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

-- 
*********************************************
Dipl. - Geogr. Philip Marzahn
Department of Geography
Physical Geography and Environmental Modeling
Ludwig-Maximilian University of Munich

Luisenstrasse 37
80333 Munich/Germany
fon: +49 (0)89 2180-6698
fax: +49 (0)89 2180-6675
email:p.marzahn@iggf.geo.uni-muenchen.de
web:www.geographie.uni-muenchen.de
*********************************************




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