I am trying to adapt spatial linear mixed models as suggested by Crabtree et al. (2009) for my thesis work.The authors suggest semivariogram for defining the spatial autocorrelation (error term?)in the spatial linear regression model according to the equation:-

Y_i=βo+ β1 xi1  (s)+⋯+βj xij (s)+Z_ik (s)

where Yi is the response for the ith variable and the vector s contains its location in space xij(s) is the jth observed value of the ith variable (where again, the vector s contains its location in space), βj the coefficient for the ith variable and Zi(s) is the random error with a mean of zero and possible autocorrelation (Hunsaker, 2001). k is spatially independent block.

By creating a different error term for each of the k blocks, (k=1 to __), the blocks are assumed independent with respect to the spatial autocorrelation between them.

I want to ask:-

1.How to do i use semivariogram to identify the spatial autocorrelation or spatially correlated errors?

2. The working procedure to find the size( e.g. 8 km2) of blocks for spatially independent blocks (or Is 8 km2 is a random size?)

2. How to add the spatial  error term in the regression equation?