climateinterpolationqgis
I tried to interpolate the mean average annual temperature to produce a "realistic" surface. In QGIS I used Raster-Interpolation-Interpolation. Both methods TIN and IDW did not deliver a "realistic" surface (e.g. compared to a good map in an atlas).
IDW (factor 3):
TIN (also showing the interpolation points):
Any hints how to get a "better, more realistic" interpolation?
The legendary triangulation is available http://www.cs.cmu.edu/~quake/triangle.html
from the page:
I timed the Delaunay triangulation of 1,000,000 vertices uniformly randomly distributed in a square. The output contained 1,999,955 triangles. (I used the -I switch to suppress the rewriting of input vertices to another file, since the vertices written would be identical to the ones read. Hence, only the triangles were written to disk.)
Delaunay triangulation time: 20.761 sec
File output time: 28.794 sec
Total time (above plus file input): 56.115 sec
This has been translated to a python library according to http://dzhelil.info/triangle/index.html# which includes documentation, download https://pypi.python.org/pypi/triangle/2013.04.05 - note, these links may become dead as the version changes. I found them with google in under 10 minutes.
I regret that I didn't see your post back when you wrote it. But I've made a picture that I think shows the essential difference between the two. Both interpolations produce continuous surfaces and both will preserve the original values (so that if you take a query point at the position of an input sample point, you get back the original value associated with that sample). The biggest difference is in the way slope is handled. In linear, the slope is constant over the entire area of one of the triangular facets. In natural neighbors it changes continuously. This characteristic results in linear "artifacts" in the linear interpolation. On the other hand, natural neighbors has a more curved appearance. Also, in linear, the slope is discontinuous across the edges of the triangular facets. In natural neighbors, it is continuous everywhere except right on top of the input sample points.
Recently, I posted a wiki article about natural neighbors, you can find it at The Tinfor Project's Introduction to Natural Neighbor Interpolation.
Here's the image. Linear interpolation is on the left, natural neighbors on the right.
Best Answer
You may take the elevation-temperature relationship into account, especially in mountainous areas. Co-kriging or splines interpolation (e.g., 3D splines as supported by GRASS GIS) can be used for this. For larger areas further variables may play a role: distance from the sea, latitude, etc.
Update: a reasonable method may also be multiple regression, for GRASS 7 there is a new Addon: r.regression.multi