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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?

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    Keep in mind that at some point is no longer interpolation and rapidly becomes extrapolation. Not sure about how to extent the estimation area in ArcGIS Geostatistical Analyst but in R you predefined the lattice that the model will be predicted to. If you are using the Kriging function in Spatial Analyst you just define the extent and the estimate will be made to the defined extent. Dec 10, 2015 at 22:52
  • Underline the word extrapolation please.
    – nickves
    Dec 11, 2015 at 0:39
  • Thanks for the helpful thread. I've got a follow up question that maybe someone can help with. I'm working on a project trying to understand the long lasting effects of historic scientific activities on delicate soil communities. Essentially, the hypothesis is that there will be fewer organisms the closer one gets to the center of where human activity took place. I've got soil data that were collected at known locations of historic camps where researchers lived and worked in the field. After locating the footprint of where each structure in the camp used to be, a sample was taken at the center
    – cms
    Apr 23, 2019 at 18:53
  • Can you post a new question and link to this question as part of your reference? As your response is not an answer to the posted question. Thanks.
    – whyzar
    Apr 23, 2019 at 19:16
  • If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. - From Review
    – csk
    Apr 23, 2019 at 19:30

2 Answers 2

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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).

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  • I believe that ArcGIS Geostatistical analyst uses the extent domain and not a convex function. Dec 10, 2015 at 23:27
  • +1 nice one. I like convex hull piece. It is worth adding that standard ArcGIS interpolation tools don't do very good either sometimes, e.g. interpolating air temperature in the mountains
    – FelixIP
    Dec 11, 2015 at 1:52
  • I have tried to struggle through adjusting the extent parameters, but when I adjust the extent it always reduces the size of the area covered. And if I adjust the extent twice, it will always get rid of the raster completely. I am not sure if it has something to do with the spatial coordinate system that I am using, but I haven't been able to extrapolate to an area outside of the convex hull.
    – jcronin
    Dec 11, 2015 at 19:08
  • What is the coordinate system you are using? On a side note, do you need to do the interpolation in Arc? You could try interpolating in R and then getting the raster back into Arc. Dec 12, 2015 at 10:20
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The accuracy of interpolation outside of your sample area is poor. You need to sample bigger than your study area when making inferences.

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