Many different phenomena are represented on maps as being continuous across a large surface area, despite the fact that the measurement for whatever is being depicted is necessarily taken from a set of discrete, measured point locations. A news station weather map of north America, for example, might show areas with more precipitation or higher temperature in different colors across the map. The methods used to estimate the values of some variable(s) in locations where samples are not directly taken from, based upon the values of sampled points in the proximity, is called spatial interpolation. There are a plethora of different interpolation methods, differing in complexity and difficulty to execute, and each has its own strengths and weaknesses. Thiessen polygons and Inverse Distance Weighting (IDW), for example, are relatively simple interpolation methods, and are somewhat easier to perform. More sophisticated methods, like splining or kriging, which use spatial statistics in their calculations, may be preferable if a higher degree of accuracy is required.
The above map depicts concentrations of biochemical oxygen demand (BOD) in Tampa Bay, and is generated from sample data that goes with each of the point locations. IDW is the interpolation method used to generate the above raster surface, which shows the estimation of concentrations across the bay based on the measurements at the sample points. IDW is a relatively simple and common measure, but it is valuable in a number of spatial analysis scenarios. This, and most other interpolation methods, rely on the assumption of autocorrelation- that what is nearer is more alike than what is further away. Although IDW is an adequate and appropriate method of interpolation in this application, it may not be appropriate for every situation- the choice of method is based upon the characteristics of the application.
