Critical scale of variation of tree biomass using variography

I have a combination of a philosophical and a technical question. I am interested in an application where I am trying to find a critical scale of autocorrelation of tree biomass on the landscape. Let’s say I have inventory plots with mapped trees. A “default” approach might be to simply use the xy locations of the trees as sample locations and create a variogram and assess the autocorrelation or semivariance function at locations where trees are found. However it occurs to me that I’m really interested in assessing the autocorrelation structure of the attribute in the study area, which includes areas where there are no trees. My study area does not just include locations where the attribute was found. If that’s the case, then I think I should have “null locations” that exist where there is a value of “0” for the attribute. Clearly, a value of “0” is a valid measurement of biomass, much like a value of “0” is a valid value of biomass on a forest inventory plot, if that plot is meant to characterize the population, which is a land area that includes treed areas and treeless areas.

If you were to accept the above logic, then the question is: how many “0” values to put in? And how? A naïve default would be an equal number of zeros as there are trees, distributed either randomly or systematically across the population. Another option would be to add 0s in the locations where trees are not present, such that the entire area is filled in with either 0s or biomass values. This seems like it would be akin to pretending that I sampled my study area in a uniform way, and sometimes I hit a tree, and sometimes I hit a “0”. This could be done by some clever tessellation of the “nontreed” portions of the analysis area, and placement of 0’s with the appropriate intensity in these nontreed areas. However, I am concerned that the chosen intensity of 0s may affect the spatial autocorrelation results.

Any thoughts on this?

• Given that your interest is in biomass, could you focus on that unit as opposed to individual trees? Then you can sample areas without trees and legitimately have '0' biomass at points compared to the biomass of specific trees. (then a question is how big of an area does an individual tree represent?). – mtreg Oct 28 '15 at 19:00