An exponential model is fitted to empirical semivariogram using gstat of R package. The variogram parameters obtained is
model psill range
1 Nug 0.04281109 0.00000
2 Exp 0.76810071 5.45954
where the nugget effect is 0.04, sill is approximately 0.80, and range is 5.5.
Since exponential model approaches the sill asymptotically, its practical range of spatial dependency is reported by literature to be distance at which the semivariance is 95% of the sill.
Having obtained 5.5 as my range from the analysis, how do I estimate the practical range at 95% of sill?
Thank you.
As implied by several of the answers, the exponential variogram model does not have a true range, i.e. a distance at which the variogram value becomes constant (the sill). The graph is only asymptotic to the horizontal line corresponding to the sill. Instead one refers to the "practical" or "effective" range, this is the distance at which the variogram value is 95% of the sill. You don't need to look at the formula used in a particular software package you just need to know that the software writer will use the practical range correctly to determine the equation for the exponential model,. Note that 95% is not a theoretical choice, it is an arbitrary but practical choice. Looking at the problem graphically, if you use the graph of the experimental variogram to estimate the sill then look for the distance at which the variogram values is 95% of that sill. Note that if you were writing your own software then you would need to know the equation and how to relate the practical range to the oarameters in the equation but you would also need to know that the relationship is different for a Gaussian variogram which also only has a practical range. The use of the practical range is so common that the documentation for most geostatistics software packages don't even bother to mention that in the case of the exponential and Gaussian models "range" really means the practical range, In particular when the fitting routine in gstat gives you a value for the range it is actually the practical range
I normally use the R package geoR for variogram fitting (function eyefit first, then variofit). The fitting procedure will yield, besides sill and nuggett, the practical range.
Cheers
Tobias
Here is the manual for geoR:
cran.r-project.org/web/packages/geoR/geoR.pdf
Also I use the R package geoR for variogram fitting.
If the sill is 0.80, the 95% is 0.76. Empirically I would estimate the practical range as the distance (h) when the variogram is equal to 0.76 in the adjusted model.
However, in the geoR package the variofit() or likfit() functions (for OLS or Maximum Likelihood, respectively) computes the estimated variogram, and give a value for the practical range; which is three times the alpha parameter in the exponential model.
Regards,
Daniel Zuleta
Hello, in an exponential variogram the practical range is h= 3a. (Wackernagel, H. (2003). Multivariate geostatistics. Springer. p.41)
I hope you find it useful
Jorge
You do have to use a little caution because some software and textbooks (e.g. Isaaks and Srivastava) write the exponential model with a 3 in the numerator, in which case the practical range h is the same as the parameter specified by the user, a. Traditionally, the exponential model was not formulated with that 3 in the numerator and h = 3a . You should check which formulation your software uses. I don't know which is the case for geoR.
As implied by several of the answers, the exponential variogram model does not have a true range, i.e. a distance at which the variogram value becomes constant (the sill). The graph is only asymptotic to the horizontal line corresponding to the sill. Instead one refers to the "practical" or "effective" range, this is the distance at which the variogram value is 95% of the sill. You don't need to look at the formula used in a particular software package you just need to know that the software writer will use the practical range correctly to determine the equation for the exponential model,. Note that 95% is not a theoretical choice, it is an arbitrary but practical choice. Looking at the problem graphically, if you use the graph of the experimental variogram to estimate the sill then look for the distance at which the variogram values is 95% of that sill. Note that if you were writing your own software then you would need to know the equation and how to relate the practical range to the oarameters in the equation but you would also need to know that the relationship is different for a Gaussian variogram which also only has a practical range. The use of the practical range is so common that the documentation for most geostatistics software packages don't even bother to mention that in the case of the exponential and Gaussian models "range" really means the practical range, In particular when the fitting routine in gstat gives you a value for the range it is actually the practical range
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