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

[Zev Ross]

Hi Edzer,

Very useful, thank you. You might be able to tell from my posts that I'm 
running these in parallel in GSTAT and geoR and comparing. It seems from 
your note and example that it might simply be easier to add a centimeter 
(provided a centimeter doesn't matter in the real world) to all the 
coordinates. This way one would not need to keep track of the different 
variances at coincident locations. Do you think this would be an 
acceptable approach?

In terms of your coding, I'm a little uncertain about the meaning of the 
add.to argument and how one might code, for example, half micro-scale 
and half-measurement error. For the example you give, if there was a 
nugget of 0.1 (half micro and half measurement) does my coding below 
look correct? Why is fit.variogram not fitting on the model with error 
-- it's not fitting any of the models I try with measurement error?

Zev

myvgmA<-vgm(.5, "Exp",300, nugget=0.1)
myvgmB<-vgm(.5, "Exp",300,nugget=0.05, add.to=vgm(.05,"Err",0))

fit.variogram(variogram(log(zinc)~1,meuse),model=myvgmA)
  model     psill    range
1   Nug 0.0000000   0.0000
2   Exp 0.7186526 449.7581


fit.variogram(variogram(log(zinc)~1,meuse),model=myvgmB)
  model psill range
1   Err  0.05     0
2   Nug  0.05     0
3   Exp  0.50   300





Edzer J. Pebesma wrote:
> 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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>>   
>
>
>

-- 
Zev Ross
ZevRoss Spatial Analysis
303 Fairmount Ave
Ithaca, NY 14850
607-277-0004 (phone)
866-877-3690 (fax, toll-free)
zev at zevross.com