[R-sig-Geo] GSTAT - measurement vs microscale variation

[Edzer J. Pebesma]

Zev,

you can use the "Err" variogram model to denote micro variation as 
opposed to nugget. The only effect it has is that for a new prediction 
on an observation location the measurement error-free process is 
predicted, and not the observation process itself. Semivariance of an 
observation with itself remains zero, so it doesn't allow for duplicate 
observations. In terms of predictions, it is "as if" you predict right 
next to a prediction location in case the prediction location coincides 
with an observation location (implying that the predicted surface is 
continuous); in terms of prediction variance, it is "as if" you predict 
for a very small block, meaning the nugget is removed from the 
prediction variance.

Below is an example for the meuse data set.
--
Edzer

 > library(gstat)
Loading required package: sp
 > data(meuse)
 > meuse0 = meuse
 > coordinates(meuse) = ~x+y
 > # prediction at observation location:
 > krige(log(zinc)~1,meuse,meuse[1,],vgm(.5, "Exp",300,.5))
[using ordinary kriging]
       coordinates var1.pred var1.var
1 (181072, 333611)  6.929517        0
 > krige(log(zinc)~1,meuse,meuse[1,],vgm(.5, 
"Exp",300,add.to=vgm(.5,"Err",0)))
[using ordinary kriging]
       coordinates var1.pred  var1.var
1 (181072, 333611)   6.57884 0.1801634
 > cc = coordinates(meuse)
 > cc[1,] = cc[1,]+0.01 # 1 cm shift on a 5 km region
 > coordinates(meuse0)=cc
 > krige(log(zinc)~1,meuse,meuse[1,],vgm(.5, "Exp",300,.5))
[using ordinary kriging]
       coordinates var1.pred var1.var
1 (181072, 333611)  6.929517        0
 > krige(log(zinc)~1,meuse,meuse0[1,],vgm(.5, "Exp",300,.5))
[using ordinary kriging]
       coordinates var1.pred var1.var
1 (181072, 333611)  6.578803 0.680188
 > krige(log(zinc)~1,meuse,meuse0[1,],vgm(.5, 
"Exp",300,add.to=vgm(.5,"Err",0)))
[using ordinary kriging]
       coordinates var1.pred  var1.var
1 (181072, 333611)  6.578803 0.1801880 # same prediction, variance 0.5 less
 > krige(log(zinc)~1,meuse,meuse[1,],vgm(.5, 
"Exp",300,.5),block=c(0.01,0.01))
[using ordinary kriging]
       coordinates var1.pred  var1.var
1 (181072, 333611)  6.578836 0.1801594



Zev Ross wrote:
> Hi All,
>
> I folded this question into a previous post, but I think it may have gotten
> missed. Just wondering if someone could tell me how, in GSTAT, one would specify
> the nugget as measurement error vs microscale variation in kriging. I have
> multiple measurements at the same location and I'd like to use these to
> determine the measurement error. I've figured out how to do this in geoR, but as
> most of my scripts are written in R using GSTAT, I'd rather use that.
>
> Thank you! Zev
>
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