Variance predictors for isotropic geometric sampling, with applications in forestry

A coherent set of explicit approximations is presented for the variance of planar area and volume estimators obtained under systematic geometric sampling. For planar objects (e.g. a land plot, or a tissue section), sampling is considered with test systems of points, lines, segments, stripes, or quadrats. For three dimensional objects analogous probes are considered. For the formulae to apply the design has to be uniform random (which suffices to estimate planar area or volume only) and also isotropic. The formulae are based on G. Matheron’s transitive theory. A synthetic example on the estimation of canopy cover is explained in detail.