Re: AI-GEOSTATS: hole effect

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• Fernando Although the hole effect model is a little ustable mathematically, we have had considerable success in practice by combining it with a spherical
Message 1 of 5 , Jan 25 7:43 AM
Fernando

Although the hole effect model is a little ustable
mathematically, we have had considerable success in
practice by combining it with a spherical component.

We call this 'model' the Paddington Mix and have used
it in several field studies where there is a cyclic
component in addition to the more usual continuity.

You can see how it works in our kriging game which can

http://uk.geocities.com/drisobelclark/briefcase.html

Isobel

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• Fernando, I m not sure what variogram you were given that works only in 1d I can think of two -- gamma(h) = 1 -cos(h) and gamma(h)=exp(-ah)*cos(h) The
Message 2 of 5 , Jan 30 5:09 AM
Fernando,

I'm not sure what variogram you were given that works only in 1d
I can think of two -- gamma(h) = 1 -cos(h) and gamma(h)=exp(-ah)*cos(h)

The problem with higher dimensions is that the 'size' of the hole, defined
as |min(C(h))|/ C(0) which takes the value 1.0 for the first of these
variograms , has to less dramatic in higher dimensions. The higher the
number of dimensions, the less important the hole size can be.

So ideally you would like a variogram that is legitimate in 2d but not in
3d. I can't remember any of those off hand - although they do exist.

The next best thing is one that works in 3d (and therefore also in 1d and
2d). This will have a smaller hole effect size than is theoretically
possible for 2d data. The one I'm giving you does attain the maximum hole
size allowed for 3d data. It is

gamma(h) = 1 - sin(r)/r

The problem is that it has quadratic behavior at the origin - so you might
need to add a small spherical or exponential variogram as suggested by
Isobel to ensure that your resultant random function model is not
differentiable.

Bye

Colin Daly

----- Original Message -----
From: <ft.maestre@...>
To: <ai-geostats@...>
Sent: Friday, January 25, 2002 12:29 PM
Subject: AI-GEOSTATS: hole effect

Dear list,

I am working with vegetation data, and I have got some variograms
that are characterized by the presence of a "hole effect" that I
would like to model. I have found in the manual of GSLIB (2nd
edition) a model with a periodical component that can be fitted to
such data, but the authors remark that this model valid only in one
direction. Since I am working with omnidirectional variograms in a
two-dimensional grid, I would be very grateful if somebody could give
me any indication about where I can find conditional negative semi-
definite (CNSD) models that incorporate a periodic component and that
are valid for two-dimensional data.

Best Regards,

Fernando T. Maestre
Departamento de EcologĂ­a
Apdo correos 99
03080 Alicante
SPAIN

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• Dear list members Omnidirectional variogram shows a dip toward the end of lags. As far as I know this is hole effect. Would you tell me how to tackle with it?
Message 3 of 5 , Apr 24, 2002
Dear list members

Omnidirectional variogram shows a dip toward the end
of lags. As far as I know this is hole effect.
Would you tell me how to tackle with it?

Ercan

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• ... Ercan What is your maximum lag compared to the size of your study area? If the maximum lag is more than one-half (some people say one-quarter) of the
Message 4 of 5 , Apr 24, 2002
> Omnidirectional variogram shows a dip toward the end
> of lags. As far as I know this is hole effect.
> Would you tell me how to tackle with it?
Ercan

What is your maximum 'lag' compared to the size of
your study area? If the maximum lag is more than
one-half (some people say one-quarter) of the maximum
distance in your area, you will be getting the common
artifact caused by diminishing numbers of pairs.

If it is a real cycle, it may be of such a large
extent that it is irrelevant to your analysis.

Isobel
http://uk.geocities.com/drisobelclark

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