[R-sig-Geo] Collocated Cokriging of snow height data

[Ashton Shortridge]

On Monday 30 November 2009 10:05:20 Edzer Pebesma wrote:
> Stefan Zollinger wrote:
> > > Any advice or help will be highly appreciated
> 
> I can see that this section of the book is indeed very dense;
> introductions to collocated cokriging are (IIRC) Pierre Goovaerts book
> and perhaps GSLIB literature. Wackernagel's book is also very brief on it.

Hi,

I'd second looking at Pierre Goovaerts' Geostatistics for Natural Resources 
Evaluation (1997). Chapter 6 discusses the use of secondary information in 
kriging, and includes a lengthy section on colocated cokriging. As Edzer 
suggests, this is a very rich but difficult section of the geostatistics corpus, 
but it is more and more relevant due to the growing amount of secondary 
geographic information.

Yours,

Ashton

On Monday 30 November 2009 10:05:20 Edzer Pebesma wrote:
> Stefan Zollinger wrote:
> > Hi
> >
> > I am trying to spatially interpolate snow height data of about 100
> > stations in a mountain range. In addition, I have a large DEM (SRTM,
> > 90 meters resolution, 2.5 million cells) which also serves as an
> > interpolation raster (just like meuse.grid). As the snow height and
> > the height above sea level correlate strongly, I intend to use
> > collocated cokriging to improve the estimation, which is why I studied
> > the example in "Applied Spatial Data Analysis with R" by Roger Bivand,
> > Edzer Pebesma and Virgilio Gómez-Rubio.
> >
> > I have the following questions (especially to the authors):
> >
> > 1. Why and how is the new attribute "distn" being calculated? Would it
> > not be sufficient to use the existing attribute "dist" for the
> > collocated cokriging (as it shows the same variogram-model properties)?
> 
> it is translated such that it has the same mean as the primary variable,
> log(zinc). This is a requirement for collocated (ordinary) cokriging.
> 
> > 2. How are the two variogram-models "vd.fit" and "vx.fit" being
> > calculated out of "v.fit"? I understand that the range and the type of
> > the three models remains the same, but how are the sills and nuggets
> > being changed?
> 
> It is assumed here that dist(n) has the same variogram form as the
> primary variable, but scaled with the variance of distn. It should be
> noted that in collocted cokriging, only the direct correlation between
> zinc and dist is relevant, the (rest of) the distn direct variogram and
> cross variogram are ignored in the equations.
> 
> > 3. How would the calculation of "vd.fit" and " vx.fit" change if a
> > trend model was used, like "log(zinc) ~ sqrt(dist)"?
> 
> Well, this is a completely different concept: regression instead of
> correlation. (Collocated) cokriging assumes zinc and dist are two random
> variables, that have a particular (spatial and cross) correlation.
> Universal kriging assumes zinc is related to dist through a regression
> relationship, implying that dist is non-random but fixed and known, and
> zinc is random. It's apples and oranges, really.
> 
> > Any advice or help will be highly appreciated
> 
> I can see that this section of the book is indeed very dense;
> introductions to collocated cokriging are (IIRC) Pierre Goovaerts book
> and perhaps GSLIB literature. Wackernagel's book is also very brief on it.
> 
> > Stefan Zollinger
> >
> > _______________________________________________
> > R-sig-Geo mailing list
> > R-sig-Geo at stat.math.ethz.ch
> > https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> 

-- 
Ashton Shortridge
Associate Professor			ashton at msu.edu
Dept of Geography			http://www.msu.edu/~ashton
235 Geography Building		ph (517) 432-3561
Michigan State University		fx (517) 432-1671