[SOLVED] Cokriging with external drift

Any question regarding the Interpolation method using Kriging

[SOLVED] Cokriging with external drift

Postby CharlineP » Tue Dec 01, 2015 9:09 am

Hello,

I am currently programming a cokriging between PM10 and PM2.5, but we would like to add external drifts to this classic cokriging.
Is there any possibility to add different external drift to the different variables (meaning PM10 external drift to PM10 observations and PM2.5 external drift to PM2.5 observations)?

Here is the code I use:

Code: Select all
tabRValC=data.frame(x1=tabvario$x,x2=tabvario$y,z1=tabvario$Mesure,z2=tabvario$Mesure_Co,f1=tabvario$Modele,f2=tabvario$Modele_Co)
        dataVC.db = db.create(tabRValC,flag.grid=F,ndim=2,nvar=2,autoname=F)
        ## Variables polluants
        dataVC.db=db.locate(dataVC.db,"z1","z",1)
        dataVC.db=db.locate(dataVC.db,"z2","z",2)
        ## Derives
        dataVC.db=db.locate(dataVC.db,"f1","f",1)
        dataVC.db=db.locate(dataVC.db,"f2","f",2)


I have no error issues but I am not sure of what the function is doing with the two variables (z1 and z2) and the two external drifts (f1 and f2).

Thank you for your help!

Charline
CharlineP
 
Posts: 1
Joined: Tue Dec 01, 2015 8:58 am

Re: Cokriging with external drift

Postby Didier Renard » Wed Feb 24, 2016 10:51 pm

Hi Charline

(and sorry for such a late answer...).
I checked the programming of the kriging interpolation feature when using several variables and several external drifts (say 2 variables and 2 external drifts). Let us demonstrate the result when the input dataset is composed of 4 samples.

The dimension of the kriging system is: 14 * 14.

The explanation:
- covariance part of the cokriging matrix for 2 variables and 4 samples: 8
- drift for the first variable: 1, f1 and f2, i.e. 3
- drift for the second variable: 3
Hence the total of 14 equations.

Unfortunately, the software is not clever enough to know what should be done with the two external drift functions, split on the two variables.
In fact, it considers that the SAME external drift terms affect both variables. This implies that:
E[Z1] = a0 + a1 * f1 + a2 * f2
E[Z2] = b0 + b1 * f1 + b2 * f2
(same drift terms but with different coefficients).

Hope this will help.
Didier Renard
 
Posts: 337
Joined: Thu Sep 20, 2012 4:22 pm


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