Inverse Distance Weighting (IDW) and Normal Distance Weighting (NDW) are interpolation techniques in which interpolated estimates are made based on values at nearby locations weighted only by distance from the interpolation location. Neither IDW nor NDW make assumptions about spatial relationships except the basic assumption that nearby points ought to be more closely related than distant points to the value at the interpolate location. IDW applies stronger weights to nearby points than does NDW.
The formula used for Inverse Distance Weighting is:
The formula used for Normal Distance Weighting is the same as that for IDW except that the 12denominator is not the [inverse of distance plus smoothing factor] but rather [distance plus smoothing factor].
The weighting power p defines the rate at which weights fall off with hij, the distance between the interpolated and sample locations. A value of 1-5 is typical.
The smoothing factor s reduces the likelihood that any one sample value will overly influence an estimated value for a given interpolation location. IDW is an exact interpolator, so where an interpolation location coincides with a sample location Zest = z and a sharp “peak” or “valley” may result; setting s > 0 reduces this peaking effect when it occurs.
The Interpolation Window contains the IDW tab:
Choose either inverse distance weighting or normal distance weighting. Inverse weighting applies stronger weights to nearby points than does Normal Distance Weighting.
The weighting power defines the rate at which weights fall off with distance between the interpolated and sample locations. A value of 1-5 is typical.
The smoothing factor s reduces the likelihood that any one sample value will overly influence an estimated value for a given interpolation location.
Restore default values to the IDW method.