Spatially Balanced Sampling of Natural Resources

TLDR

The spatial distribution of a natural resource is crucial for designing efficient surveys, and spatially balanced sampling—more evenly dispersed sites—offers greater efficiency than simple random sampling. We review a unified strategy for selecting spatially balanced probability samples of natural resources. The strategy maps two‑dimensional space into a one‑dimensional ordered address, applies restricted randomization to generate a random sequence, and then uses systematic sampling along this sequence to produce a spatially balanced sample, while allowing variable inclusion probabilities proportional to ancillary variables and extending to finite populations, one‑dimensional continua, and ordered subsets of points. This ordered‑subset property is highly useful for correcting frame imperfections common in environmental sampling.

Abstract

The spatial distribution of a natural resource is an important consideration in designing an efficient survey or monitoring program for the resource. Generally, sample sites that are spatially balanced, that is, more or less evenly dispersed over the extent of the resource, are more efficient than simple random sampling. We review a unified strategy for selecting spatially balanced probability samples of natural resources. The technique is based on creating a function that maps two-dimensional space into one-dimensional space, thereby defining an ordered spatial address. We use a restricted randomization to randomly order the addresses, so that systematic sampling along the randomly ordered linear structure results in a spatially well-balanced random sample. Variable inclusion probability, proportional to an arbitrary positive ancillary variable, is easily accommodated. The basic technique selects points in a two-dimensional continuum, but is also applicable to sampling finite populations or one-dimensional continua embedded in two-dimensional space. An extension of the basic technique gives a way to order the sample points so that any set of consecutively numbered points is in itself a spatially well-balanced sample. This latter property is extremely useful in adjusting the sample for the frame imperfections common in environmental sampling.