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I have a spatial dataset that consists of a large number of point measurements (n=10^4) that were taken along regular grid lines (500m x 500m) and some arbitrary lines and blocks in between. Single measurements taken with a spacing of about 0.3-1.0m (varying) along these lines (see example showing every 10th point).

The data can be assumed to be normally distributed but shows a strong small-scale variability in some regions. And there is some trend with elevation (r=0.5) that can easily be removed.

Regardless of the coding platform, I'm looking for a good or "the optimal" way to interpolate these points to a regular 25 x 25m grid over the entire area of interest (5000 x 7000m). I know about the wide range of kriging techniques but I wondered if somebody has a specific idea on how to handle the "oversampling along lines" with rather large gaps between the lines.

Thank you for any advice!

Leo

Leo
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Kriging technique does not perform well when the points to interpolate are taken on a regular grid, because it is necessary to have a wide range of different inter-points distances in order to well estimate the covariance model.

Your case is a bit particular... The oversampling over the lines is not a problem at all. The main problem is the big holes you have in your grid. If think that these holes will create problems whatever the interpolation technique you use.

However it is difficult to predict a priori if kriging will behave well. I advise you to try it anyway.

Kriging is only suited for interpolating. You cannot extrapolate with kriging metamodel, so that you won't be able to predict values in the bottom left part of your figure for example (because you have no point here).

To perform kriging, I advise you to use the following tools (depending the languages you're more familiar with):

  • DiceKriging package in R (the one I use preferably)
  • fields package in R (which is more specialized on spatial fields)
  • DACE toolbox in matlab

Bonus: a link to a reference book about kriging which is available online: http://www.gaussianprocess.org/

PS: This type of question is more statistics oriented than programming and may be better suited to the stats.stackexchange.com website.

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  • Thanks a lot for your helpful comment! The empty part in the lower left is not part of the study area. The main issue is the gaps between the grid lines. I'll try your recommended R packages! – Leo Oct 09 '14 at 07:17