I have data measuring a variable Z say at several locations on a fixed network (each location at a fixed longitude and latitude). values of Z are measured daily at the same time.

At the moment I am employing ordinary Kriging to interpolate values for each day (ie. run the procedure separately for each day). I am using the gstat package in R.

However, when I look at the autocorrelation function of Z at a given location I see values are correlated up to a lag of about a week. Can I use this additional information to improve my spatial interpolation estimates using spatio-temporal Kriging? (Just to be clear, I want to interpolate spatially, but to the same times that the data is measured at.) Or is it the case, that by interpolating to the same times as in the data I am essentially using the one dimensional slice of the space-time variogram that corresponds to zero time lag, which means I am just doing ordinary kriging?

  • This is a very complicated situation. Many different models are possible. A good introduction to the subject of spatio-temporal analysis is Cressie and Wikle.
    – whuber
    Commented Feb 19, 2016 at 13:57
  • If you insist that you'd need a hierarchical model for this, I would agree. There are also simpler models. Commented Feb 25, 2016 at 17:32

1 Answer 1


CRAN package gstat comes with functions for spatio-temporal variogram modelling and prediction. The vignettes on this topic might be a good starting point.


demonstrates ST kriging using a local neighbourhood.

  • Thanks, I was thinking to use your package to do this. I ran the demo - in that example you are interpolating to different time slices than the original data is sampled at - in this case I can clearly see the benefit of ST Kriging. My question however, is whether there is any benefit to interpolating spatially (using STK) to the same times (sampled at the same hour each day) as the observed data.
    – piyushnz
    Commented Feb 26, 2016 at 18:22
  • I guess this depends on the nature of the spatio-temporal correlation of the variable at hand. Commented Feb 26, 2016 at 18:38
  • okay I've thought about it again and I see that even if I interpolate to the same time but a different spatial point the interpolated value would be a weighted sum of field values at different locations and times (both previous and current). Since my spatial network is fixed the contribution of any observed values from previous days is going to depend on how large the temporal correlation is relative to the spatial correlation. I think I'm just going to give it a go and see if it works. Thanks.
    – piyushnz
    Commented Feb 27, 2016 at 20:42

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