Question 22 of 23: Spatial Interpolation vs Spatial Extrapolation

Question 22: Spatial Interpolation vs Spatial Extrapolation (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Both estimate values at locations where no measurement exists, but they differ in where those locations lie relative to the sample data. Spatial interpolation estimates values within the area covered by the sample points — inside the convex hull of, and bracketed by, the known observations. Because every predicted location is surrounded by data, interpolation is generally reliable, and methods such as inverse-distance weighting, spline and kriging are designed for this bounded, "fill-in-between" situation. Spatial extrapolation estimates values outside the sampled area or beyond the range of the observations — projecting the modelled trend into a region where there are no surrounding control points. It is inherently far less reliable and carries much larger uncertainty, because the estimate rests on the assumption that the pattern observed inside the data continues unchanged outside it, which frequently fails (a trend fitted over a valley need not hold on the ridge beyond). In practice a GIS should be used to interpolate wherever possible and to extrapolate only with explicit caution: predictions beyond the data envelope should be flagged as low-confidence, and geostatistical methods such as kriging usefully report the rising prediction variance that signals this degradation as one moves outside the sampled region.