How to determine the optimal raster resolution when interpolating a surface from points?

I'm looking for guidance on how to determine the desired output resolution, when interpolating a surface from irregularly-spaced point samples.

I have a series of boreholes taken across a city, and the density of the samples varies considerably - sometimes boreholes are located within ~5m of each other, while in other locations they are ~1km apart.

What techniques should I use to determine the applicable cell-size, when interpolating a surface from these points? Does the optimal cell-size depend on the interpolation method?

I'd like the highest resolution which is supported by the dataset. eg I assume that a 1m grid is no more accurate than a ~10m grid - but how do I determine that number?

• I read a fantastic paper on this topic once by Tomislav Hengl called "Finding the right pixel size" Computers & Geosciences Volume 32, Issue 9, November 2006, Pages 1283–1298 sciencedirect.com/science/article/pii/S0098300405002657 In the paper he states, "It was concluded that no ideal grid resolution exists, but rather a range of suitable resolutions. One should at least try to avoid using resolutions that do not comply with the effective scale or inherent properties of the input dataset. Three standard grid resolutions for output maps were finally recommended..." Sep 26, 2014 at 13:05
• What is the positional accuracy of the data? I suspect this is the most important factor. Sep 26, 2014 at 20:20
• @blah238 could you expand on that, and how it would have an effect? If the positional accuracy was less than the minimum distance between the points, would the positional accuracy then be irrelevant? (eg say the points are accurate tp with ~1m and the closest distance between them is ~5m) Sep 28, 2014 at 23:53
• Well it also depends on why you are interpolating in the first place, and what you need to do with the resulting surface. But "optimally", in terms of not losing information, you would want to use a resolution of no more than 1m (as points within this distance of each other may be considered coincident). But in terms of providing a "representative surface", if your average (not minimum) point spacing is, say 100m, use that for your resolution. You will be binning multiple samples into the same cell quite often, but depending on your use case that may or may not be desirable. Sep 29, 2014 at 1:35
• Stephen, @blah238 is right on: the answer must depend somewhat on the purpose of the surface. Good answers could range over a few orders of magnitude. The answer also depends a little bit on positional accuracy and a whole lot on the statistical nature of the observations at these points, particularly their local means, variances, and covariances. Oct 27, 2014 at 14:21