[R-sig-Geo] Two scale process in experimental variogram - how to fit a theoretical variogram?

[Tom Gottfried]

Hi Philip,

though this does not answer your question: tractor tracks and seedbed rows suggest strong anisotropy 
and a periodical structure perpendicular to them. If you are interested in roughness induced by 
different tillage practices (i.e. seedbed preparation) you might be more interested in only the 
anisotropic variogram parallel to tracks and rows, thus excluding the effects of wheels and seeding 
machinery.

HTH anyhow,
Tom

Am 14.10.2011 12:19, schrieb philsen:
> Dear list,
>
> I am trying to characterize different tillage patterns of agricultural
> fields using variogram analysis for microwave remote sensing. Basis for
> the analysis is a high resolution DSM with a 2x2  mm^2 resolution and a
> size of 1x6 m^2 (see pdf at
> URL:http://www.geographie.uni-muenchen.de/department/admin/lehre/upload/1094/Disp_Vario_Surface.pdf).
>
> The aim is to characterize the horizontal roughness component by using
> the autocorrelation length /l/ derived from an autocorrelation function
> (ACF) at which e.g. the exponential ACF drops under 1/e.
>
> When using a subsample of 10000 points the variogram is calculated using
> gstat by
>
>   >library(gstat)
>   >data<-
> read.table(url("http://www.geographie.uni-muenchen.de/department/admin/lehre/upload/1094/subsample_DSM.csv"),
> header=TRUE)
>   >maxdist=max(dist(data, method="maximum"))/2
>   >coordinates(data)<- c("X","Y")
>   >v<- variogram(Z~1, data, cutoff=maxdist, width=5)
>   >plot(v)
>
>   From my understanding, there are two processes of different scale
> visible. The first maximum of the experimental variogram is related to
> the small scale seedbed rows, while the second max. is related to the
> appearance of tractor tracks with a distance of ca. 150 cm (see DGM-plot
> in pdf).
>
> So the question is how to fit a theoretical variogram to the data, which
> allows me to characterize both processes in terms of an autocorrelation
> length /l/_1 and /l/_2?
>
>   From searching trough the archive I have found a discussion about
> nested variograms. Therefore I tried to fit the sum of two exponential
> variogram models to my data:
>
>   >nest.vfit<- fit.variogram(v, model=vgm(1, "Exp", 90, add.to=vgm(1,
> "Exp", 200)))
>   >plot(v, nest.vfit)
>
> However I am not sure about the output? To characterize /l/_1 and /l/_2,
> I think I need at least two theoretical variograms to invert
> /C(h) = 1 - ?(h) / ?(inf)/ with /C/(h)= fitted ACF at distance h
>
> Hopefully there is somebody who can help me .....
>
> Kind regards,
>
> Philip
>

-- 
Technische Universität München
Department für Pflanzenwissenschaften
Lehrstuhl für Grünlandlehre
Alte Akademie 12
85350 Freising / Germany
Phone: ++49 (0)8161 715324
Fax:   ++49 (0)8161 713243
email: tom.gottfried at wzw.tum.de
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