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\begin{document}
\title{Proposal For An Igloo Partitioner}
\author{Manu Natarajan}


\date{}
\maketitle
\clearpage
\tableofcontents


\noindent
\section{Introduction}
The objective of this proposal is to explore viable alternatives
to developing a constrained igloo decomposition for the 2-D Shallow Water 
Model.
Before specifying the constraints we define the aspect ratio \( \alpha \) of 
an {\em individual partition } in the igloo decompostion on a sphere as 
follows;

\( \alpha = R cos \theta * \Delta \phi / R * \Delta \phi \)
where, R is the radius of the sphere; \(\theta\), \(\Delta \phi\) are
the angles as shown in Figure 1.


The igloo partition needs to meet the following constraints :

\begin{itemize}
\item At the polar regions the partition be a long strip.
\item At the equator, the partition be almost square (on the sphere)
i.e. the aspect ratio of the partition dimensions be close to 1.
\item  The aspect ratio at the polar region and the equator form a bound
       on the aspect ratios of the partitions in the intermediate regions. 
\end{itemize}



\end{document}












