Two-dimensional systematic sampling and maximal stratification are frequently used in spatial surveys, because of their ease of implementation and design efficiency. An important drawback of these designs . however, is that no direct estimator of the design variance is available. In this paper estimation of the sampling variance of a total in a model based context is considered. The estimation strategy is based on the use of the sample variogram which can be either a non-parametric or a parametric one. Consistency of the estimators is discussed; simulations and an application to real data show the good performance of the proposed procedure in practice.

Keywords: spatial survey, two-dimensional systematic sampling, two-dimensional maximal stratification, semi-variogram, Gaussian random field.