practices but unfortunately with little success in actual practice. Numerous non-point source models exist which are basically watershed based and are limited to simulate the in-stream processes of non-point source pollution in water channels. Most existing non-point source models are site-specific, cumbersome to manipulate, need high-level operational skills and extensive data sets. Consequently, these models are difficult to use in areas apart from where they were developed and with limited data sets, as is the case with developing countries. Hence, to develop a non-point source pollution model that would adequately and effectively, simulate non-point source pollution in water bodies, towards restoring good river health is needed. This is required to enhance the proper monitoring and remediation of water sources affected by Non-Point Source Pollution especially in areas that have scarce data. Using the concept of the Hybrid Cells in Series model in this study, a hydrodynamic riverine Non-point source pollution model is conceptualized to simulate conservative pollutants in natural rivers. The Hybrid Cells in Series model was conceptualized to address the limitations identified in the classical advection dispersion model which is the foundation for all water quality modelling. The proposed model is a three-parameter model made up of three zones, which describes pure advection through time delay in a plug zone, and advection and dispersion occurring in two other thoroughly mixed zones linked in sequence. The model considers lateral inflow and pollutant loading along the river reach in addition to the point source pollutant entry and flow from upstream stations. The model equation for water quality along with hydrodynamic equation has been solved analytically using Laplace Transform. The derived mathematical formulation is appropriately coded, using FORTRAN programming language. Other components such as hyporheic exchange process and first order kinetic reaction simulations are incorporated to the proposed model. The response of these models matches the numerical solution of the classical Advection Dispersion Equation model satisfactorily when compared. The potential of the proposed model is tested using field data obtained from verifiable existing literature. A performance evaluation at 95 percent confidence is carried out. The correlation results of the observed and simulated data are seen to be in good agreement. The breakthrough curves obtained from the proposed model shows its capability to simulate Non-point source pollution transport in natural rivers effectively. The simplicity of the Hybrid Cells in Series model makes it a viable model for simulating contaminant transport from non-point sources. As the model has been validated using recorded data collected from the field for a specific tracer injection event, it is imperative to carry out investigation on changes in model parameters before, during and after storm events. However, this study adequately addressed and attempted to develop, validate new model components for simulating non-point source pollutant transport processes in stream.