Obtaining a Balanced Area Sample for the Bureau of Land Management Rangeland Survey

Abstract

In agricultural and environmental surveys, obtaining spatially balanced area samples that are also representative probability samples in the presence of auxiliary variables is a challenge, especially when the study regions have fragmentary boundaries and possess holes of various shapes. This paper describes a sampling procedure that achieves this goal and is implemented in the U.S. Department of the Interior Bureau of Land Management (BLM) Rangeland Survey, a longitudinal environmental survey. This survey aims to assess status and trends of rangeland conditions on BLM-managed lands. In the sampling procedure, we first generate a 10-year master sample using Thiessen polygons and then draw annual samples through rejective sampling techniques using elevation as the auxiliary variable. The resulting annual samples as well as any consecutive multi-year combined samples are spatially well-dispersed and representative probability samples. Details about the sampling design, weighting procedure and replicate variance estimation are provided. Issues related to boundary error, ineligibility and nonresponse are also discussed. Some of the empirical results from the BLM Rangeland Survey are presented. Supplementary materials accompanying this paper appear online.