Spatial sampling in the presence of a trend

The spatial sampling designs suggested by Quenouille (1949) are investigated under a number of trend assumptions, namely a linear trend, linear trend and periodic variation, and spatially correlated populations. The results obtained provide a planar analogue to the one-dimensional results appearing in Cochram (1977, Ch. ε). Centrally located systematic sampling and the planar analogue of Yates' (1948) method of end corrections are put forward as methods which eliminate the linear trend. The comparisons of the two methods provide the planar analogue to results obtained by Bellhouse and Rao (1975).