Interpolation outside the contour of a set of points

Question

I have a field contour in a shape layer. I have another layer compound by a set of points which are the locations where soils samples have been taken within the field. I have in the attribute table of this second shape layer the Phosphorus content of the soil in those points.

As I have said, the contour of the set of points is smaller than the field contour, being the contour of the set of points enclosed within the field contour.

I have interpolated this set of points by creating a TIN in order to have a value of Phosphorus content for any point in the field. But through this procedure, the area between the contour of the set of points and the contour of the field is excluded from the TIN.

I have also tried the Kriging method (this method allows to enter the field contour shape as the Processing Extent in the Environments section, being the referred problem solved) but through this interpolation method a new problem arises: the sample points are lying over classes which value ranges don’t include the real values of the sample points. Then, the original data is in some way adulterated.

I guess the IDW method isn’t good for this purpose: there isn’t any point in the field contour, and thus the value will go down towards the field contour in an unreal way due to this fact.

Any idea or solution for this issue (interpolating the area excluded from the TIN)?

Answer 1

Strictly speaking you are not doing an interpolation, but an extrapolation because you are outside of the convex hull defined by your points. The safest methos in this case is to allocate the value of the closest point (aka using Thiessen polygon). This might not look so nice, but you avoid many artefacts.

Remark : If you want a nice looking result, you can try a spline, but I would only use it for visualisation.