Pollution models and inverse distance weighting: Some critical remarks

When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard’s method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model), and polluted rivers. The case where a station is confused with the reference point (or zero distance) is also discussed: in real cases this station imposes its measurement on the whole area regardless of the measurements made by other stations. This is a serious flaw when evaluating the mean pollution of an area. However, it is shown that this is not so in the case of a continuum of monitoring stations, and the measurement at the reference point and for the whole area may differ, which is satisfactory. ► In Inverse Distance Weighting the distance exponent should be adapted to reality. ► For radiant pollution the exponent of distance should be 2. ► For plumes (or puffs) the exponent's upper bound may vary from 1 to 3 (or 2 to 4). ► For polluted rivers, the exponent may be 1 or 0. ► A continuum allows to treat the case of a station located at the reference point.