[gdal-dev] Kriging Interpolation

[Thomas Knudsen]

Hi Ian,

If you find IDW on N points slow, you will find Kriging on the same number
of points unbearably slow, since for Kriging you will have to solve a
system of N linear equations (essentially inverting an NxN matrix) to
compute the Kriging weights. To set up the matrix you will even need to
compute the same distance elements you need for IDW. So Kriging will never
become faster than IDW.

Hence, the only realistic way to use Kriging on large data sets is to base
each estimate on local subsets - typically by working in a TIN model, just
like in the linear interpolation case. And if your data set is dense, the
difference between Kriging and linear interpolation will be miniscule.
Kriging will, however, provide a variance estimate for the prediction,
which may be realistic assuming you provide a realistic covariance function
for the phenomenon under investigation.

So to make any difference wrt the linear interpolation, you will need to
include a larger number of data, e.g. by including neighbouring triangles
of the TIN, or using another data structure to subset your observations.

Some years ago I wrote an informal note about this subject. The title is
“Data Assimilation for Updates of Digital Terrain Models” and it is
available over at http://sdfe.dk/media/2916626/kms_technical_report_14.pdf

/Thomas




2018-06-25 5:19 GMT+02:00 Ian Reese <ireese at linz.govt.nz>:

> Hi Gdal,
>
> I'd like to know if it is possible to make Kriging Interpolation part of
> gdal_grid.  We work with a good deal of scattered point elevation data and
> neither IDW or Linear interpolations(smooth or not smooth)  produce the
> desired visual results.  Nor are they fast enough for the density of data
> we commonly work with. Linear interpolation is a reliable and fast method,
> however the triangulated results are difficult to work with visually.
>
> For some visual comparisons and reference, here is a link to a folder of
> sample points(shp) for a test area, two examples of kriged data for that
> test region, and a BASH script to reproduce IDW and Linear interpolations
> of the same region.
>
> https://drive.google.com/open?id=1HKbK4wMmVN6JZSvhxBQDub1WXBLE710H
>
> Here is an example of the Kriging method used by ArcGIS:
> http://desktop.arcgis.com/en/arcmap/latest/extensions/
> geostatistical-analyst/kriging-in-geostatistical-analyst.htm
>
> Few graphs explaining best interpolation methods to use with given data.
> Gridded vs. scattered.
> https://www.neonscience.org/spatial-interpolation-basics
>
> If it is possible, we are curious to know what type of funding would be
> needed.
>
> Cheers,
>
> Ian
>
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