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The estimation of the total of an attribute defined over a continuous planardomain is required in many applied settings, such as the estimation of canopycoverage in the Monterano Nature Reserve in Italy. If the design-based approachis considered, the scheme for the placement of the sample sites over the domainis fundamental in order to implement the survey. In real situations, a commonlyadopted scheme is based on partitioning the domain into suitable strata, insuch a way that a single sample site is uniformly placed (i.e., selected withuniform probability density) in each stratum and sample sites are independentlylocated. Under mild conditions on the function representing the targetattribute, it is shown that this scheme gives rise to an unbiased spatial totalestimator which is "superefficient" with respect to the estimator based on theuniform placement of independent sample sites over the domain. In addition, thelarge-sample normality of the estimator is proven and variance estimationissues are discussed.

Properties of design-based estimation under stratified spatial sampling with application to canopy coverage estimation