[R-sig-Geo] Problems with gstat gaussian variogram and cross validation when fix nugget at 0

[Stefano Menichetti]

Dear all, I have a question about fixing nugget at 0 in a Gaussian 
variogram using *gstat *package

I have encountered a serious problem on a variogram of piezometric data 
that give "strange" results if I want to fix nugget to 0.

This is the file and how to import:

/library(gstat)/
//file => 
https://drive.google.com/open?id=1AOilEhR8G8YANVuFIBUcmEg-6UG1Ajrr//

/lay1 =� read.delim(paste(path,*file*,sep=""),sep="\t",dec=",")//
//SpData = na.exclude(subset(lay1, select = c("X","Y","Observed"))) //
//colnames(SpData)=c("X","Y","Z")/

The initial variogram:

/coordinates(SpData) = ~X+Y//
//var = variogram(Z~1,SpData)/

show a slow initial rise and so suggest a *Gaussian *type.

After a first variogram with:

/m = vgm(200,"Gau",3000,0)//
//
//plot(var, model=m, //
//main = paste(m$model[2],"//
//Nug=",m$psill[1],", Sill=",round(m$psill[2]),", 
Range=",round(m$range[2]),sep ="")//
//)/

I have obtained a fitted variogram like this,

/m = fit.variogram(var, m)/

with a reasonable cross-validation results:

/krg_cv = krige.cv(Z~1, SpData, model = m)//
//plot(krg_cv$observed,krg_cv$var1.pred, xlab="Z observed", ylab="Z 
predicted")//
//abline(a=0,b=1)//
//paste("media residui =",mean(krg_cv$residual))//
//paste("RMS residui =",mean(krg_cv$residual^2)^0.5)/

Resulting map it is very smooth, despite the small, it seems, nugget and 
so *I have tried to fix nugget at 0* (exact interpolation).

But cross validation results with

/m = vgm(216,"Gau",3640,*0*)/

are dramatically wrong and also very different from cv results with

/m = vgm(216,"Gau",3640,*1e-3*)/

What happens ? I wrong in something ? Why nugget paraneter at 0 or at 
small value influnce so hard the results ?

Thank you very much in advance,


Stefano


Dott. Geol. Stefano Menichetti
=============================================================
ARPAT - Agenzia per la Protezione dell'Ambiente della Toscana
Settore Tecnico SIRA - Sistema Informativo Regionale Ambientale via Nicola Porpora 22 - 50144 Firenze
tel. 0553206333 cell. 3668217978 (3383550147) fax 0553206410
s.menichetti using arpat.toscana.it  http:\\www.arpat.toscana.it  http:\\sira.arpat.toscana.it


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