Interpolation

Interpolation is the estimation of values for points in an area not actually sampled. There are many different interpolation techniques, ranging from simple linear techniques that average the values of nearby sampled points, to more complex techniques like kriging that use base weights on distance to nearby sample points and the degree of autocorrelation for those distances.

GS+ provides four broad types of interpolation. All are nearest-neighbor techniques in which values at locations close to the interpolation point are used to estimate the interpolation point value. They differ in the way that nearby locations are weighted and interpolations calculated. The four techniques are:

•      Kriging, in which interpolation estimates are based on values at neighboring locations plus knowledge about the underlying spatial relationships in a data set. Semivariograms provide knowledge about the underlying relationships. The estimated value at a given location is a weighted moving average of best estimates calculated to minimize local area variance. There are a number of different types of kriging, described below.

•      Cokriging, in which kriging interpolations include a covariate that is related to the primary variate and is measured at more locations than the primary variate. In cokriging there is a variogram for the primary variate, for the covariate, and for the cross-variate.

•      Conditional Simulation, in which interpolations are based on a form of stochastic simulation in which data values are honored at their locations. This means that local details are not obscured by smoothing as they are in kriging.

•      Inverse Distance Weighting (IDW) and Normal Distance Weighting (NDW), in which interpolation 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.