Collocated Cokriging of snow height data

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 G?mez-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)?

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?

3. How would the calculation of "vd.fit" and " vx.fit" change if a
trend model was used, like "log(zinc) ~ sqrt(dist)"?

Any advice or help will be highly appreciated

Stefan Zollinger

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.

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 G?mez-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