Ash Tree Distribution Layer
Authored By: R. E. McRoberts, M. A. Hatfield, S. J. Crocker
Because the ash tree distribution layer was for forest land, only data for the 1,953 FIA forest subplots were used in its construction. Using these plot data, an empirical variogram was constructed, and an exponential variogram model was fit to the data (Zhang and Goodchild 2002). An interpolated surface was constructed for which the ash tree count per hectare, Ai, for the ith pixel was estimated as,
where
vij is the predicted covariance from the variogram model corresponding to the distance, dij, between the ith pixel and the jth plot; 
is the estimate of the variogram sill; and
The variance of 
was estimated as,
and is a measure of the uncertainty of the estimate,. This approach to constructing the ash tree count per hectare was selected to illustrate a sample-based method for estimating variances. Other approaches such as kriging could have been used to construct the ash tree count-per-hectare layer. Realizations of the ash tree count-per-hectare distribution were obtained by selecting for each pixel a random number from a normal distribution with mean 0 and variance, 
from (Equation 4), and adding the number to from (Equation 1).
- Zhang, J.; Goodchild, M. 2002. Uncertainty in geographical information. London: Taylor and Francis. 266 p.
