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How IDW works |
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Release 9.2
Last modified January 3, 2008 |
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Inverse distance weighted (IDW) interpolation determines cell values using a linearly weighted combination of a set of sample points. The weight is a function of inverse distance. The surface being interpolated should be that of a locationally dependent variable.
The {power} option of IDW 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. The default value is 2.
By defining the higher {power} option, 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 the power increases, the interpolated values begin to approach the value of the nearest sample point. Specifying a lower value for power will provide a bit more influence to surrounding points a little farther away. 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.
An optimal value for the power can be considered to be where where the minimum mean absolute error is at its lowest. ArcGIS Geostatistical Analyst provides a way to investigate this.
IDW relies mainly on the inverse of the distance raised to the power. If the distances are large, or the power value is large, the results may be incorrect.
The characteristics of the interpolated surface can also be controlled by limiting the input points for calculating each interpolated point. The input can be limited by the number of sample points to be used or by a radius within which there are points to be used in the calculation of the interpolated points.
References
Philip, G.M., and D.F. Watson. A Precise Method for Determining Contoured Surfaces. Australian Petroleum Exploration Association Journal 22: 205-212. 1982.
Watson, D.F., and G.M. Philip. A Refinement of Inverse Distance Weighted Interpolation. Geoprocessing, 2:315-327. 1985.