An adaptive inverse-distance weighting spatial interpolation technique

One of the most frequently used deterministic models in spatial interpolation is the inverse-distance weighting (IDW) method. It is relatively fast and easy to compute, and straightforward to interpret. Its general idea is based on the assumption that the attribute value of an unsampled point is the weighted average of known values within the neighborhood, and the weights are inversely related to the distances between the prediction location and the sampled locations. The inverse-distance weight is modified by a constant power or a distance-decay parameter to adjust the diminishing strength in relationship with increasing distance. Recognizing the potential of varying distance-decay relationships over the study area, we suggest that the value of the weighting parameter be allowed to vary according to the spatial pattern of the sampled points in the neighborhood. This adaptive approach suggests that the distance-decay parameter can be a function of the point pattern of the neighborhood. We developed an algorithm to search for “optimal” adaptive distance-decay parameters. Using cross validation to evaluate the results, we conclude that adaptive IDW performs better than the constant parameter method in most cases, and better than ordinary kriging in one of our empirical studies when the spatial structure in the data could not be modeled effectively by typical variogram functions.