\begin{center}
\begin{Large}
\textbf{
Module 3 Project for Group S2G2\\ Due 3$^\text{rd}$ November 2008 }
\end{Large}
\end{center}
\section{Research Paper}
\begin{description}
\item[Authors] M.D. MacNeil, M.R. Haferkamp, L.T. Vermeire, J.M. Muscha
\item[Year] 2008
\item[Title] Prescribed fire and grazing effects on carbon dynamics in a northern
mixed-grass prairie
\item[Journal] Agriculture, Ecosystems and Environment 127 (2008) 66--72
\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{Photosynthetically Active Radiation (PAR, mmol m$^{-2}$ s$^{-1}$)}\\\hline
3 & 1122\\
6 & 1308\\
9 & 575\\
15 & 1266\\
18 & 1529\\
21 & 597\\
\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{Two Parameter Model}
Fit an optimal model of the form:
\[
1066.17+A\sin\left(\frac{2\pi}{12}t\right)+B\cos\left(\frac{2\pi}{12}t\right)
\]
where $t$ is the month.
\subsection{Four Parameter Model}
Fit an optimal model of the form:
\[
A\sin\left(\frac{2\pi}{12}t\right)+B\cos\left(\frac{2\pi}{12}t\right)+Ct+D
\]
where $t$ is the month.
\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}



