Spatial interpolation - Spatial Data Analysis: An Introduction for GIS Users - page 130

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Figure 9.1 Thiessen polygons.

h ere are many approaches to spatial interpolation. A simple global approach is to
i t a trend surface to all of the data, and values of the i tted surface can then be read of
at any location, whether there is a sample at the location or not. Trend surface analysis
entails i tting a plane or a curved surface through the data that represents the general
trend of values (e.g. a 'gradual' increase in values from south to north). Trend surface
analysis is simply multiple regression whereby the dependent variable is the variable
of interest (e.g. precipitation) and the independent variables are the data coordinates
or some function of them. Conceptually, the most simple interpolation method is
h iessen polygons. With this approach, the values assigned to unsampled locations are
those of the nearest observation. Figure 9.1 gives an example of h iessen polygons—
the point value is assigned to the area which is closer to that point than any other.
h e focus in this section is on methods that have a raster grid as their output. One
interpolation framework that does not is triangulation. h e output of triangulation is
a triangulated irregular network (TIN), which is essentially a surface comprising trian-
gular facets that connect the observations (see Heywood et al. (2006) for an example).
h e following sections introduce i ve of the most widely used spatial interpolation
methods: regression (introduced in Section 3.3, and expanded on in the previous
chapter), TINs, inverse distance weighting (IDW), thin plate splines (TPS), and ordi-
nary kriging (OK). h ere is a whole literature on TPS and geostatistical interpolation
(kriging), and the accounts provided below are necessarily brief.

Triangulated irregular networks

9.3

h e TIN is a vector-based representation of a surface. In essence it comprises a set of
vertices joined by arcs, which together form triangles. TINs are more ei cient than