## Re: [ai-geostats] Definition of Nugget Effect

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• Colin Alwyn is a graduate of the Leeds University programme in geostatistics. Bon Royle, who was the first in the UK to go to Fontainebleau and learn
Message 1 of 5 , Jun 8, 2005
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Colin

Alwyn is a graduate of the Leeds University programme in geostatistics. Bon Royle, who was the first in the UK to go to Fontainebleau and learn geostatistics, coined the term "nugget variance" for the nugget effect. He also used the notation "N" for nugget effect unlike the more general notation of C_sub_zero.

Whatever you call it, it represents the micro-scale variation which cannot be predicted at the current scale of your sampling. Since we use a semi-variogram, it is one-half of the variance between two samples at almost exactly the same location.

Geostatistics schools differ on what to do at exactly zero distance (and software packages reflect this). Some schools (e.g. Stanford) insist that nugget effect is due solely to sampling error and use the nugget semi-variance at zero distance. Others say that the nugget effect is micro-scale (even microscopic scale) and use it everywhere except at zero distance. At zero the semi-variance is set to zero. A good question to ask your software vendor is "what does your software do with the semi-variogram (or covarianc) at zero distance".

Reality is somewhere in between, but I do not know any software which allows you to allocate some of the nugget effect at zero. Of course, you can always get round this by adding a component with a very short range of influence.

Isobel

http://geoecosse.bizland.com
• Hi Isobel, Thanks - that s the answer I am looking for. To illustrate why I am asking this question, and why I think the definition is important : Assume a
Message 2 of 5 , Jun 8, 2005
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Hi Isobel,

Thanks - that’s the answer I am looking for. To illustrate why I am asking this question, and why I think the definition is important :

Assume a single structure spherical correlogram model with

Co = 0.25

C = 0.75

Co+C (Sill) = 1.0

Using Alwyn’s / Royle’s terminology:

Nugget variance (Co) = 0.25

Nugget effect (epsilon) = 0.27 / 0.75 = 33% (or 0.33)

To quote Alwyn :

“There is confusion in the scientific literature concerning [nugget effect] which is also reflected in the terminology used in software programs. The nugget variance is often misleadingly referred to as nugget effect which is incorrect as, as we have seen, is the ratio of Co/C. Similarly, the spatial variance is referred to as the sill or sill variance which is also misleading in the authors opinion, as the sill variance is Co+C which corresponds to the dispersion variance of the date used to produce the semi-variogram”  Mining Geostatistics Course Book – Cardiff University, 1998 – this course book is taken verbatim from Alwyn’s book.

You are quite correct, it doesn’t really matter what you call it as long as you understand its meaning.

Regards,

Colin

From: Isobel Clark [mailto:drisobelclark@...]
Sent: 08 June 2005 11:06
Cc: AI Geostats mailing list
Subject: Re: [ai-geostats] Definition of Nugget Effect

Colin

Alwyn is a graduate of the Leeds University programme in geostatistics. Bon Royle, who was the first in the UK to go to Fontainebleau and learn geostatistics, coined the term "nugget variance" for the nugget effect. He also used the notation "N" for nugget effect unlike the more general notation of C_sub_zero.

Whatever you call it, it represents the micro-scale variation which cannot be predicted at the current scale of your sampling. Since we use a semi-variogram, it is one-half of the variance between two samples at almost exactly the same location.

Geostatistics schools differ on what to do at exactly zero distance (and software packages reflect this). Some schools (e.g. Stanford) insist that nugget effect is due solely to sampling error and use the nugget semi-variance at zero distance. Others say that the nugget effect is micro-scale (even microscopic scale) and use it everywhere except at zero distance. At zero the semi-variance is set to zero. A good question to ask your software vendor is "what does your software do with the semi-variogram (or covarianc) at zero distance".

Reality is somewhere in between, but I do not know any software which allows you to allocate some of the nugget effect at zero. Of course, you can always get round this by adding a component with a very short range of influence.

Isobel

http://geoecosse.bizland.com

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