Sample size estimation for multinomial autocorrelated data

I'm trying to work out the minimum sample size needed to accurately characterise land cover data. The idea is to set out the a number of quadrats across the study site and identify what land cover type occurs in each.

I have an idea as to how many categories there should be. So this is a problem of estimating multinomial proportions.

This answer seems to get close to what I'm after
However, I don't know how to deal with the problem of spatial autocorrelation. With land cover data, the neighbours of a given patch are likely going to be of the same type. This will mess up my sample size estimate surely?

There is also the issue of the size of my quadrats, if I increase these from say 1m^2 to 2m^2 and again characterise the landcover this will affect sample size.