\begin{center}
\begin{Large}
\textbf{
Module 3 Project for Group S2G1\\ Due 3$^\text{rd}$ November 2008 }
\end{Large}
\end{center}
\section{Research Paper}
\begin{description}
\item[Authors] Akira Watanabe, Masahiro Kasuya, Ayumi Tsunekawa, Mieko Maeda, Atsuko Sugimoto,
Makoto Kimura
\item[Year] 2008
\item[Title] Spatial and seasonal variations in CH4 in groundwater used for agriculture in
central Japan. 
\item[Journal] Agriculture, Ecosystems and Environment, 127 (2008) 207--214 
\item[Web-site] \verb+www.elsevier.com/locate/agee+
\end{description}
\section{Data}
\begin{center}
\begin{tabular}{|c|c|}\hline
\textbf{Month (0=January)}\rule{0pt}{14pt} &
\textbf{Methane production rate (nmol L$^{-1}$ day$^{-1}$)}\\\hline
0&3.08\\7&4.61\\10&-1.65\\15&1.31\\\hline
\end{tabular}
\end{center}
\section{Models}
\subsection{Exact Fit Polynomial}
Find a polynomial model that passes through all the data points.Note
that the
first homework assignment of this module was to find this model.
\subsection{Cyclic Model with a 12 month period}
Fit an optimal model of the form:
\[
1.8375+A\sin\left(\frac{2\pi}{12}t\right)+B\cos\left(\frac{2\pi}{12}t\right)
\]
\subsection{Cyclic Model with a 6 month period}
Fit an optimal model of the form:
\[
1.8375+A\sin\left(\frac{2\pi}{6}t\right)+B\cos\left(\frac{2\pi}{6}t\right)
\]
\section{Conclusion}
Select the model that is most suitable for the data. When making this
choice it will help to ask yourselves which model :
\begin{enumerate}\renewcommand{\theenumi}{\alph{enumi}}
\item matches the data most accurately?
\item best captures the general pattern and trends of the data?
\item is the most efficient description of the data?
\item will make the most reliable predictions of future behaviour?
\end{enumerate}



