Spatially Balanced Sampling in GIS

Basic Information
Name: Spatially Balanced Sampling in GIS using RRQRR
Acronym: none
Author/Owner/Steward: Natural Resource Ecology Laboratory, Colorado State University
Type: Tool
Platform: ArcGIS Toolbox

Description from Website

Sampling of a population is frequently required to understand trends and patterns in natural resource management because financial and time constraints preclude a complete census. A rigorous probability-based survey design specifies where to sample so that inferences from the sample apply to the entire population. Probability survey designs should be used in natural resource and environmental management situations because they provide the mathematical foundations for statistical inference. Development of long-term monitoring designs demand survey designs that achieve statistical rigor and are efficient, but remain flexible to inevitable logistical or practical constraints during field data collection. The Reversed Randomized Quadrant-Recursive Raster (RRQRR) algorithm is an implementation of the Generalized Random Tessellation Stratified (GRTS) algorithm. The RRQRR toolbox allows for probability-based spatiality balanced sample designs to be implemented within a Geographic Information System (GIS).

This toolbox consists of three tools that generate a RRQRR sequence raster, filter the RRQRR sequence raster against a probability raster, and generate sample site locations. The RRQRR toolbox is flexible because it allows existing points to be incorporated into the RRQRR sequence raster, uses the ArcInfo raster format as its data backbone, and is scripted in Python for ArcGIS version 9.1. The functionality and flexibility of the RRQRR toolbox makes it useful for natural resource sampling applications.


  • 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(1): 134-146.

Contact Information

Contact Name: Dave Theobald
Contact Email:

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