HPGL provides some interpolation techniques, among which you will find some variants of kriging. 

And there is another kriging script from Ambhas.

Finally rpy2 connects python to R. In R kriging is implemented in several packages: kriging, geoR, fields, Gstat

http://hpgl.mit-ufa.com/

http://www.ambhas.com/tools/html/krige_8py_source.html

If you check the help of Whitebox (http://www.uoguelph.ca/~hydrogeo/Whitebox/Help/MainHelp.html) you could see, among other issues, the python scripts for several interpolation methods.

Dear Prof. Rubiano did not find any Kriging methods there, nevertheless, thanks for the clue... very nice tools! Even its predecessor is quite an impressive tool and site (http://www.geomorphometry.org/)!

Dear Efra, You probably did not make a good search. The kriging tool is one of the several one in that application, together with the variogram plot. Here an extract of the text explaining how it works. "This tool can be used to interpolate a regular grid raster from a vector points file using a kriging interpolation method. The user must specify the name of the input vector shapefile and the name of the field within the vector's attribute table that is used to indicate height. The output file name, and optionally, the name of the associated error variance file, must also be provided...."the python script is also there. I can send it if you want, but better to have a proper look at it to see if this is what you need.

Regards

Gandin's method is exactly the same as kriging, it may look slightly different but it is not. See the R packages for geostatistics, better than re-inventing the wheel.  "kriging interpolation method" is redundant, much better to go to the geostatistics literature.

Dear Donald, Krigging and Gandin methods share some similarities but are not equal. Gandin method is an application of the optimal interpolation development propossed by Kolmogorov (1939) and it is capable of taking in account the full correlation structure of the studied process. This method lacks a friendly computer  inplementation but  several authors claim its performance is better. Krigging method can be treated as a particular case of optimal interpolation.

I have a python pure implementation of Kriging, https://github.com/exepulveda/geostatpy

A little late, but you may try scikit-learn (http://scikit-learn.org/stable/supervised_learning.html#supervised-learning). Among other methods, it provides a kriging implementation (as gaussian process) based on DACE from Matlab and is quiet good to begin with.

I'll throw pyKriging (www.pykriging.com) into the ring. Only handles the Kriging, not interpolation.

This looks like a good alternative

https://github.com/bsmurphy/PyKrige

In French the name was/is "krigeage". G. Matheron chose this to honor/recognize some pioneering work done by the South African Mining engineer Dany Krige. In English "krigeage" became "kriging" not "krigging". That was never used in the geostatistical literature. G. Matheron was fully aware of Ghandin's work (he explicitly acknowledged it in some of his writings). Ghandin's work was not widely known outside of the Russian literature until Ghandin migrated to Ireal.

Ghandin focused on the use of the covariance function, whereas Matheron also stressed the use of the variogram (originally he called it the "semivarioigram" but changed in 1988). The vaqriogram is a special case of a generalized covariance function (see G. Matheron, Annals of Applied Probability, 1973).

It is nonsense to claim that optimal interpolation " is capable of taking in account the full correlation structure of the studied process" and that kriging does not. Note that there are several forms of the kriging estimator and kriging equations depending on the statistical assumptions including whether the mean of the random function is constant or non-constant, whether the constant mean is iknown or not.

Parzen showed that in the case of a multivariate distribution, the conditional expectation is the minimum variance estimator/predictor. In the case of a Gaussian multivariate distribution it is easy to show that the conditional expectation is linear. This is the Simple kriging estimator but the derivation of the equations (to determine the weights) assume that.covariance function is known and the mean is constant (the variogram is not sufficient for the SK equations, i.e second order stationarity is necessary rather than intrinsic stationarity).

Finally note that the kriging estimator is in fact equivalent to the Radial Basis function interpolator which is deterministic rather than stochastic. The RBD interpolator derivation is based on the use of conditionally positive definite functions (generalized covariances) to obtain a norm (rather than just a semi-norm). The RBF interpolator is given explicitly as an interpolating function whereas the kriging estimator only implies the function. Each has certain advantages, e.g. the RBF interpolator does not provide a kriging variance (minimized estimation variance) and does not allow for the use of a moving search neighborhood.

G. Matheron acknowledged the work of Kolmorgov in his writings.  Ghandin's work was much better known in the atmospheric sciences/meteorology originally whereas Matheron's work was better known in mining, petroleum and hydrology. They were working at about the same time. Likewise Matern's work was at about the same time but originally was only available in Swedish (Springer published an English version in the 1980's). Matheron's work became better known for several reasons including: (1) the proceedings of a NATO ASI conference in 1975 (Advanced Geostatistics in the Mining Industry), (2) the English version of A. Journel's text on Mining Geostastistics (with Ch Huijbregts, Academic Press 1978), (3) the work and publications of a number of Matheron's students (e.g. Journel, Delfiner, Chiles) (4) Journel's move to Stanford University, (5) Matherron's visits to Syracuse University and the Kansas Geological survey, (6) a series of papers in the J. of Soil Science by Richard Webster and his students circa 1981, (7) collaboration between the group at the Centre de Geostatistiques (Fontainebleau) and Shell oil company which led to the software package BLUEPACK (originally only available on VAX computers but subsequently replaced by ISATIS). (8) the journal Mathematical Geosciences (originally known as the J. of the International Assn of Mathematical Geologists, and also as Mathematical Geology) (9) the journal Water Resource Research & the J. of the Soil Science Society of America (10). a series of international conferences on geostatistics held every four years beginning in 1983

I have not used any of them but I have seen references to PYTHON versions of kriging software.Geostatistics and kriging have been incorporated into ArcGIS and also SAS as well as various packages in the open source software R. R works very well with MatLab, SQL, various open source GIS software packages.

Dear Donald: Thank you for your comprehensive answer. Due to this thread we already found the required python module, see the Bidhya N. Yadav answer. Not to argue, but from Kolmogorov optimal interpolation principles Kriging can be derived, while the opposite is not possible. Isn't it?

http://www.mathnet.ru/php/getFT.phtml?jrnid=im&paperid=3775&what=fullt&option_lang=eng