How Create Spatially Balanced Points works

There are many considerations to take into account when designing a sampling network. Some designs can be found here: An introduction to sampling monitoring networks. Spatially balanced designs, in particular, are constructed to improve the efficiency of estimated values by maximizing spatial independence among sample locations (Theobald et al. 2007). They also lead to more efficient sampling by providing more information per sample unit as every sample is distributed across the population. Note that these comments refer to statistical efficiency, which is one of several criteria that could be applied to a sampling design. A different measure of efficiency may be that of optimal semivariogram estimation, which usually requires samples to be taken at varying distances from one another, and often clustered samples are used to determine the nugget value more accurately (see Warrick and Myers 1987 for an optimization algorithm with semivariogram fitting criteria in mind).

The Create Spatially Balanced Points tool was developed based on the algorithm proposed by Theobald et al. (2007), which is based in part on the method developed by Stevens and Olsen (2004). The method is based on the following:

The input to the tool is a raster that simultaneously defines the following:

The resulting spatially balanced design has the following properties:

For best results, Theobald et al. (2007) recommend that the number of samples be less than 1 percent of all the possible sample locations in the study area.


  1. Stevens, D.L., and A.R. Olsen. 2004. "Spatially balanced sampling of natural resources."Journal of the American Statistical Association 99 (465): 262–278.
  2. Theobald, D.M., D.L. Stevens, Jr., D. White, N.S. Urquhart, A.R. Olsen, and J.B. Norman. 2007. "Using GIS to Generate Spatially Balanced Random Survey Designs for Natural Resource Applications."Environmental Management 40: 134–146.
  3. Warrick, A.W., and D.E. Myers. 1987. "Optimization of sampling locations for variogram calculations."Water Resources Research 23 (3): 496–500.