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Mathematical Model for the Transport of Degrading Atrazine Herbicide from the Surface

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Chapter 1 Introduction
1.1 Background
To meet the food needs of a growing world population and an apparent decline in arable lands available for cultivation each year, the incorporation of pesticides have become an essential component of modern day agriculture. Herbicides are a class of pesticides used for the control of weeds on farmlands or other areas where plants may be undesirable. They have become ever more popular for use in agriculture since the 1950s when phenoxyacetic acid was first discovered and found to be less toxic to mammals than other pesticides. The selective action of these herbicides enabled the control of many broadleaved and grassy weeds that compete with many grain crops (Waxman, 1998).
Atrazine, a member of the Triazine group of herbicides was first released in the United States for commercial use in 1958 by Syngenta, and since then became the most popular herbicide used (US EPA, 2007) for the control of weeds in maize, sorghum, sugarcane, guava, etc. (Eisler, 2007). According to the USEPA 2006-2007 market estimates, 5.2billion pounds of pesticides were used worldwide with the United States alone accounting for about 22% of that total. Of the amount of herbicides used worldwide, 25%  was in the United States with atrazine being the second most widely used after glyphosate; 33-55million kilograms and 82-85 million pounds of atrazine and glyphosate respectively (Grube, Donaldson, Kiely, & Wu, 2011).
There has been a worldwide increase in the production of cereals since the 1960s, maize in particular, with some researchers attributing the improvement in the maize yield to the use of atrazine in the control of weeds and reduction in expensive tillage practices compared to the prices of herbicides which have been relatively cheap (Gianessi, 2013). Benson (1982) reports that maize yield in Nigeria almost increased two-fold when atrazine was used to control weeds. It was also shown that in Zimbabwe, there was a 50% boost in the yield of maize (Chivinge, 1990) and a 33% better maize yield in weed trials in Kenya was also realized (Muthamia, 2001). However, since the purpose of herbicides is specifically to kill weeds, they are fundamentally toxic and can negatively affect living organisms which may not be intended, and their use, therefore, create danger of damage despite the positives they bring to improving the yield of crops and in the control of noxious weed (Pohanish, 2014).
A number of health concerns have been raised and linked with the use of atrazine over the years both on human and wildlife. A principal target of atrazine in humans when ingested is the endocrine system, where it acts as an endocrine disruptor (Bohn, Cocco, Gourdol, Guignard, & Hoffmann, 2011; Pohanish, 2014; Komsky-Elbaz & Roth, 2017; Deng, Jiang, Zhang, Hu, & Crawford, 2008). Atrazine has also been implicated in causing birth defects, reproductive tumours, and weight loss in both humans and amphibians (Singh & Cameotra, 2013).
According to Bohn et al (2011), Atrazine has a high Groundwater Ubiquity Score (GUS), which indicates the capability of atrazine to act as a pollutant to groundwater systems because of its persistence and moderate mobility in soils. Although Atrazine is labeled as a Restricted Use Chemical by the USEPA, it is still one of the most detected chemicals in surface and ground waters in the United States and Mexico since it is still very popular (Prado et al., 2014, Abu-Zreig & Abu-Ashour, 2004). It has been banned in the European Union since  June 2003 because of its continuous detection above the maximum limits of detection in surface and groundwater set for countries within the European Union (Cherrier, Boivin, Perrin-Ganier, & Schiavon, 2005).
No-till technologies in agriculture in Ghana has promoted the use of herbicides with atrazine a very commonly used herbicide on the market alongside glyphosate in the control of weeds in maize, pineapples, and tomatoes  (Ekboir, Boa, & Dankyi, 2002; Yeboah, Lowor, & Akpabli, 2005). There have been calls for atrazine to be banned in Ghana as well due to its consistent use on maize farms in Ghana,  (Mensah, 2011), with the Northern Presbyterian Agricultural Services reporting of the Ghana government considering the suspension of atrazine (NPAS, 2012).
Since the dynamics of research sometimes do not allow a mass transfer of research results from one environment to another, there is a need to model the transport and fate of atrazine in the Ghanaian context. It is against this background that this research is undertaken to enable a viable understanding of atrazine transport in Ghanaian soils.
1.2 Problem Statement
Despite the numerous advantages derived from the use of atrazine in controlling weeds, it has received considerable attention due to its persistence in the soil and its ability to contaminate surface and ground water resources. Once applied, because of its moderate solubility, atrazine is able to leach into groundwater with several research publications reporting on the detection of atrazine in groundwater sources.
In Ghana, there is the added danger of misapplication of pesticides (in general) since most farmers are ill-informed about the dangers that may be associated with the incorrect use of such chemicals and therefore some resort to wrong application rates hoping that will yield maximum results. Such approaches tend to increase the concentration of the pesticides in the soil. Some past research have reported about the detection of atrazine in ground waters especially in certain areas of the Brong Ahafo and Ashanti regions where maize is the main crop grown (Miensah, 2015).
The research problem considered in this thesis is to mathematically model the transport of the very popular, moderately soluble herbicide atrazine through a vertically heterogeneous unsaturated soil column.
Most works in Ghana deal with assessment and monitoring of groundwater systems by regular sampling, but this can be expensive and time-consuming. With the appropriate parameters, a mathematical model that will be able to provide a quick and easy estimation of the travel time of any concentration of applied herbicide into the soil.
1.3 Research Relevance and Justification
This research seeks to formulate and develop a mathematical model to predict, monitor and estimate the fate of the moderately soluble herbicide atrazine at different depths and times as it is transported through the soil and into aquifers. This could contribute to the general simulation of non-point source pollution problems usually associated with chemicals that are applied in agricultural production.
The chemical transport model will aid in providing understanding of transport of the atrazine considering that atrazine transport is heavily influenced by the saturation of the soil and its chemical degradation pathways.
1.4 Objectives
The overall aim of this research work is to formulate a mathematical model for the transport of degrading atrazine herbicide from the surface through a heterogeneous soil of varying moisture saturation.
The specific objectives are:

  1. Derive a simple one-dimensional Convective-Dispersive Equation (CDE) with a first order decay term for the solute transport model
  2. Derive the Richards’ equation governing the unsaturated-saturated flow of a fluid in porous medium
  3. Solve the CDE and Richards’ equation numerically using implicit finite difference methods under heterogeneous soil conditions.
  4. Test the model with a one-dimensional analytical solution for solute transport in a homogeneous soil.
  5. Verify and validate the model developed from results of similar studies in literature.
  6. Ascertain how long it takes for atrazine applied at a given rate on a soil surface to reach the groundwater as well as the amount that enters the groundwater over a given period in a selected hypothetical situation.

1.4 Scope of Study
This thesis work involves the mathematical modeling of atrazine herbicide that is assumed to undergo a first order degradation reaction as it is transported through the unsaturated zone of a layered heterogeneous soil using numerical methods for the solution of the solute transport and the fluid flow problem through porous media. The numerical technique to be employed is the one- dimensional finite difference method for the solution of partial differential equations.
This thesis is organized as follows:
Chapter one (1) contains an introduction to the research problem enumerating why the research is to be carried out, the research problem statement, relevance and justification, and objectives. Chapter two (2) gives a review of the pertinent literature regarding the atrazine, it’s degradation in soil, flow in porous media, factors affecting the transport of solutes, and the transport models.
Chapter Three presents the Research methodologies regarding the derivation of the convective-Dispersive Equation, derivation of the Richards’ equation and the numerical solutions to these respectively. A Matlab program is written to simulate the transport process. The results of the simulation and a discussion of the results are given in Chapter Four (4). In Chapter Five (5), we present our conclusions of the study and make recommendations and suggestions for further research. A bibliography of the relevant literature cited in this study as well as an appendix is also provided at the end.

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