\section{Interpolating TEC Data}
 
This chapter has introduced various commonly used and state-of-the art
interpolation methods. These methods have ranged from ubiquitous triangulation
based methods, such as the cubic and linear methods, to more obscure methods
such as natural neighbour. It also included \ac{RBF} interpolation, kriging
and \ac{ANC}.
 
As discussed in Chapter~\ref{sec:intro_to_the_ionosphere}, information on
the electron content of the ionosphere can be collected using the \ac{GPS}, by
examining the phase and amplitude changes which occur in paths between
transmitting satellites and ground based receivers. These data can then be
processed in order to create maps of the ionospheric \ac{TEC}.
 
Chapter~\ref{cha:performance} examines the performance of
the algorithms described in this chapter, using both simulated and real data,
and quantitative techniques known as simulation- and cross-validation. This
study forms the most complete examination of interpolation methods for
\ac{TEC} mapping of its kind, and the first application of \ac{NC} to
geophysical data.
 
The interpolation schemes evaluated represent a broad
cross-section of those in common use. Specifically they are:
 
\begin{itemize}
 \item Triangulation based (nearest neighbour) --- Section~\ref{sec:paper_triangulation_interp}
 \item Natural neighbour --- Section~\ref{sec:paper_natural_neighbour}
 \item Radial basis function --- Section~\ref{sec:paper_rbf}
 \item Biharmonic spline --- Section~\ref{sec:paper_biharmonic}
 \item Ordinary kriging --- Section~\ref{sec:paper_kriging}.
\end{itemize}
 
Of the list above, only ordinary kriging, \ac{RBF} interpolation and \ac{BSI}
are considered truly global techniques. Natural neighbour, nearest neighbour
and triangulation based interpolation all use a neighbourhood defined by the
Delaunay triangulation of the input data coordinates.