If spatial sampling is an efficient way of capturing knowledge of spatial variation, then there must be reliable ways of filling in the unknown variation between sample points. Spatial interpolation attempts to do this, by providing a method of estimating the value of a field anywhere from a limited number of sample points. Spatial interpolation is no more and no less than intelligent guesswork, supported by Tobler’s First Law.

Many methods of spatial interpolation exist, all of them based to some extent on the principle that conditions vary smoothly over the Earth’s surface. Methods have even been devised to cope with exceptions to Tobler’s First Law, by recognising the discontinuities that exist in some geographic phenomena, such as faults in geologic structures, or the barriers to human interaction created by international boundaries. Arguably the most rigorous is Kriging, a family of techniques based on the theory of geostatistics (Isaaks and Srivastava, 1989). Kriging and a wide range of other interpolation methods are described in Chapter 6 of this Guide.