[R-sig-Geo] variogram question

[Paul Hiemstra]

Hi Wesley,

Good to know that the package helped you.

A note the choice between the different variogram models. At this stage 
I do this by computing the sums of squares between the model and the 
sample variogram and choose the one with the smallest SS. This is a 
rather crude way of selecting between the models. But my package is 
about automatic interpolation and this makes it more automatic. I would 
like to invest some time in improving this part of automap.

cheers,
Paul

Wesley Roberts wrote:
> Dear Paul and the rest of the users who replied to my question,
>
> Firstly many thanks for all your input, reading your emails this morning improved my mood exponentially. 
>
> I have installed automap and am getting to know the program nicely, it is so easy to run it is almost unfair. I do have one question regarding the choice of models (Exp, Sph, Gau, Mat). I have experimented with each one individually as well as all models (selection based on residual sum of squares) and have found that the Matern family of models returns the lowest residual sum of squares and produces a semivariogram that models the Experimental semivariogram very well (Visually). However, the range returned by the Mat model is almost twice that of the Sph model (Mat = 6.25 m, Sph = 3,27 m). This would not ordinarily be a problem but a colleague of mine ran a similar analysis last year and returned a range of +- 3.5 meters (He was using a surface and not point data). We are working in managed Eucalyptus plantations where espacement is 2 meters between trees and 3 meters between rows indicating that a range of +- 3 meters is more likely than 6 meters. I guess this is where we get to make "informed" decisions regarding model choice based on "expert knowledge". I just want to make sure my decision is correct. 
>
> My gut tells me go with the Mat model as it describes the semi-variance better than the rest. I am interested in quantifying the distance at which all variability is captured in the Lidar data. Am I making the correct choice?
>
> Paul, I am not sure if I have any constructive comments, other than, a real layman was able to get automap up and running in less than 1 hour and is now making some significant progress, many thanks!
>
> Kind regards,
> Wesley
>
>   
>>>> Paul Hiemstra <p.hiemstra at geo.uu.nl> 08/19/08 12:32 AM >>>
>>>>         
> ...in addition, any feedback on the package would be more than welcome!
>
> Paul
>
> Edzer Pebesma schreef:
>   
>> In general: no, in special cases: yes.
>>
>> Fitting variograms involves non-linear regression for most models 
>> (Sph, Exp, Gau, ...) for the range parameter, so you need starting 
>> values. Given the initial range, linear regression is sufficient to 
>> find the nugget/sill component(s), as they are linear. In principle, 
>> gstat could be made simpler in that respect, I'd say.
>>
>> For an initial range, you could use some heuristics (20% of the 
>> longest distance in your data?), but it is often not so hard to think 
>> of cases where this would fail.
>>
>> Another issue is automatic values for the width and cutoff.
>>
>> You could have a look at package automap, by Paul Hiemstra, which 
>> tries to do some of these heuristics--good or bad, who will tell.
>> -- 
>> Edzer
>>
>> Wesley Roberts wrote:
>>     
>>> Dear r-sig-geo users,
>>>
>>> I am currently analyzing some Lidar data we have collected over our 
>>> study area. I am interested in identifying the range of the 
>>> semi-variogram as this value will determine the width of 
>>> pseudo-flight lines I intend to use to sample the lidar data. Our 
>>> point density is upwards of 5 points per square meter captured over 
>>> even-aged managed Eucalyptus plantations with an espacement of 2 
>>> meters between trees and 3 meters between rows.
>>> I have imported an x,y,z data set containing canopy height and 
>>> coordinates and successfully run the experimental variogram using the 
>>> "variogram" module in gstat.
>>> cpy.pts2 <- variogram(dbl_5 ~ 1, cutoff=50, width=2, D)
>>>
>>> I have also managed to fit several models using the
>>> cpy.pts2.fit <- fit.variogram(cpy.pts2, model = vgm(2, "Sph", 4, 5))
>>>
>>> command as suggested by the gstat manual. I would like to fit the 
>>> various models "Sph, Exp..." etc without having to specify the nugget 
>>> psill and range. Essentially I would like an objective method to 
>>> measure and record these values as I will be running several hundred 
>>> variograms. Is it possible to perform this type of analysis using gstat?
>>>
>>> Many thanks for all your help and suggestions
>>> Wesley
>>>
>>> Wesley Roberts MSc.
>>> Researcher
>>> Earth Observation (Ecosystems)
>>> Natural Resources and the Environment
>>> CSIR
>>> Tel: +27 (21) 888-2490
>>> Fax: +27 (21) 888-2490
>>>
>>> "To know the road ahead, ask those coming back."
>>> - Chinese proverb
>>>
>>>   
>>>       
>
>
>   


-- 
Drs. Paul Hiemstra
Department of Physical Geography
Faculty of Geosciences
University of Utrecht
Heidelberglaan 2
P.O. Box 80.115
3508 TC Utrecht
Phone: 	+31302535773
Fax:	+31302531145
http://intamap.geo.uu.nl/~paul