Using kriging to extrapolate values outside of sampling polygon in ArcMap?
I have data points with values along 4 perpendicular transects. The kriging tool that I am currently using interpolates within the polygon created by the 4 transects, essentially a rectangle. I am looking for a way to extend the output of the kriging outside of the rectangle created by the 4 transects.
Is a way to do this by creating a linear interpolation for the area outside of the polygon created by the transects?
Following a bit on what Jeffrey Evans said, you must remember that your data points define an area that's called convex hull. It is the (convex) polygon of minimum area that contains your data points.
Values of locations inside that polygon can be estimated by interpolation (kriging, splines, IDW, etc). Outside that polygon you don't have interpolation, but extrapolation, and you can't be sure of the validity of values in the extrapolation zone, because the algorithms usually go crazy there (since there are no points around to constrain the function).
So you have 4 transects, and they define a rectangle (your convex hull) and your kriging interpolator is honoring the convex hull. I'm not much an ArcGIS person but maybe (maybe) there's an option somewhere that will turn off this, but in any case, I would advise against present any map with extrapolated data (quite often people just want to do it because the grid/contours fill all the map area and it looks nicer).
The accuracy of interpolation outside of your sample area is poor. You need to sample bigger than your study area when making inferences.