Is co kriging appropriate for interpolation of three spatial co variates?

Question

I want to estimate an interpolation model(s) for daily minimum temperature, daily maximum temperature and daily rainfall. I have samples of approximately the same size for all three variables at different locations although for certain days and locations only 1 or 2 of the 3 covariates are sampled . All three variables have some correlation, especially minimum temperature and maximum temperature. I read that co-kriging is especially adequate in cases where:

• one wishes to interpolate one variable that is relatively sparsely sampled
• one has available another covariate which is more densely sampled

This is not my case. Rather I have available samples for three covariates and want to interpolate all three. I have the following questions:

1. Is it better to develop a separate ordinary/universal kriging model for each variable or to develop a co-kriging model for all three.

2. I am using days and locations with no missing values to estimate the parameters of the interpolation model , but want to use it to interpolate missing values in different days and locations. Is it possible to do this in cases where:

   • certain locations have all three variables missing
   • certain locations have one o two out of the three variables missing

I am working in R in case there are any special considerations to heed.

Answer 1

Yes, it is appropriate. Prediction by kriging can theoretically only get better when you bring in more correlated information, and that is what you do when moving from kriging to co-kriging. In practice, the gain can be disappointing, considering the effort it takes.

There can also be other reasons to favor co-kriging. An example is when you need the correlation of the kriging prediction errors for two or more variables, e.g. because you want to sum them or compute their difference.