# In jgrasstools kriging, what is the variogram model used when defaultVariogramMode = 0?

In jgrasstools 0.78, what are the variogram models corresponding to the values `0` and `1` of the `defaultVariogramMode` field?

For mode `1`, it seems to be a Gaussian variogram, by looking at the source. But for mode `0`, it uses the variance of the measurements and something called an "integral scale" (fields `pVariance` and `pIntegralscale`).

The formula for the covariance in this mode is `variance * exp(-h^2)`, where `variance` is the supplied variance, `exp(x)` is the exponential function, and `h^2` is the square of the distance between the points (the distance in each axis is "normalized" by the integral scale).

What variogram model is this? The formula for the exponential variogram model is more complex, according to Wikipedia. I also did not find a corresponding formula in Isaaks & Srivastava's An Introduction to Applied Geostatistics either.

As you pointed out the mode 1 is a Gaussian Variogram.

Mode 0, which always made this Kriging "simple & quick" to use, is based on the use of integral scales, hence not needing a variogram.

This method has been researched and developed by professor Bellin of the University of Trento.

The following literature should contain the above mentioned theory:

A. Bellin, A. Rinaldo, A. Fiori, M. Pannone, "On Transport In Porous Formations Characterized by Heterogeneity of Evolving Scales" in WATER RESOURCES RESEARCH, v. 32, n. 12 (1996), p. 3485-3496. - URL:http://www.agu.org/journals/wr/

and

A. Bellin, Y. Rubin, "Hydro-Gen - A Spatially Distributed Random Field Generator For Correlated Properties" in STOCHASTIC HYDROLOGY AND HYDRAULICS, v. 10, n. 4 (1996), p. 253-278. - URL:http://www.springerlink.com/content/101943/ . - DOI: 10.1007/BF01581869

Also there is a manual of the original fortran code where the jgrasstools version was derived from at the following link: http://www.ing.unitn.it/~bellin/frames/hydrogen.php

Have a look at the manual.ps, it cites the integral scales that are used.