Introduction

In this lesson, we will examine one of the most important methods in all of spatial analysis. Frequently, data are only available at a sample of locations when the underlying phenomenon is, in fact, continuous and, at least in principle, measurable at all locations. The problem, then, is to develop reliable methods for 'filling in the blanks.' The most familiar examples of this problem are meteorological, where weather station data are available, but we want to map the likely rainfall, snowfall, air temperature, and atmospheric pressure conditions across the whole study region. Many other phenomena in physical geography are similar, such as soil pH values, concentrations of various pollutants, and so on.

The general name for any method designed to 'fill in the blanks' in this way is interpolation. It may be worth noting that the word has the same origins as extrapolation, where we use some observed data to extrapolate beyond known data. In interpolation, we extrapolate between measurements made at a sample of locations.