[R-sig-Geo] spatial averaging of interpolation data

[Wouter Buytaert]

Hi list,

this is a rather theoretical question, so sorry if it is not very 
appropriate for this list, but with a bit of luck someone may feel 
challenged to reply.

I am looking for the correct procedure to average spatially interpolated 
data over an area. Specifically, I used kriging to interpolate point 
rainfall over a grid covering a catchment and now I want to estimate the 
average rainfall over the catchment, including the uncertainty on the 
estimation.

Obviously, taking just the mean and the variance of all the grid 
cell values doesn't work because it does not take into account spatial 
correlation and thus underestimates the uncertainty.

So what is/are the best method(s)? Suggestions on how to implement them in 
R are very welcome, as well as suggestions for literature if the answer 
would turn out to be more complicate than I imagined.

Many thanks!

Wouter Buytaert
Lancaster University