Spatial interpolation - Spatial Data Analysis: An Introduction for GIS Users - page 129

9

Spatial interpolation

Introduction

9.1

h is chapter introduces a variety of approaches for the generation of surfaces, includ-
ing topographic surfaces and other properties that can be treated as surfaces, such as
precipitation amount or airborne pollutants. h e term 'spatial interpolation' refers to
the prediction of values at locations where no sample is available; a common objective
in GIS contexts is to predict values on a regular grid using irregularly distributed point
data, and this is the principal focus here.
h ere is a wide range of applications that depend on tools for predicting values on a
regular grid from a set of samples irregularly distributed in space. An example is pre-
cipitation mapping. Precipitation amount may be measured using a set of rain gauges
but if values are required elsewhere then it may be necessary to predict these values
using the sample data. Another class of techniques that fall within the remit of this
chapter are those that are used to transfer counts from one set of zones (e.g. census
areas) to another set of zones or from zones to a grid. h e term 'areal interpolation'
describes such approaches.

Interpolation

9.2

Spatial interpolation approaches can be divided into those that are global and those
that are local. Global approaches make simultaneous use of all sample data in the pre-
diction process. Local approaches use only a subset of data (in a moving window) to
make predictions. Another division into which spatial interpolation methods can be
divided is exact and approximate methods. Exact methods 'honour' data locations—
that is, observed values are not replaced and the predicted value at a location where
there is a sample is the same as the sample value. With approximate methods, there is
no guarantee that this is the case.