Interpolation methods, like other methods discussed in this book, can be divided into two broad groups: global and local methods. A widely used distinction between interpolation methods is that global methods, such as trend surface analysis, use all data for prediction, while local methods, including inverse distance weighting, usually use only some subset of the data to make each prediction (that is, a moving window approach is employed). One benefit of local methods is that computational time is reduced by using only some subset of the data to make a prediction. Some methods may make use of all available data but may take into account distance from the prediction location. Such methods may still be considered local; therefore, many widely used interpolation techniques are local methods. A global approach may be used to remove large scale variation, to allow focus on local variation and spatial prediction can proceed with the residuals from a fitted trend model. Lam (227) and Mita´s and Mita´sova´ (275) provide overviews of interpolation

methods. In this chapter, some of the most widely used approaches are discussed and some key locally-based techniques are illustrated through a case study. Interpolation methods may be divided into two groups, point interpolation and areal interpolation, each with two subdivisions as outlined below. Point interpolation is based on samples available at specific locations that

can be approximated as points. A further division of methods comprises exact methods and approximate methods. Exact interpolators honour the data, while approximate interpolators do not. In other words, exact interpolators retain the data values in the output. Areal interpolation is used where the data comprise measurements made

over areas, and the desire is to convert between the existing zonal system and another zonal system. Alternatively, various procedures have been developed for interpolating from a zonal system to a surface. Areal interpolation methods can be divided into nonvolume preserving methods and volume preserving methods. Volume preservation is defined in Section 6.6.3. This chapter discusses some techniques used widely in GISystems as well

as recent developments. In Sections 6.1 through 6.3, several widely used local point interpolation procedures are outlined, while the subject of Sections 6.4 through 6.6 is areal interpolation. In both cases, a short discussion of

for

global approaches is given for context prior to more in-depth discussion about local methods. Case studies illustrating the application of point and areal interpolation methods are given in the text. Some of the advantages and disadvantages of these methods are outlined in Section 6.7. The application of selected point interpolation methods is illustrated using the monthly precipitation dataset described in Section 1.8.1. (the application of kriging to the same dataset is explored in Chapter 7). An approach to areal interpolation is illustrated using the Northern Ireland 2001 Census data described in Section 1.8.6.