I would agree with Gregoire's assessment. The presence of a global trend does not prohibit the use of geostatistics. As illustrated in the following paper by Journel and Rossi: Journel, A.G. and M.E. Rossi. 1989. When do we need a trend model in kriging? Mathematical Geology, 21(7):715--739. global trends can be easily handled by the use of local search windows in kriging, which allows us to rely on the assumption of quasi-stationarity.
Of course if the trend is complex and can be described using process-based models (e.g. urban pollution), it is better to use this physical model for the trend and use geostatistics to interpolate the residuals, provided there is some spatial correlation left. Cheers, Pierre <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Dr. Pierre Goovaerts President of PGeostat, LLC Chief Scientist with Biomedware Inc. 710 Ridgemont Lane Ann Arbor, Michigan, 48103-1535, U.S.A. E-mail: [EMAIL PROTECTED] Phone: (734) 668-9900 Fax: (734) 668-7788 http://alumni.engin.umich.edu/~goovaert/ <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> On Thu, 2 Sep 2004, Gregoire Dubois wrote: > > -----Original Message----- > From: Gregoire Dubois [mailto:[EMAIL PROTECTED] > Sent: 02 September 2004 09:42 > To: [EMAIL PROTECTED] > Cc: [EMAIL PROTECTED] > Subject: Re: spatial relationships > > > > Hi Mark, > > re-reading Isobel's mail, I thought about a proviso on the proviso. I > personally do consider that a semivariogram showing a pure trend is > decent. Not in a geostatistical point of view, but it does provide you > with some useful information. If you have a trend, the variogram becomes > incompatible with the intrinsic hypothesis. but you still have a slope > in the experimental correlation functions (semivariograms, correlograms, > madogram, etc.). Thus you have a structure, that is you "have something" > there that may provide you with some useful information about your data > set that can be used for estimating values of your variable at unsampled > locations. If you have a flat correlation function, that is a pure > nugget effect, then certainly you are in troubles. > > Regards, > > Gregoire > > > Isobel Clark <[EMAIL PROTECTED]> wrote: > > > Mark > > > > I could not agree more with Gregoire (with one > > proviso, see below). > > > > Both geostatistics and any weighted average estimators > > are based on the same assumptions -- that relationship > > between values at two locations depends on the > > distance between them and (possibly) their relative > > orientation. If you cannot get a decent semi-variogram > > after trying every type of graph [normal, robust, > > relative] and every transformation and/or > > interpretation of your data [logarithm, indicator, > > rank transforms, Normal scores, mixed populations], > > you do not have a distance-based relationship. This > > conclusion also rules out: inverse distance weighting > > of any kind; Delaunay triangles; Thiessen polygons and > > so on. > > > > My proviso: there are other forms of spatial > > relationship than pure distance/direction types. The > > simplest example of this is data with a trend, where > > the value at a specified point will depend on its > > absolute position. There may be an added component for > > the 'residuals' which turns out to be > > distance/direction based. There are also many examples > > where, for example, flow characteristics, connectivity > > and so on play a large part in the structure of your > > variable. > > > > In short: no decent semi-variogram does NOT mean no > > spatial relationship. It means no simple second-order > > stationary geostatistical type spatial relationship. > > > > Isobel > > <http://geoecosse.bizland.com/whatsnew.htm> > http://geoecosse.bizland.com/whatsnew.htm > > > > > > > > > > > > ___________________________________________________________ALL-NEW > Yahoo! Messenger - all new features - even more fun! > <http://uk.messenger.yahoo.com> http://uk.messenger.yahoo.com > > > > > > > > --------------------------------------------- > > Attachment: message-footer.txt > > MIME Type: text/plain > > --------------------------------------------- > > __________________________________________ > Gregoire Dubois (Ph.D.) > JRC - European Commission > IES - Emissions and Health Unit > Radioactivity Environmental Monitoring group > TP 441, Via Fermi 1 > 21020 Ispra (VA) > ITALY > > Tel. +39 (0)332 78 6360 > Fax. +39 (0)332 78 5466 > Email: <mailto:[EMAIL PROTECTED]> [EMAIL PROTECTED] > WWW: <http://www.ai-geostats.org> http://www.ai-geostats.org > WWW: <http://rem.jrc.cec.eu.int> http://rem.jrc.cec.eu.int > > "The views expressed are purely those of the writer and may not in any > circumstances be regarded as stating an official position of the > European Commission." > >
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