Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning

Abstract

One of the major sources of uncertainty associated with geographical data in GIS arises when they are the outcome of a sampling process. It is well known that when sampling from a spatially autocorrelated homogeneous surface, stratification reduces the error variance of the estimator of the population mean. In this study, we evaluate the efficiency of different spatial sampling strategies when the surface is not homogeneous. When the surface is first-order heterogeneous (the mean of the surface varies across the map), we examine the effects of stratifying it into first-order homogeneous zones prior to the usual stratification for a systematic or stratified random sample. We investigate the effect of this form of spatial heterogeneity on the performance of different methods for estimating the population mean and its error variance. We do so by distinguishing between the real surface to be surveyed (ℜ), the sampling frame (ℑ) including the choice of zoning, and the statistical estimators (Ψ). The study shows that zoning improves estimator efficiency when sampling a heterogeneous surface. Systematic comparison provides rules of thumb for choice of sample design, sample statistics and uncertainty estimation, based on considering different spatial heterogeneities on real surfaces.

Keywords:

• spatial sampling
• uncertainty
• heterogeneity
• grid strata
• zoning strata
• efficiency and strategy

Acknowledgments

This material is based on work supported by the NSFC (40471111, 70571076), CAS (KZCX2-YW-308) and the MOST (2006AA12Z215, 2007DFC20180 and 2007AA12Z241). The authors thank Iain Macleod for his help in preparing the manuscript and also wish to record their thanks to three anonymous referees who provided helpful comments on an earlier draft of this paper.