Variance estimation for spatially balanced samples of environmental resources

Abstract

SUMMARYThe spatial distribution of a natural resource is an important consideration in designing an efficient survey or monitoring program for the resource. We review a unified strategy for designing probability samples of discrete, finite resource populations, such as lakes within some geographical region; linear populations, such as a stream network in a drainage basin, and continuous, two-dimensional populations, such as forests. The strategy can be viewed as a generalization of spatial stratification. In this article, we develop a local neighborhood variance estimator based on that perspective, and examine its behavior via simulation. The simulations indicate that the local neighborhood estimator is unbiased and stable. The Horvitz-Thompson variance estimator based on assuming independent random sampling (IRS) may be two times the magnitude of the local neighborhood estimate. An example using data from a generalized random-tessellation stratified design on the Oahe Reservoir resulted in local variance estimates being 22 to 58 percent smaller than Horvitz-Thompson IRS variance estimates. Variables with stronger spatial patterns had greater reductions in variance, as expected.

A modification of balanced acceptance sampling

“…The variance ofτ can be estimated using the Sen-Yates-Grundy estimator (Yates & Grundy, 1953), but this estimator is biased and tends to be unstable for spatially-balanced designs (Grafström et al, 2012;Robertson et al, 2013). The local mean variance estimator (Stevens & Olsen, 2003) is commonly used for spatially balanced designs and is recommended for the modified BAS approach. The estimator is…”

“…The weights decrease as the distance between the ith unit and jth unit increases and i w ij = j w ij = 1. Details on how to compute neighborhoods and weights can be found in (Stevens & Olsen, 2003).…”

Airborne LiDAR and Aerial Imagery to Assess Potential Burrow Locations for the Desert Tortoise (Gopherus agassizii)

“…These 4-ha plots were distributed across the LiDAR survey area using the Generalized Random Tessellation Stratified design (GRTS) [28,29] and georeferenced using a handheld GPS receiver (Trimble GeoExplorer 3000, accuracy 0.5 m). The experimental design for each plot ( Figure 2) consisted of four 1-ha subplots (oriented as 2 × 2 ha for each field plot, except one, where only two subplots were established; 318 total).…”

Application and Development at Home of Geographical Information System in Forestry Resource

“…What's more, GIS play a significant role in wildlife administration, forest ecology, forestry project, biodiversity protection, and forest construction [36]. As an effective tool to deal with spatial ubiety, GIS could be beneficial to solve lots of forest problems decided by its own features.…”