First, the range of a variogram (if it actually has one) is the distance at
which the variogram value becomes constant with respect to lag distance (note
that a variogram with a geometric anisotropy will have a different range for
different directions. The "constant" value is the sill
Second, some variogram models do not have a true range (e.g., exponential and
gaussian). In that case what is commonly reported is the "effective" range.
This is the distance at which the variogram value is 95% of the sill. The
variogram is only asymptotic to the sill, it never actually reaches it. You
need to verify any software, etc to be sure that they are reporting the
effective sill and not the parameter in the equation for the model.
Third, now as to interpreting the range. It is the distance (or nearly
so) such
that for two locations farther apart than the range the random function
will be
uncorrelated. Intuitively this means there is no statistical dependence for
values at locations farther apart than this.
Note that the range does not in and of it self tell you about the shape of the
variogram, i.e. compare a spherical, exponential and gaussian model with the
same sills and same ranges (effective ranges in the case of the
exponential and
gaussian). The "third" statement above is applicable but the question
of exactly
how the dependence changes with lag distance is quite different in the three
cases (i.e. with lag distance less than the range).
As for you question about the difference between the two results, you did not
say what the transformation was. Assuming that it is non-linear one would
expect the transformation to have a significant effect.
Donald E. Myers
Quoting Charles Serele <[EMAIL PROTECTED]>:
Dear list members,
Does anyone can help me understanding variogram range interpretation or send
me some specific references.
I am currently analyzing variograms computed over the same site of a remote
sensing image. The first variogram was derived from the original image and
the second one was derived from the transformed image (using a mathematical
model). All the variograms were fitted with an exponential model. The range
value I got from the transformed image is higher than the one from the
original image. I would like to know:
1. For ranges of 4 pixels (original image) and 9 pixels (transformed image),
does this difference can impact significantly on a ground sampling for
instance ? What should be the acceptable range difference ?
2. In terms of spatial correlation, can we say that a high range value is
associated with a less spatial correlation between data points (pixels)? On
other hands, the spatial information content was reduced by the
transformation ?
3. Can we say that data with small variogram range is more heterogeneous
than data with high variogram range ?
Regards,
Charles
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