Modeling Diffusive Flux of Non Point Source Pollutants in Lake Victoria: A Comparison Study of Fick's Law and the Fokker-Planck Law

Abstract

Mathematical models have the potential to conceptually quantify, link and simulate the interactive processes of nature. In this study 68 samples were collected at Gaba landing site in Uganda during a rainy season and were analyzed for nutrients, namely, Ammonia, Nitrite, Nitrate, and Phosphate. In addition, portable meters were used to measure Total Dissolved Solids (TDS) and Dissolved Oxygen (DO) instantaneously at point of sample collection. Within the lake, sam- ples were taken at for horizontal transects of 10 metres (m) interval over a distance of 50 m from the shore where surface runoff was released. At each 10 m sampling point, three samples were drawn at vertical distances of 0.5 m, 1.0 m and 1.5 m from water surface using a hand pump with graduated delivery pipe. This paper presents the results obtained from the application of two alternative expressions, fick's law and Fokker-Planck law to gain insight into the pollutants diffusive flux patterns within the lake. We conclude that in general the Fokker-Planck model should be given preference, in model- ling Ammonia and Phosphate flux profiles while Fickian model should be deployed in modelling DO, TDS, Nitrites and Nitrates.