The IDW (Inverse Distance Weighted) tool uses a method of interpolation that estimates cell values by averaging the values of sample data points in the neighborhood of each processing cell. The closer a point is to the center of the cell being estimated, the more influence, or weight, it has in the averaging process. It is a very popular technique in GIS and considers one of the simplest interpolation methods. There are a variety of methods that use weighted moving averages of points within a zone of influence.
IDW relies mainly on the inverse of the distance raised to mathematical power. The Power parameter lets you control the significance of known points on the interpolated values based on their distance from the output point. It is a positive, real number, and its default value is 2. By defining a higher power value, more emphasis can be put on the nearest points. Thus, nearby data will have the most influence, and the surface will have more detail (be less smooth). As power increases, the interpolated values begin to approach the value of the nearest sample point. Specifying a lower value for power will give more influence to surrounding points that are farther away, resulting in a smoother surface.
Since the IDW formula is not linked to any real physical process, there is no way to determine that a particular power value is too large. As a general guideline, a power of 30 would be considered extremely large and thus of questionable use. Also keep in mind that if the distances or the power value are large, the results may be incorrect. An optimal value for the power can be considered to be where the minimum mean absolute error is at its lowest. The ArcGIS Geostatistical Analyst extension provides a way to investigate this.
In general the simplified formula for IDW is:
- V0 is the predictable value at point 0,
- Vi is the V value at control point i,
- Di is the distance between control point i and
- 0, and n is the number of known values used in the evaluation.
The weights are a decreasing function of distance and the user has control over the mathematical form of the weighting function. The size of the neighborhood can be expressed as a radius or a number of points.
The characteristics of the interpolated surface can also be controlled by limiting the input points used in the calculation of each output cell value. Limiting the number of input points considered can improve processing speeds. Also, consider that input points far away from the cell location where the prediction is being made may have poor or no spatial correlation, so there may be reasons to eliminate them from the calculation.
You can specify the number of points to use directly, or specify a fixed radius within which points will be included in the interpolation.