This repository provides a Python implementation of the formal algorithms for fast Barnes interpolation as presented in the corresponding paper published in the GMD journal.
Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field. It is defined as
with Gaussian weights
Naive computation of Barnes interpolation leads to an algorithmic complexity of O(N x W x H), where N is the number of sample points and W x H the size of the underlying grid.
As pointed out in the paper, for sufficiently large n (in general in the range from 3 to 6) a good approximation of Barnes interpolation with a reduced complexity O(N + W x H) can be obtained by the convolutional expression
where δ is the Dirac impulse function and r(.) an elementary rectangular function of a specific length that depends on σ and n.
The module interpolation implements the Barnes interpolation algorithms using the Euclidean distance metric, as described in chapter 4 and 5.4 of the paper.
The Barnes interpolation algorithms that use spherical distance metric on the sphere S^2, as outlined in chapter 5.5, are implemented im module interpolationS2.
However, be aware here that the supported geographical domain and projection - as in the paper - is currently fixed to the European latitudes and Lambert conformal projection and cannot be freely chosen.
These algorithms are also available as fast-barnes-py package on PyPI, where you also find a minimal working example.
The directory demo provides Python scripts that reproduce the figures and the tables shown in the paper.
In order to execute them you can follow these instructions.
If you want to find out how to use the code, you best read through the provided minimum working example.