Inverse distance weighting is a deterministic, nonlinear interpolation technique that uses a weighted average of the attribute (i.e., phenomenon) values from nearby sample points to estimate the magnitude of that attribute at non-sampled locations. The weight a particular point is assigned in the averaging calculation depends upon the sampled point's distance to the non-sampled location (see Figure 6.cg.25, below). The method is called inverse distance weighting because according to Tobler's first law of geography, (see Interpolation) the similarity of two locations should decrease with increasing distance.
To use inverse distance weighting interpolation to create a surface, there are several factors that cartographers need to consider. One important question is the type of relationship the phenomenon has with distance (e.g., does it decrease dramatically with distance, or do even relatively distant points have some degree of similarity with the non-sampled location?). Many cartographers choose to specify an inverse distance-squared relationship, where the weight of a point differs with the inverse square of distance (i.e., 1/distance2) rather than a simple inverse distance (i.e., 1/distance) (see Figure 6.cg.26, below).
A second important factor is determining how large the neighborhood of influence should be: all points within some fixed distance of the non-sampled location, or whether the neighborhood should consist of some particular number of points, regardless of their distance to the non-sampled location. A variation on this second method might be to specify some combination of distance and number of points (e.g., select the nearest n number of points within 10 km of the non-sampled location). Each of these decisions can have an impact upon the final appearance of the interpolated surface and therefore needs to be carefully considered (see Figure 6.cg.27, below).
Because inverse distance weighting is a deterministic technique, it does not take into account the spatial structure (i.e., arrangement) of the sample points. Therefore, the results that you get using this technique can be influenced by the spacing and density of the samples, and it is good to be cautious about the accuracy of the interpolated values. Also, because inverse distance weighting computes an average value, the value it calculates for a non-sampled point can never be higher than the maximum value for a sample point or lower than the minimum value of the sample point, so if the peaks and valleys of the data are not represented in your sample, this technique may be wildly inaccurate in some locations.