Geostatistical R Package - Board

Hello,

I've got some issues while trying to perform a collocated cokriging.
Here is the code I use :

Code: Select all

data.db=db.locate(data.db,"NOx","z",1)
data.db=db.locate(data.db,"NO2","z",2)
grid.db=db.locate(grid.db,"NOx","z",1)
v_exp=vario.calc(data.db,lag=350,nlag=15)
v_fit=model.auto(v_exp,nvar=2,struct=c('Nugget Effect','Spherical','Exponential','Linear','Cubic'))
# krigeage sur la grille
grid.db=kriging(data.db,grid.db,v_fit,data.u.neigh,radix="CKC",calcul="block",flag.colk=T)


And the code for a "classic" cokriging :

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data.db=db.locate(data.db,"NO2","z",1)
data.db=db.locate(data.db,"NOx","z",2)
v_exp=vario.calc(data.db,lag=350,nlag=15)
 v_fit=model.auto(v_exp,nvar=2,struct=c('Nugget Effect','Spherical','Exponential','Linear','Cubic'))
# krigeage sur la grille
grid.db=kriging(data.db,grid.db,v_fit,data.u.neigh,radix="CK",calcul="block")


The classik cokriging is performed very fast, 10-20 second with acceptable outputs but the collocated cokriging is very long, more than 20 minutes and returns me aberrant values for the NO2 variable. I can't understand what I am doing wrong.

Do you have any ideas ?

Thanks a lot for your help !

Maxime Beauchamp

Hello

Without any data set, I can only give you intuitive answers.

In the classical estimate, you define 2 variables are perform a standard cokriging (with 2 variables), a bivariate model and a Unique neighborhood. The calculation consists in establishing the ordinary cokriging matrix (dimension = 2 * nech +2). This matrix is inverted once for all. This explains why the ordinary cokriging goes very fast.

In the Collocated case, there are two issues: the time consumption and the strange results.

For the time consumption, the reason is obvious. In the collocated ordinary cokriging, the size of the system if now 2 * nech + 3. The additional pseudo-sample corresponds to the collocated grid node. Therefore the location of this pseudo-sample varies per target grid node. For that reason, the cokriging matrix cannot be inverted once for all. Instead an algebraic solution is provided which benefits from the inversion of the (2 * nech + 2) system inverted once for all and massaged to incorporate gently the additional sample. This may explain the additional time consumption.

For the strange results, I only have an intuition. The collocated cokriging methodology consists in adding systematically one sample (the target grid ndoe) where one of the two variables is considered as already known. If we imagine that one data sample coincides with the target grid node, then the methodology must be adapted. As a matter of fact, adding the grid node will lead to duplicates and therefore an impossible matrix inversion. So the program checks if this coincidence exists: then we do not add the grid node. This does not create any discontinuity, provided that the variable value (at the coinciding grid node) coincides with the data value. If this is not the case, we introduce a discontinuity. This may be the reason of your strange results.

Hope this will help.

Thanks a lot.

I better understand now the matter of time consumption. However, even if I understand your response for the strange results issue, it seems that it does not apply to my dataset, in which I am pretty sure there is no duplicates between dataset and grid nodes.
If you are interested in helping me and solve this case, I can provide you the dataset with variables NO2 (to estimate on the grid) and NOx (used as secondary variable), and the grid nodes (NOx is provide in the file), but I cannot attach these files to my message (extension csv not alloawed ?)

Thanks again,

Maxime

That would definitely help.
Just put any extension you want and send them by any mean.